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Modeling crash severity and speed profile at roadway work zones
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by Zhenyu Wang.
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Dissertation (Ph.D.)University of South Florida, 2008.
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ABSTRACT: Work zone tends to cause hazardous conditions for drivers and construction workers since work zones generate conflicts between construction activities and the traffic, therefore aggravate the existing traffic conditions and result in severe traffic safety and operational problems. To address the influence of various factors on the crash severity is beneficial to understand the characteristics of work zone crashes. The understanding can be used to select proper countermeasures for reducing the crash severity at work zones and improving work zone safety. In this dissertation, crash severity models were developed to explore the factor impacts on crash severity for two work zone crash datasets (overall crashes and rearend crashes). Partial proportional odds logistic regression, which has less restriction to the parallel regression assumption and provides more reasonable interpretations of the coefficients, was used to estimate the models. The factor impacts were summarized to indicate which factors are more likely to increase work zone crash severity or which factors tends to reduce the severity. Because the speed variety is an important factor causing accidents at work zone area, the work zone speed profile was analyzed and modeled to predict the distribution of speed along the distance to the starting point of lane closures. A new learning machine algorithm, support vector regression (SVR), was utilized to develop the speed profile model for freeway work zone sections under various scenarios since its excellent generalization ability. A simulationbased experiment was designed for producing the speed data (output data) and scenario data (input data). Based on these data, the speed profile model was trained and validated. The speed profile model can be used as a reference for designing appropriate traffic control countermeasures to improve the work zone safety.
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Advisor: Jian John Lu, Ph.D.
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Support vector regression
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Modeling Crash Severity and Speed Profile at Roadway Work Zones by Zhenyu Wang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Civil and Environment College of Engineering University of South Florida Major Professor: Jian John Lu, Ph.D. Edward Miezejewski, Ph.D. Sastry Putcha, Ph.D. Huaguo Zhou, Ph.D. George Yanev, Ph.D. Date of Approval: March 25, 2008 Keywords: logit model, ordered logit regre ssion, parallel assump tion, simulation, support vector regression Copyright 2008 Zhenyu Wang
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Acknowledgments I am indebted to my academic advisor, Dr. Jian John Lu, for his guidance, patience, encouragement and support throughou t my fiveyear Ph.D. study. I thank Dr. Edward Miezejewski, Dr. Sastry Putcha, Dr. Huaguo Zhou, and Dr. George Yanev for serving on my committee and providing their valu able suggestions. Dr. Xin Ye used to be one of my colleagues and close friends at USF. At the early stage of this study, I greatly benefits from his help and discussion with him. I also want to express my gratitude to my colleague, Pan Tao. Tao gave me an important assistant for data collection and reduction.
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Table of Contents List of Tables iii List of Figures v Abstract vii Chapter 1: Introduction 1 1.1 Background 1 1.2 Objectives 7 1.3 Scope 7 1.4 Outline 8 Chapter 2: Literature Review 9 2.1 Previous Researches on Work Zone Crashes 9 2.2 Previous Researches on Crash Severity Modeling 13 2.3 Previous Researches on Work Zone Speed 16 Chapter 3: Modeling Methodology for Crash Severity Models 19 3.1 Crash Severity Models 19 3.2 Ordinal (Ordered) Logit Regression 20 3.2.1 Introduction to the Regression 20 3.2.2 Parallel Regression Assumption 21 3.3 Partial Proportional Odds Regression 23 3.3.1 Generalized Ordered Logit Regress 23 3.3.2 Partial Proportional Odds Logit Regression (POLR) 24 3.3.3 Criteria for Assessing the Model 25 3.3.3.1 Tes t z 25 3.3.3.2 Likelihood Ratio (LR) Test 26 3.3.3.3 Pseudo2 R 26 3.3.4 Interpretation of Model Coefficients 27 Chapter 4: Estimation Results of Crash Severity Models 29 4.1 Data Preparation 29 4.2 Data Description 30 4.3 Overall Work Zone Crash Severity Model 34 4.3.1 Estimation Procedure 34 i
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4.3.2 Cross Tabulations between Explanatory Variables and Crash Severity 35 4.3.3 Estimation Results 37 4.3.4 Interpretation 41 4.4 Crash Severity Model for Rearend Work Zone Crashes 47 4.4.1 Description of Rearend Dataset 48 4.4.2 Estimation Results for Rearend Dataset 51 4.4.3 Interpretation 54 4.5 Summary 55 Chapter 5: Modeling Methodology for Wo rk Zone Speed Profile Models 58 5.1 Introduction 58 5.2 Simulationbased Experiment Design 60 5.2.1 Simulation Model 61 5.2.2 Model Calibration 61 5.2.3 Input Variables and Simulation Scenarios 63 5.2.4 Data Collection 65 5.3 Support Vector Regression 66 5.3.1 Introduction to Learning Machine 66 5.3.2 Empirical Risk Minimization and Structural Risk Minimization 67 5.3.3 Support Vector Regression 70 5.3.4 Procedure to Apply SVR 74 Chapter 6: Experiment Results of Speed Profile Models 77 6.1 Data Preparation 77 6.2 Analysis on Speed Profiles 79 6.3 Results of Modeling Training 81 Chapter 7: Conclusions and Discussions 92 7.1 Conclusions 92 7.2 Contributions to the Field 94 7.2.1 Methodological Contribution 94 7.2.2 Practical Contribution 95 7.3 Future Research Direction 95 List of References 97 Appendices 102 Appedix A: Variables and C odes of Work Zone Crash 103 Appedix B: Sample of CORSIM Input File 110 About the Author End Page ii
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List of Tables Table 3.1 Definition of Crash Severity 19 Table 4.1 Description of Selected Variables for Model Development 30 Table 4.2 Descriptive Statis tic of Continues Variables 32 Table 4.3 Frequencies of Discrete Variables 33 Table 4.4 Cross Tabulation between Explanat ory Variables and Crash Severity 35 Table 4.5 Estimation of Ordinal Logit Regr ession for Work Zone Crash Severity Model 38 Table 4.6 Results of Brant Test of Parallel Regression Assumption 39 Table 4.7 Estimation Results of Coefficients of Par tial Proportional Odds Regression 40 Table 4.8 Statistic Criteria for Assessing Partial Proportional Odds Regression 41 Table 4.9 Odds Ratio of Explan atory Variables in the Ordinal Logit Models 41 Table 4.10 Odds Ratio of Explanatory Variable s in the Partial Regression Models 43 Table 4.11 Description of Response Variable for Rearend Dataset 49 Table 4.12 Cross Tabulations between Explan atory Variables and Crash Severity for Rearend Dataset 49 Table 4.13 Descriptive Statis tic of Continues Variables 51 iii
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Table 4.14 Estimation of Ordinal Logit Regression for Crash Severity Model (Rearend Dataset) 52 Table 4.15 Results of Brant Test of Parallel Regression Assumption (Rearend Dataset) 52 Table 4.16 Estimation Results of Coefficients of Par tial Proportional Odds Regression (Rearend Dataset) 53 Table 4.17 Statistic Criteria for Assessing Partial Proportional Odds Regression (Rearend Dataset) 53 Table 4.18 Odds Ratios for the Ordinal Logit M odels (Rearend Dataset) 54 Table 4.19 Odds Ratios for the Partial Regression Models (Rearend Dataset) 54 Table 4.20 Summary of the Influenc e of the Explanatory Variables 57 Table 5.1 Calibration Parameters 63 Table 5.2 Input Variables 65 Table 6.1 Definition of Variables for Speed Profile Model 77 Table 6.2 Comparison Table of LOCATION to CLOSELENGTH 78 Table 6.3 Descriptive Statis tics for Training Dataset 78 Table 6.4 Descriptive Statis tics for Testing Dataset 78 Table 6.5 Results of Mode l Training and Validation 81 iv
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List of Figures Figure 1.1 Work Zone Types 2 Figure 1. 2 Work Zone Layouts (Lane Closure) 3 Figure 3. 1 Illustration of the Parallel Regression Assumption 22 Figure 4. 1 Effects Utility of Presence of Day Light 44 Figure 4. 2 Effects Utility of Urban Area 45 Figure 4. 3 Effects Utility of Curve or Grade 45 Figure 4. 4 Effects Utility of I nvolvement of Alcohol or Drugs 46 Figure 4. 5 Effects Utility of Involvement of Heavy Vehicle 47 Figure 4. 6 Distribu tion of Crash Type 47 Figure 5.1 Speed Profile at Work Zones (Open La nes) 59 Figure 5.2 Simulation Model 62 Figure 5.3 Concept of Learning Machine 67 Figure 5.4 Concept of Structural Risk Minimization 69 Figure 5.5 tube Parameters used in SVR (linear kernel) 71 Figure 6.1 Speed Profile under Different Congestion Condition 80 Figure 6.2 Comparison of Speed Profile Models to Observat ions (low FFS and low VOLUME) 83 Figure 6.3 Comparison of Speed Profile Models to Observat ions (low FFS and medium VOLUME) 84 v
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Figure 6.4 Comparison of Speed Profile Models to Observat ions (low FFS and high VOLUME) 85 Figure 6.5 Comparison of Speed Profile Models to Observations (medium FFS and low VOLUME) 86 Figure 6.6 Comparison of Speed Profile Models to Obse rvations (medium FFS and medium VOLUME) 87 Figure 6.7 Comparison of Speed Profile Models to Ob servations (medium FFS and high VOLUME) 88 Figure 6.8 Comparison of Speed Profile Models to Observ ations (high FFS and low VOLUME) 89 Figure 6.9 Comparison of Speed Profile Models to Observ ations (high FFS and medium VOLUME) 90 Figure 6.10 Comparison of Speed Profile Models to Observations (high FFS and high VOLUME) 91 vi
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Modeling Crash Severity and Speed Profile at Roadway Work Zones Zhenyu Wang ABSTRACT Work zone tends to cause hazardous c onditions for drivers and construction workers since work zones generate conflic ts between construction activities and the traffic, therefore aggravate the existing tra ffic conditions and result in severe traffic safety and operational problems. To address the influence of various factors on the crash severity is beneficial to understand the characteristics of work zone crashes. The understanding can be used to select proper countermeasur es for reducing the crash severity at work zones and improving work zone safety. In this dissertation, crash severity models were developed to explore the factor impacts on cr ash severity for two work zone crash datasets (overall crashes a nd rearend crashes). Pa rtial proportional odds logistic regression, which ha s less restriction to the para llel regression assumption and provides more reasonable interp retations of the coefficients was used to estimate the models. The factor impacts were summarized to indicate which factors are more likely to increase work zone crash se verity or which factors tends to reduce the severity. vii
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viii Because the speed variety is an important factor causing accidents at work zone area, the work zone speed profile was analyzed and modeled to predic t the distri bution of speed along the distance to the starting point of lane closures. A new learning machine algorithm, support vector regression (SVR), wa s utilized to develop the speed profile model for freeway work zone sections under various scenarios since its excellent generalization ability. A simulationbased experiment was designed for producing the speed data (output data) and scenario data (input data). Based on these data, the speed profile model was trained and validated. Th e speed profile model can be used as a reference for designing appropr iate traffic control counterme asures to improve the work zone safety.
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Chapter One Introduction 1.1 Background Work zone is defined in the 1994 Highw ay Capacity Manual as an area of highway in which maintenance and constructio n operations are taking place that impinge on the number of lanes available to moving tra ffic or affect the operational characteristics of traffic flowing through the area. Two work zone types on multilane highways are shown in Figure 1.1 and their de finitions are given as follows: (1) Lane Closure When one or more lanes in one direc tion are closed, there is little or no disruption to traffic in the opposite direction. (2) Crossover When one roadway approach is closed and the traffic which normally uses that roadway is crossed over the median and twoway traffic is maintained on another roadway approach. As the description in the Manual on Un iform Traffic Control Devices (MUTCD) 2003, a work zone is typically marked by si gns, channelizing devices, barriers, pavement markings, and/or work vehicles. It extends from the first warning sign or highintensity 1
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rotating, flashing, oscillati ng, or strobe lights on a ve hicle to the END ROAD WORK sign or the last Temporary Traffic Control devi ce. Most work zones ar e divided into four areas: the advance warning area, the transition area, the activity area, and the termination area (see Figure 1.2). Work Zone Lane Closure Crossover Work Zone Figure 1.1 Work Zone Types The advance warning area is the sect ion of highway where road users are informed about the upcoming work zone or incident area. The transition area is that section of highway where road users are redi rected out of their normal path. Transition areas usually involve strategic use of tapers, which because of their importance are discussed separately in detail. The activity area is the section of the highway where the work activity takes place. It is comprised of the work space, the traffic space, and the buffer space. The work space is that portion of the highway closed to road users and set 2
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aside for workers, equipment, and material, a nd a shadow vehicle if one is used upstream. Work spaces are usually delineated for road users by channelizing devices or, to exclude vehicles and pedestrians, by temporary barrier s. The termination area shall be used to return road users to their normal path. The termination area shall extend from the downstream end of the work area to the la st TTC device such as END ROAD WORK signs, if posted. Figure 1. 2 Work Zone Layouts (Lane Closure) 3
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Work zone tends to cause hazardous conditions for vehicle drivers and construction workers since work zones generate conflicts between construction activities and the traffic, and therefore aggravate the ex isting traffic conditions and result in severe traffic safety problems. Improving safety at work zones has become one of the overwhelming challenges that traffic engineers and resear chers have to confront. Nationally, great efforts have been devoted to improve the safety and mobility of work zone traffic (Bai and Li, 2004). Congress addressed the work zone safety issue in the Intermodal Surface Transportation Effici ency Act (ISTEA) of 1991 and National Highway System designation Act of 1995 (FHW A, 1998). In addition, Federal Highway Administration (FHWA) and Am erican Association of State Highway and Transportation Officials (AASHTO) have b een developing comprehensive highway work zone safety guidelines and programs. Many state Departments of Trans portation (DOTs) have funded various projects to improve work zone sa fety in their states. Other concerned organizations or research communities have also participated in this campaign and devoted their contributions by conducting mean ingful researches on various work zone safety issues. Regardless of these efforts, there is litt le indication of significant improvements in work zone safety in Florida. Work zone cr ash rates by work zone travel mileage are not precisely known, but statistics of work zone fatalities have shown a serious traffic safety problem. Annual work zone fatal crashes rose from 79 in 2002 to 128 in 2005, with the increase of fatalities from 99 in 2002 to 148 in 2005. It was estimated that the direct cost of highway work zone crashes was as hi gh as $6.2 billion per year between 1995 and 1997 with an average cost of $3,687 per cr ash (Mohan and Gautam 2002). The alarming 4
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numbers indicate an urgent need for impr oving every work zonesafety related field including traffic control and information, project management, public education, and regulation/policy making. Actual crash data is an important so urce for identifying safety problems and developing effective countermeasures. Inves tigating the characteristics of work zone crashes is the first step towards improving wo rk zone safety. The Investigation enables researchers to identify unique work zone safety problems. Accordingly, appropriate countermeasures could be developed to reduc e the harm to both construction workers and drivers. Crash severity is an impo rtant criterion to evaluate the social and economic impacts of work zone crashes. Fatalities re sult in great losses in economy even in life, while no injury crashes just lead to the pr operty damage only. Diffe rent traffic factors (driver, vehicle, environmental, and roadway features) have different influences on crash severity levels. To address the diversity of influences of tra ffic factors is beneficial to understand the characteristics of work zone cr ashes more deeply. And the analysis results can be used to develop the proper counterm easures for eliminating the factors that deteriorate work zone safety. Vehicle speed is a critical topic in hi ghway design and operations because of relationships to crash probability and severi ty. This issue is further complicated in construction work zones due to speed reducti ons from conditions existing prior to the work zone and transitions into the work zone. Additional design features at work zones such as temporary traffic barriers, reduced lane widths, and crossover sections may influence vehicle speeds. Vehicle operating speed is a factor affecting a variety of work 5
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zone design and management decisions, includ ing those related to ge ometric and roadside features and possible regulatory (posted) speed reduction (Taylor et al, 2007). The relationships between travel speed a nd accident rates indi cate that accident rates increase as speed variance increases (Migletz and Graham, 1991). A large speed variance coupled with hazardous conditions at work zones (e.g., workers presence, lane closure, and narrow lane) may lead to higher accident rates at work zones (Maze et al., 2000). Speed variance was generally higher at work zones than that at common roadway sections. Therefore, it could be conjectured that by reducing the speed variance, that is, by having vehicles travel at about the aver age speed, accident rate s would decrease at work zones. Speed profiles, which are a representation of speeds as a function of position, can be used to assess the characteristics of speed variances at work zones. Accordingly, the understanding of speed profiles is beneficial to developing proper countermeasures to reduce the speed variance. It is well known th at vehicle operating speed is affected by various traffic factors, such as driver, ve hicle, environment, and roadway features. However, most of the existing operating speed profile models use ordinary linear regression methods (McFadden et al. 2001). The assumptions and limitations inherent to linear regression may at the very least compli cate model formulation and, if not corrected for, the deviations from these assumptions can adversely affect the efficacies of such models (Taylor et al, 2007). 6
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1.2 Objectives This dissertation intends to reach two major objectives: (1) To develop crash severity models for addressing the influences of traffic factors (driver, vehicle, environmenta l, and roadway features) on the work zone crash severity. (2) To develop work zone speed profile models by utilizing a new regression methodology based on learning machine theory. The new methodology has the capability to overcome the issues associated with existing models. 1.3 Scope The crash severity models will be developed for understanding the relationship between work zone crash severity and various factors. Two kinds of logit regressions will be utilized for the model estimation: ordered logit regression and partial proportional odds logit regression. The crash severity mode ls using ordered log it regression will be estimated with the stepwise variable selecti on process. And then the violation of the parallel odds assumption will be tested. If the assumption is violated, the partial proportional odds logit regression will be implemented to ree stimate the crash severity models. The results of two kinds of models will be compared and explained. A simulationbased experiment will be designed for providing speed profile data for developing speed profile models. The speed profile model describes the relationship between speed pattern and various traffic factors. The model based on a new learning machine algorithm will be trained and tested. The result of validation will be used to assess the effectiveness of the new algorithm on predicting work zone speed profile. In 7
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this dissertation, only the work zone section on twoway (one direction) freeways will be considered for the development of the speed profile model. 1.4 Outline The remainder of the dissertation is organized as follows. Chapter 2 initially reviews the past researches on work zone cr ashes, crash severity modeling, and work zone speed. Chapter 3 briefly introduces orde red logit regression and partial proportional odds logit regression, including their forms, assessing criteria, and interpretation methods. The parallel assumption and its testing method are also introduced. Chapter 4 presents the estimation results of crash severity models, and interpretation of the factors that have significant influence on work zone crash severi ty is also provided. Chapter 5 offers the introduction of the simulationbased experi ment design and the new learning machine algorithm, Support Vector Regression. Chapter 6 gives the training a nd testing result of the speed profile model. Conclusions a nd contributions are summarized and some recommendations for future research are provided in Chapter 7. 8
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Chapter Two Literature Review 2.1 Previous Researches on Work Zone Crashes Many studies have been conducted to anal ysis on highway work zone crashes over past years in several states. These researches focused on examining the characteristics of work zone crashes, and ev aluated the effectiveness of traffic control countermeasures on traffic sa fety at work zones. Bai and Li (2004) conducted a study to the investigate the characteristics of work zone fatal crashes in Kansas and dominant contributing factors to these crashes in the work zones so that effective safety countermeasures coul d be developed and implemented in the near future. A total 157 crashes during 1992 and 2004 were examined using descriptive analysis and regr ession analysis. They found that (1) Male drivers cause about 75% of the fatal work zone crashes in Kansas; Drivers between 35 and 44 years old, a nd older than 65, are the highrisk driver groups in work zones; (2) The daytime nonpeak hours (10:00 a.m. 4:00 p.m.) are the most hazardous time period in work zones; 9
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(3) Work zones on rural roads with speed limit from 51 mph to 70mph or located on complex geometric alignments are high risk locations; (4) Most fatal crashes are multi vehicle crashes, and headon, angleside impact, and rearend are the three most frequent collision types for the multivehicle crashes; (5) Inefficient traffic controls and human e rrors contributed to most fatal work zone crashes, and Inattentive drivi ng and misjudgment/disregarding traffic control are the top contributing fact ors for work zone fatal crashes. In Taxes, Hill et al. (2003) analyzed the ch aracteristics of work zone fatalities and then evaluated the effectiveness of existing work zone traffic safety countermeasures based on 376 work zone fatal crashes in Texas from January 1, 1997 to December 31, 1999. In this study, three comparisons were conducted between daytim e versus nighttime, male drivers versus female drivers, and commercialtruckinvolved versus noncommercialtruckinvolved. Then logistic regression was implemented to examine the effectiveness of traffic counter measures su ch as using an officer/flagman and using a stop/go signal. Results of this study indicated that there wa s a significant difference in crash type and driver error between daytime crashes and nighttime crashes. This difference also existed between driver gende rs. In addition, comm ercial truck related crashes were more likely to involve multip le vehicles. According to the logistic regression results, the use of an officer/fla gman or a stop/go signal would reduce the chance of having a crash by 68% or 64% respectively. Ullman et al. (2006) conducted a study on th e safety effects of night work activity upon crashes at two types of construction proj ects in Texas. The first project type 10
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involved both day and night work (hybrid project), whereas the other project type performed only at night. Researchers determ ined the change in crash likelihood during periods of active night work, active day work (if applicable), and during times of work inactivity day and night. Some conclusi ons were derived from this study: (1) Crashes increased significantly during periods of work ac tivity than during periods of work inactivity; (2) A large crash increase at night was expected because the night work more likely involved lane closur e than the day work; (3) For the hybrid project, crashes increa sed at night more than at day. Garber and Zhao (2002) studied the distribution of work zone crashes in Virginia in terms of severity, crash type, and road t ype over four different locations within the work zone referred to as the advance warni ng area, transition area (taper), longitudinal buffer area, activity area, and termination area. In total, 1484 work zone related crashes during 1993 and 1999 were analyzed. The result s indicate that the activity area is the predominant location for work zone crashes fo r all crash types, and the rearend crashes are the predominant type of crashes except for the terminat e area, where the proportion of angle crashes is significantly higher than other types. A study on the typical characteristics of multistate work zone crashes was conducted by Chambless et al. (2002) to perf orm a set of comprehensive comparisons of computerized work zone and nonwork zone crash data in Alabama, Michigan, and Tennessee. The Information Mining for Producing Accident Counter measure Technology (IMPACT) module of Critical Analysis Re porting Environment (CARE) software 11
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developed by University of Alabama was used in this study to pr ocess the statistical analysis to obtain the conclusions: (1) 63% of work zone crashes take place on interstate, US, and state roads, as compared to 37% of nonwork zone crashes. (2) 48% of work zone crashes occur on 45and 55mph speed zones, as opposed to 34% of nonwork zone crashes. (3) Misjudging stopping distance/following too close accounted for 27% of the prime contributing crash circumstances for work zone crashes as opposed to 15 percent for nonwork zone crashes. In the study conducted by Mohan and Gaut am (2002), the various injury types and their cost estimates were analyzed. As the results, researchers found that (1) The average direct cost of a motorist s injury is estimated at $3,687; (2) An overturned vehicle has the largest average cost of $12,627, followed by a rearend collision av eraging $5,541; and (3) Rearend collisions are the most common (31%) vehicle crashes, followed by hitsmallobject collisions at 11% of the total motor vehicle crashes. Ha and Nemeth (1995) conducted a study in an effort to identify the major causeand effect relationships between work zone crashes and traffic controls in order to make the first step towards development of effectiv e work zone traffic control strategies. They analyze the crash data during 1982 and 1986 at nine sites in Ohio, and focused on the impacts of factors such as inadequate or c onfusing traffic control, edge drop or soft shoulder, traffic slowdowns, lane changi ng or merging, guardrails, and alcohol impairment on work zone crashes. Results of the study indicates that 12
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(1) The predominant type of crash was rearend; (2) Improper traffic control was one of the sa fety problems in construction zones; (3) Involvement of trucks in crashes at crossovers was significant; (4) Work zone crashes were slightly less seve re than other types of crashes; and (5) Although work zone crashes increased at nights, they actua lly decreased in proportion to all crashes. Pigman and Agent (1990) studied the traffic data and traffic control devices of 20 highway work zones for 3 years (198 31986) in Kentucky, and found that (1) Most work zone crashes occur on interstate roads; (2) Work zone crashes are more server than other crashes, especially in night or truck involved; (3) The dominant crash type is rearend and samedirectionsideswipe; and (4) The dominant contributing factor is following to close. Hall and Lorenz (1989) investigated the crashes at work zones in New Mexico from 1983 to 1985 by comparing the differe nce of crashes beforeand duringconstruction at same road sections. They c oncluded that the propor tion of crashes caused by following too close was much higher in duri ngwork zone periods than in beforework zone periods. Another conclusion was that improper traffic control was the prevalent problem causing high crash rate s in work zones. 2.2 Previous Researches on Crash Severity Modeling There has been considerable number of studies on the development of injury or crash severity models, even though none of th em address work zone crashes. The general 13
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models developed in the past to identify th e most important parameters which are crucial in reducing or increasing the level of injury severity of the passengers, drivers or crashes are discussed in this section. Holdridge et al. (2004) performed a study to analyze the inservice performance of roadside hardware on the entire urban State Route system in Washington State by developing multivariate statistical models of in jury severity in fixedobject crashes using discrete outcome theory. The objective is to pr ovide deeper insight in to significant factors that affect crash severities involving fixed roadside objec ts, through improved statistical efficiency along with disaggregate and multivar iate analysis. The developed models are multivariate nested logit models of injury seve rity and they are estimated with statistical efficiency using the method of full inform ation maximum likelihood. The results show that leading ends of guardra ils and bridge rails, along with large wooden poles increase the probability of fatal injury. The face of guard rails is associated with a reduction in the probability of evident injury, and concrete barriers are shown to be associated with a higher probability of lower se verities. The presented models show the contribution of guardrail leading ends toward fatal injuries. It is therefore important to use wellprotecting vehicles from crashe s with rigid poles and tree stum ps, as these are linked with greater severities and fatalities. A study was conducted in 1995 to develop a statistical model explaining the relationships between certain driver characte ristics and behaviors, crash severity, and injury severity (Kim et al, 1995). Applying the techniques of categorical data analysis to comprehensive data on crashes in Hawaii dur ing 1990, authors built a structural model relating driver characteristics and behaviors to type of crash and injury severity. The 14
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structural model helped to clarify the role of driver characteristic s and behaviors in the causal sequence leading to more severe injuri es. Odds multipliers that are how much dies each factor increase or decrease the odds of more severe cr ash types or injuries were estimated in this study. It was found that the driver behaviors of al cohol and drug use and lack of seal belt use greatly in creased the odds of more severe crashes and injuries. Driver errors were found to have small effect, wh ile personal characteris tics of age and sex generally insignificant, as found in this study. Another study by Mercier et al used logistic regressi on to assess whether age or gender or both influenced severity of injuri es suffered in headon automobile collusions on rural highways (Mercier et al. 1997). The initial hypo thesis that, because of physiological changes, and possi bly other changes related to aging including loss if bone density, older drivers and passe ngers would suffer more severe injuries when involved in headon crashes was utilized fi rst. It was later found through logistical regression that 14 individual and interact ive variables were strongly relate d to injury severity. Individual variables included age of driver or passenger, position of the vehicle, and the form of the protection used, along with a set of interactiv e variables. The impor tance of age related effects in injury severity was verified in this study by hierar chical and principal components logistic regression models, amp lifying findings of e xploratory stepwise logistic analysis. Variations in findings resulted when the population was divided by gender. Age remained as a very important factor in predicting injury severity for both men and women, but the use of lap and s houlder restraints wa s found to be more beneficial for men than women, while deploy ed air bags seemed more beneficial for women than men. 15
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2.3 Previous Researches on Work Zone Speed A study conducted by Taylor et al (2007) developed a speed profile model for construction work zone on high speed highw ays using neural networks and made available for use by practitioners through a MS EXCEL interface. The model inputs include horizontal and vertical alignment vari ables, cross section dimensions and traffic control features. A linear reference system is used for model input and output. Three categoriescars, trucks, and all vehicles were used in this study. Models for the 15th speed, mean speed, and 86th speed were developed. The result s of Measured Squared Error in (km/h) 2 indicate the neural network is able to predict the vehicle operating speeds to a good accuracy. Jiang (1999) conducted a study to analyze the traffic flow characteristics of freeway work zones based on the traffic data collected from Indiana fourlane freeways. The study found that vehicle speeds at work zones under uncongested conditions remained stable and close to the work zone speed limit of 55 miles per hour, while they dropped 31.6% to 56.1% from the normal work zone speeds during congestion. Sisiopiku, Et al. (1999) inve stigated the effectiveness of various standard speed limits in work zones and the effects of relate d factors on work zones. The mainly factors influencing work zone speed included number of lanes in work zone, worker presence, and type of lance closure. From the study, five findings were: (1) under free flowing traffic conditions, speeds in work zones were higher than the posted speed limits. (2) Motorists were responsive to the request for reduced speeds when traversing work zones. However, the observed speed reduction was only a fraction (55 to 75%) of that requested. (3) Speed reduction appeared to be highly co rrelated with the number of open lanes. (4) 16
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The effects of the presence of workers were difficult to isolate. The analysis supported the conclusion that worker pres ence did not always make a di fference in motorist speeds. (5) Lower speeds were associated with less fo rmidable types of lane closure/separation. Overall, the results showed that motorists speeds within work zones exceeded posted speed limits and were associated with the num ber of open lanes. Regardless of the posted work zone speed limit, motorists selected higher speeds when more lanes were open to traffic. This indicated that attempts to increase the road capacity during construction were likely to result in higher speeds through the work zones when free flow conditions existed. Rouphail and Tiwari (1985) studied flow ch aracteristics in freeway lane closures in Illinois. The work activity descriptors were numerated. The sum of the numerical codes was termed as the activity index (AI) of the work zone. The work activity data were collected manually in fiveminute in tervals corresponding to the speed flow observations. The results from the project s howed that on an average the observed mean speed at lane closure was 3 mph lower than the predicted mean speed. The difference in mean speeds was found to increase with increa sing AI but the difference was less than 1 mph. The difference in speed increased significantly as the proximity of work zone moved to within 6 ft of the traffic lane. Sun and Benekohal (2004) investigated platooning and gap ch aracteristics of shortterm and longterm freeway work zones. The finding showed that the average gap was the shortest when a car was following anot her car. The next shortest gap was when a car was following a truck. The gap was l onger when a truck was following a car or a truck. When a truck was followi ng a car or a truck, the gap si zes were not as different as when a car was following a car or a truck. Th is indicated that car drivers were more 17
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sensitive to what type of vehi cles they were following than the truck drivers. Additionally, the researcher also found that the gaps at shor tterm work zone were longer than the gaps at long term work zone for the same combination of leader and follower. 18
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Chapter Three Modeling Methodology for Crash Severity Models 3.1 Crash Severity Models A set of crash severity models were de veloped in this study to identify the variables that were significantly influential on the injury severity degree of work zone crashes. These models utilized the crash se verity of work zone crashes as a dependent variable and described the relationship between the injury severity and a set of explanatory variables. Crash se verity, defined as the most severe injury sustained by a person involved in the crash, is scaled in to five major levels shown in Table 3.1. Obviously, crash severity is an ordinal (ord ered) categorical variable ranked from the least severe level (no injury) to the most severe level (fatal). Table 3.1 Definition of Crash Severity Level Definition 1 No Injury 2 Possible Injury 3 NonIncapacitating Injury 4 Incapacitating Injury 5 Fatal (within 30 days) The models were developed based on the hi story crash data; so that they explain the effects of various factors on crash severity given that the person is involved in a crash. In other words, the models estimate the probability of a certain crash severity when a 19
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crash has been happened. Several statistical methods are used to estimate the model with ordinal categorical outcomes. In the rest of the chapter, the statistical methods were discussed in detail. 3.2 Ordinal (Ordered) Logit Regression 3.2.1 Introduction to the Regression When the scale of a multiple category outcome is ordinal scale rather than nominal scale, Ordinal Logit Regression (OLR), also called as Ordered Logit Regression, is used to describe the relationship betw een the outcomes and a set of explanatory variables. In contrast to the multinomial log it regression, the ordinal logit regression can reflect the ordinal features of the model outcomes. Assume that the ordinal outcome variable, Y can take on K values coded The probability of K ,...,2, 1 Y adopting a specific value can be defined by KjjYpj,...,2,1 ),Pr(( x (3.2.1) where is the vector of explanatory variables. The ordinal logit regr ession model can be written as x 1,...,2,1 )Pr(1 )Pr( ln )Pr( )Pr( ln)...(1 Kj jY jY jY jY ppLogitj jx x x x x (3.2.2) where j is the j th constant coefficient (interpret); is the vector of slope coefficients associated with the explanatory variables. 20
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With this model, the probability of the probability of a larger response, j Y is compared to an equal or smaller response, j Y The cumulative probability can be calculated as j jKj jy jY11,...,2,1 ) exp(1 1 )Pr()Pr(x x x (3.2.3) or 1,...,2,1 ) exp(1 ) exp( )Pr(1)Pr( Kj jY jYj jx x x x (3.2.4) where exp() is the exponential function. 3.2.2 Parallel Regression Assumption From Equation 3.2.2, it can be concluded that the ordinal logit regression assumes common slope parameters associated with the predictor variables. This model is also knows as proportionalodds model because the ration of the odds of the event j Y is independent of the category j In other words the odds ratio is constant for all categories. For example, Figure 3.1 plots the cumula tive probability curves when there are four ordered categories, resul ting in three curves. To see why these curves are parallel, a value point of the outcome probability is pick ed. At this point, the following equation can be derived as x Y x Y x Y )3Pr()2Pr()1Pr( x x x It is in sense that the regression curves are parallel. 21
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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00Pr(Y j) Pr(Y 1x) Pr(Y 2x) Pr(Y 3x) Figure 3. 1 Illustration of the Parallel Regression Assumption A Wald test is proposed by Brant to assess the parallel assumption of the ordinal regression. This test allows both an overall te st that the coefficients for all variables are equal and tests of the equa lity of the coefficients for individual variables. For overall test, 1 K binary regressions are c onstructed as following: 1,...,2,1 j 0 1 Kj jY Y zj (3.2.5) so we have 1,...,2,1 )][Pr( Kj zLogitj j jx x (3.2.6) the hypothesis of the overall test is 1 210... :KH (3.2.7) A Wald test statistic is derived as chisquare with MK )2( degrees of freedom, where M is the number of explanatory variables. For theindividual variable, the null hypothesis is mth 22
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(3.2.8) m Km m m mH 1, 2,1,0... :The resulting test statistic follows chisquare distribution with K2 degrees of freedom. If the probability of these tests ( pvalue ) is less than a value (usu ally is 0.05), the hypothesis is rejected; in other words, there are strong evidences for th e violation of the assumption for overall variables or individual ones. 3.3 Partial Proportional Odds Regression 3.3.1 Generalized Ordered Logit Regress A key problem with the ordinal logit regression is that the parallel assumption is often violated. It is common for one or more coefficients of the e xplanatory variables ( ) to differ across values of the outcome In this situation, the ordinal logit regression is overly restrictive. For passing ove r the restriction, a generali zed ordered logit regression was proposed by Clogg and Shihadeh (1994). Th is regression can be written as )( j 1,...,2,1 exp(1 ) exp( )()Pr() Kj gjYjj jj jx x x x (3.3.1) The probabilities that Y will take on each of the values is equal to (3.3.2) )()Pr( 1,...3,2 ),()()Pr( )(1)1Pr(1 1 1 K j jgKY Kj ggjY g Y x x x x x x x When2 K the generalized logit regression is equi valent to the binary logit regression. When2 K the regression becomes equivalent to a series of binary logistic regressions where categories of the respons e variable are combined. The generalized ordered l ogit regression gives freedom to each coefficient of variables across the outcome values. When th e parallel assumption is violated for only 23
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some of variables but not for all variables, the regression estimates far more parameters than is really necessary. For overcoming the less restriction, a partial proportional odds logit regression was proposed by Peterson & Harrel (1990). 3.3.2 Partial Proportional Odds Logit Regression (POLR) In the partial proportional odds regression, some of the regression coefficients can be same for all outcome values where the para llel assumption for the variables associated with the coefficients is not violated. Other coefficients can differ if their associated assumptions are violated. We assume that N independent random observations are sampled and that the responses of these observations on an ordinal variable Y are classified in K categories with The cumulative probabilities is KY ,..,2,1 1,...,2,1 ) exp(1 ) exp( )Pr( Kj jYn j a j n j a j i x x x x xn i a i n i a i i (3.3.3) where is a vector containing the values of observation i on that subset of explanatory variables for which the parallel assumption is not violated; is the vector of coefficients associated with the nonviolated variab les, and is same across values of a ixa Y is a vector containing the values of observation on that subset of explan atory variables for which the parallel assumption is violated; is the vector of coefficients associated with the violated variables, and differs across the response values. nixin j For estimating the constants )( and coefficients )( through Maximum Likelihood Estimation (MLE), the loglikelihoo d function for the model is defined as 24
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(3.3.4) N i K j jijYIL1 1 1 ,}) ln{Pr( lnixwhere is an indicator variable for observation such that jiI,i 1, jiI if and if jYi 0,jiI jYi 3.3.3 Criteria for Assessing the Model 3.3.3.1 Tes t z Tes t z is used to test the statistical significance of individual estimated coefficients of the ordered logit regression or the partial pr oportional odds logit regression. For MLE, estimators are distributed asymptotically normally. This means that as sample size increases, the sampling distribution of an ML estimator becomes approximately normal. So the hypothesis is 0 :0 mH and the z Statistic follows the standard normal distribution given as ) 1,0( N n zmm/ (3.3.5) where m is the mth coefficient of the model, and is the estimator of mm ; m is the estimator of standard deviation of the coefficient m ; is number of observations. nIf is true, the coefficient 0Hm of the model is not statistically significant. If is rejected at a confidence level (usually is 0.05), the coefficient 0Hm is significant to the response. 25
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3.3.3.2 Likelihood Ratio (LR) Test It is often useful to take an overall si gnificance test for all coefficients of the model, that means, to test if all coefficien ts are simultaneously equal to zero or not. The hypothesis can be written as 0 :0 H Such hypothesis can be tested with likelihood ratio (LR) test, which can be thought of as a comparison between the estimates obtained after the constraints im plied by the hypothesis ( 0 ) have been imposed to the estimates obtained without the constraints. To define the test, let model be the unconstrained model that includes constants (Mm ) and slope coefficients (m ). Let model be the constrained model that excludes all slop coefficients. To test the hypothesis, the test statistic is used: M)(ln2)(ln2)(2aMLML MG (3.3.6) where is the loglikelihood function defined in Equation 3.3.4. If the null hypothesis is true, the test st atistic is di stributed as chisquare with degrees of freedom equal to the number of slope co efficients. If the test statisti c falls to the rejection region, () ln L p value is less than a confidence level (usu ally is 0.05), then the null hypothesis is rejected. It can be concluded th at not all slope coefficients ar e equal to 0, in other words, at least one explanatory va riable has significant influe nce on the model response. 3.3.3.3 Pseudo2 R To assess the goodnessoffit of the model, which is a statistical model that describes how well the model fits a set of observations, the Pseudo2 R is provided as )(ln )(ln 12aML ML R (3.3.7) 26
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where is the unconstrained model with all slope coefficients; is the constrained model with only constants; and is the loglike lihood function. If the unconstrained model does much better than the constrained mode l, this value will be close to 1. If the unconstrained model does not explain much at all, the value will be close to zero. In this study, the purpose focused on exploring the influence of explanatory variables on the response. So this value was just taken as a reference. MaM () ln L 3.3.4 Interpretation of Model Coefficients The generalized ordered logit model is often interpreted in terms of odds ratios for cumulative probabilities. The odds that a response is j or less versus greater than j given can be derived from Equation 3.3.1 as x ) exp( )Pr( )Pr( )Pr(1 )Pr( )(jjjY jY jY jY j x x x x x x (3.3.8) To determine the effect of a change in x from to the odds ratio at versus is sxexsxex )] exp([ ) exp( ) exp( )( )(jes jej jsj ej j xx x x x xs When only a single variable ( ) changes by mx then ) exp( ),( ),(,jm mj mjx x x x (3.3.9) With an increase of in the odds of a response that is less than or equal to mx j are changed by the factor ) exp(,jm holding all other variables constant. If changes by 1, the odds ratio equals mx 27
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)exp( ),( )1,(,jm mj mjx x x x (3.3.10) Because the exponential function is a monotonic increasing function, if jm is greater than zero, the odds ratio is greater than 1; and if jm is negative, the odds ratio falls into (0, 1). Positive coefficients mean that higher values on the explanatory variables make higher values on the dependent variable more likely. For the ordinal logit regression, the odds ratio is same across all values of the response. So the interpretation of coefficients is same for all responses values. In contrast, for the partial proportional odds logit regr ession, some coefficients have same interpretation if the parallel assumption is not violated for these coefficients, and violatedvariables have various interpretations acr oss the response values. 28
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Chapter Four Estimation Results of Crash Severity Models 4.1 Data Preparation The dataset used for analysis and model estimation was extracted from the Florida Crash Analysis Reporting (CAR) system. This system is maintained by the Florida Department of Transportation (FDOT) and contains comprehensive information of Florida motor vehicle collisions, and that of the involved vehicles and persons. The dataset contains all work zone crash data fr om 2001 to 2005 which were identified by the variable FIRST_ROAD_ CONDITION_ CRASH_COD equal to 04 (Road under Repair/Construction). This original dataset was downloaded from the FDOT mainframe, and was transformed to SPSS data file for data arrangement and data reduction. From the original dataset, some variable s were selected for data analysis. These variables could be measured at ordinal scal e, nominal scale, or continuous scale. For handling the data in an easy way, except fo r three continuous variables, all categorical variables were transformed to binary data. Some records have empty values for continuous variables. These records were deleted from the dataset. The description of the original variables is given in Appendix A. 29
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4.2 Data Description Table 4.1 gives the description of the se lected variables for the crash severity model development. The response variable is cr ash severity level, which can be ranked at 5 levels in ascending order from no injury to fatal. The explanatory variables can be classified into 4 categories: driverrelated fa ctors, environmentalrelated factors, crashrelated factors, and road wayrelated factors. Table 4.1 Description of Selected Variables for Model Development Variable Description Type Value Definition ACCISEV Crash Severity Level Ordinal 1 No Injury 2 Possible Injury 3 NoCapacitating Injury 4 Incapacitating Injury 5 Fatal DriverRelated ALCHDRUG If driver was under influence of Binary 0 No alcohol or drugs 1 Yes AGE Drivers Age Categorical 1 Young (<24) 2 Adult ( 25 and <65) 3 Old ( 65) Environmentalrelated DAYLIGHT If the crash occurred during day Binary 0 No light condition 1 Yes BDWTHER If weather was clear Binary 0 No 1 Yes 30
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Table 4.1 (continued) Variable Description Type Value Definition Roadwayrelated SPEC_SECT If road section was specific type Binary 0 No (Intersection, Interchange ) 1 Yes SURF_DRY If road surface was dry Binary 0 No 1 Yes GR_CUR If there was a curve or grade at Binary 0 No the crash location 1 Yes TRAF_CONT If there was a traffic control Binary 0 No strategy 1 Yes VIS_OBS If there was a vision obstruction Binary 0 No at the crash location 1 Yes URBAN If the crash occurred in a urban Binary 0 No area 1 Yes FREEWAY If the crash occurred in a freeway Binary 0 Surface Road 1 Freeway SURWIDTH Road Surface Width Continuous MAXSPEED Speed Limit Continuous SECTADT Annual Average Daily Traffic Continuous CrashRelated HVINV If heavy vehicle was involved Binary 0 No 1 Yes Tables 4.2 and 4.3 illustrate the statistic description of the variables. In Table 4.2, the minimum value, maximum value, range, mean, and standard deviation of the three continuous variables are provided. Surface wi dth is the width of roadway except for shoulders with the mean of 28.75 feet and th e range of 80 feet. The minimum speed limit at work zones is 15miles/h and the maximum speed limit is 70 miles/h. The mean speed limit is 52.75 miles/h. The AADT has a large range from 250 vehicles per day to over 300 thousand vehicles per day. 31
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The distribution of crash severity is give n in Table 4.3. The percentage of the severity level descends with the increase of crash severity. The slight injury crashes (ACCISEV=1, 2, 3) hold 90.7% of the total wo rk zone crashes, and Incapacitating Injury crashes only holds the percentage of 7.9%, followed by the fatal crashes of 1.5%. There is 8.0% of work zone crashes involved alc ohol or drugs. And about 66% of work zone crashes occurred under good w eather or good light conditions. 46% of the locations where work zone crashes occurred are under th e influence of specific section, like bridge, intersection, interchange, or railway cross. Most of work zone crashes occurred where road surface is dry (83.1%), road section has not grade or curv e (79.1%), and vision condition is good (89.9%). The percentage of heavy vehicle involveme nt, urban area, and freeway is 15%, 41%, and 85% respectively. The distribution of drivers age groups is 9.4% for old drivers, 24.2% for young drivers, and 66.4% for adult drivers. The most frequent crash type is rearend with 37.7% percent, followed by angle crash (11.9%) a nd side swipe crash (11.0%). Table 4.2 Descriptive Statis tic of Continues Variables Variable N Minimum Maximum Range Mean Std. Deviation SURWIDTH 16868 8 88 80 28.75 8.845 MAXSPEED 16868 15 70 55 52.75 11.457 SECTADT 16868 250 302,000 301,750 63,149.89 50,543.123 32
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Table 4.3 Frequencies of Discrete Variables Variable Value Frequency Percent Sample Size: 16,868 ACCISEV 1 7,654 45.4% 2 4,268 25.3% 3 3,368 20.0% 4 1,325 7.9% 5 253 1.5% ALCHDRUG 0 15,521 92.0% 1 1,347 8.0% AGE 1 4,083 24.2% 2 11,202 66.4% 3 1,583 9.4% DAYLIGHT 0 5,642 33.4% 1 11,226 66.6% BDWTHER 0 11,173 66.2% 1 5,695 33.8% SPEC_SECT 0 9,112 54.0% 1 7,756 46.0% SURF_DRY 0 2,854 16.9% 1 14,014 83.1% GR_CUR 0 13,345 79.1% 1 3,523 20.9% TRAF_CONT 0 5,479 32.5% 1 11,389 67.5% VIS_OBS 0 15,163 89.9% 1 1,705 10.1% URBAN 0 2,663 15.8% 1 14,205 84.2% FREEWAY 0 9,930 58.9% 1 6,938 41.1% CRASHTYPE 0 6,646 39.4% 1 6,355 37.7% 2 2,009 11.9% 3 1,858 11.0% HVINV 0 14,341 85.0% 1 2,527 15.0% 33
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4.3 Overall Work Zone Crash Severity Model 4.3.1 Estimation Procedure This section presents the estimation results of the work zone crash severity model for all work zone crashes. At first, cross tabulation analysis was performed to check the distribution of explanatory va riables across injury severi ty levels and ensure enough observations in each cell. And AGE variable was transformed to three dummy variables: YOUNG_AGE (AGE=0), MIDDLE_AGE (AGE=1), and OLD_AGE (AGE=2). After then, the ordinal logit regression model was developed using the OLOGIT procedure available in the STATA software package. Stepwise model selection was carried out where the significant levels for entry into th e model was 0.05 and it for removal from the model is 0.15. Variables were entered into and removed from the model in such a way that each forward selection step was followed by one or more backward elimination steps. The stepwise selection procedure terminated wh en further variable can be added into the model, or if the variable just entered into the model is the only variable removed in the subsequent backward elimination. Thirdly, th e Brant test was performed to test if the parallel regression assumpti on was violated. The Brant pr ocedure in the STATA was used to execute this test with the confidence level 0.05. Finally, if the assumption was violated, the partial odds regression model was developed with the selected explanatory variables in the first step. The GOLOGIT2 pr ocedure in the STATA was carried out for the estimation. This procedure is developed by Richard Williams to estimate generalized ordered logit models for ordinal dependent vari ables, including three special cases of the generalized model: the proportional odds/paral lel lines model, th e partial proportional odds model, and the logistic regression model. Hence, the GOLOGIT2 can estimate 34
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models that are less restrictive than the pr oportional odds /parallel lines models (whose assumptions are often violated) but more parsimonious and interpretable than those estimated by a nonordinal method, such as multinomial logistic regression. 4.3.2 Cross Tabulations between Explan atory Variables and Crash Severity In order to obtain a better understanding about the selected ex planatory variables, cross tabulations of binary or categorical va riables with crash severity were developed and given in Tables 4.4 and 4.5. Table 4.4 Cross Tabulati on between Explanatory Variables and Crash Severity Crash Severity Frequency Row % Value 1 2 3 4 5 Total DAYLIGHT 0 2502 1318 1176 500 146 5642 44.3% 23.4% 20.8% 8.9% 2.6% 100.0% 1 5152 2950 2192 825 107 11226 45.9% 26.3% 19.5% 7.3% 1.0% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% BDWTHER 0 5119 2775 2242 871 166 11173 45.8% 24.8% 20.1% 7.8% 1.5% 100.0% 1 2535 1493 1126 454 87 5695 44.5% 26.2% 19.8% 8.0% 1.5% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% SPEC_SEC 0 4105 2248 1823 766 170 9112 45.1% 24.7% 20.0% 8.4% 1.9% 100.0% 1 3549 2020 1545 559 83 7756 45.8% 26.0% 19.9% 7.2% 1.1% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% SURF_DRY 0 1256 751 593 216 38 2854 44.0% 26.3% 20.8% 7.6% 1.3% 100.0% 1 6398 3517 2775 1109 215 14014 45.7% 25.1% 19.8% 7.9% 1.5% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% 35
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Table 4.4 (Continued) Crash Severity Frequency Row % Value 1 2 3 4 5 Total TRAF_CONT 0 2508 1395 1068 442 66 5479 45.8% 25.5% 19.5% 8.1% 1.2% 100.0% 1 5146 2873 2300 883 187 11389 45.2% 25.2% 20.2% 7.8% 1.6% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% VIS_OBS 0 6942 3812 2985 1190 234 15163 45.8% 25.1% 19.7% 7.8% 1.5% 100.0% 1 712 456 383 135 19 1705 41.8% 26.7% 22.5% 7.9% 1.1% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% URBAN 0 1053 577 626 323 84 2663 39.5% 21.7% 23.5% 12.1% 3.2% 100.0% 1 6601 3691 2742 1002 169 14205 46.5% 26.0% 19.3% 7.1% 1.2% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% FREEWAY 0 4362 2563 2045 813 147 9930 43.9% 25.8% 20.6% 8.2% 1.5% 100.0% 1 3292 1705 1323 512 106 6938 47.4% 24.6% 19.1% 7.4% 1.5% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% HVINV 0 6069 3843 3041 1192 196 14341 42.3% 26.8% 21.2% 8.3% 1.4% 100.0% 1 1585 425 327 133 57 2527 62.7% 16.8% 12.9% 5.3% 2.3% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% ALCHDRUG 0 7070 4029 3112 1160 150 15521 45.6% 26.0% 20.1% 7.5% 1.0% 100.0% 1 584 239 256 165 103 1347 43.4% 17.7% 19.0% 12.2% 7.6% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% 36
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Table 4.4 (Continued) Crash Severity Frequency Row % Value 1 2 3 4 5 Total GR_CUR 0 6058 3428 2628 1064 167 13345 45.4% 25.7% 19.7% 8.0% 1.3% 100.0% 1 1596 840 740 261 86 3523 45.3% 23.8% 21.0% 7.4% 2.4% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% AGE 0 1674 1107 911 333 58 4083 41.0% 27.1% 22.3% 8.2% 1.4% 100.0% 1 5307 2779 2101 847 168 11202 47.4% 24.8% 18.8% 7.6% 1.5% 100.0% 2 673 382 356 145 27 1583 42.5% 24.1% 22.5% 9.2% 1.7% 100.0% Total 7654 4268 3368 1325 253 16868 45.4% 25.3% 20.0% 7.9% 1.5% 100.0% 4.3.3 Estimation Results The estimation of results of the ordinal lo git regression is given in Table 4.6. The sample size is 16,868 observations, and the Like lihood Ratio (LR) test statistic falls into the rejection area ()05.00 valuep. That means the overall explanatory variables of the model have significant influence on the responses (crash severity levels) at a statistical significance level 0.05. Except for VIS_OBS, all slope coefficients are significant at a confiden ce level 0.05. Although the pvalue of VIS_OBS is little greater than 0.05, the variable was still included in the model since more variables increase the explanation ability of the model. Because the response variable has 5 levels, four models were fitted with same slope coefficients and different constants (i nterprets). Model I indi cates the probability ratio of the high injury severity levels (greater than no injury) to the lowest injury severity level (no injury); M odel II presents the probability ratio of the higher injury 37
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severity (greater than possible injury) to th e low severity levels (possible injury and no injury); Model III and Model IV denote the probability ratios at a resemble way. In the STATA, the cut point on the latent variable is estimated as a substitute of model constant coefficient (j ). Actually, the cut point is equal to the reversed value of the constant. Table 4.5 Estimation of Ordinal Logit Regre ssion for Work Zone Crash Severity Model Ordered logistic regression Number of observation = 16868 LR chi2(11) = 669.52 Prob > chi2 = 0.0000 Log likelihood = 21438.289 Pseudo R2 = 0.0154 ACCISEV Coef. Std. Err. z zp [95% Conf. Interval] DAYLIGHT 0.0883 0.0317 2.7900 0.0050 0.1504 0.0263 GR_CUR 0.0850 0.0360 2.3600 0.0180 0.0145 0.1556 VIS_OBS 0.0895 0.0470 1.9100 0.0570 0.0026 0.1815 URBAN 0.2839 0.0450 6.3100 0.0000 0.3721 0.1958 FREEWAY 0.4392 0.0462 9.5000 0.0000 0.5299 0.3486 MAXSPEED 0.0227 0.0021 10. 8300 0.0000 0.0186 0.0268 ALCHDRUG 0.2927 0.0575 5.0900 0.0000 0.1799 0.4054 HVINV 0.7720 0.0448 17.2400 0.0000 0.8598 0.6842 MIDDLE_AGE 0.1434 0.0304 4.7200 0.0000 0.2030 0.0838 /cut1 (Model I) 0.2862 0.1306 0.0303 0.5420 /cut2 (Model II) 1.3845 0.1310 1.1277 1.6413 /cut3 (Model III) 2.8030 0.1327 2.5430 3.0631 /cut4 (Model IV) 4.7298 0.1446 4.4463 5.0132 Table 4.7 illustrates the results of the Brant Test of the parallel regression assumption. Four binary logistic models were constructed to perform the Wald test on the identification of slope coefficients across the four binary models. From Table 4.7, the pvalues of DAYLIGHT, GR_CUR, URBAN, ALCHDRUG, and HVINV are less than 0.05. That means the hypothesis that these slope coefficients are identical across the models is rejected at a confidence level 0.05. So it can be concluded that a significant test statistic provides evidence that the parallel regression assumption has been violated for 38
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these variables. However, the assumption is not violated for FREEWAY, MAXSPEED, MIDDLE_AGE, and VIS_OBS. Table 4.6 Results of Brant Test of Parallel Regression Assumption Binary Logistic Model 1 Y 2 Y 3 Y 4 Y DAYLIGHT 0.0481 0.1544 0.1918 0.5071 GR_CUR 0.0487 0.1230 0.0755 0.6317 VIS_OBS 0.1191 0.0793 0.0456 0.1883 URBAN 0.1519 0.3567 0.5290 0.6107 FREEWAY 0.4609 0.4375 0.3933 0.6015 MAXSPEED 0.0234 0.0224 0.0219 0.0401 ALCHDRUG 0.0075 0.3636 0.8972 2.0421 HVINV 0.8667 0.5855 0.2988 0.6685 MIDDLE_AGE 0.1461 0.1638 0.1038 0.1752 Cons 0.4887 1.3731 2.7409 5.9643 Brant Test of Parallel Regression Assumption Variable ChiSquare pvalue DF ALL 499.88 0.0000 27 DAYLIGHT 17.3300 0.0010 3 GR_CUR 24.1900 0.0000 3 VIS_OBS 3.6800 0.2980 3 URBAN 31.3600 0.0000 3 FREEWAY 1.9100 0.5910 3 MAXSPEED 4.2600 0.2340 3 ALCHDRUG 217.2100 0.0000 3 HVINV 110.2200 0.0000 3 MIDDLE_AGE 1.8700 0.5990 3 Tables 4.8 and 4.9 present the estimate results of the partial proportional regression for work zone crashes. The model estimation is presented in Table 4.8, and the statistic criteria for assessing the partial pr oportional odds model are given in Table 4.9. As same as the ordinal logit regression, f our models were estimated. The variables for which the parallel assumption is not violated (FREEWAY, MAXSPEED, MIDDLE_AGE, and VIS_OBS) have same coefficients across the models and those for which the parallel assumption is vi olated (DAYLIGHT, GR_CUR, URBAN, ALCHDRUG, and HVINV) have different coefficients. 39
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Table 4.7 Estimation Results of Coefficients of Partial Proportional Odds Regression ACCISEV Coef. Std. Err. z zp [95% Conf. Interval] Model I: 1 j DAYLIGHT 0.0433 0.0347 1.2500 0.2120 0.1113 0.0247 GR_CUR 0.0445 0.0392 1.1300 0.2570 0.0325 0.1214 VIS_OBS 0.0900 0.0471 1.9100 0.0560 0.0024 0.1823 URBAN 0.1434 0.0491 2.9200 0.0030 0.2395 0.0472 FREEWAY 0.4522 0.0462 9.7800 0.0000 0.5428 0.3616 MAXSPEED 0.0233 0.0021 11. 0900 0.0000 0.0192 0.0274 ALCHDRUG 0.0170 0.0606 0.2800 0.7790 0.1358 0.1017 HVINV 0.8677 0.0460 18.8600 0.0000 0.9578 0.7775 MIDDLE_AGE 0.1431 0.0305 4.6900 0.0000 0.2028 0.0833 Cons 0.4956 0.1263 3.9300 0.0000 0.7431 0.2482 Model II: 2 j DAYLIGHT 0.1440 0.0374 3.8500 0.0000 0.2174 0.0707 GR_CUR 0.1347 0.0422 3.1900 0.0010 0.0520 0.2174 VIS_OBS 0.0900 0.0471 1.9100 0.0560 0.0024 0.1823 URBAN 0.3474 0.0494 7.0300 0.0000 0.4443 0.2505 FREEWAY 0.4522 0.0462 9.7800 0.0000 0.5428 0.3616 MAXSPEED 0.0233 0.0021 11. 0900 0.0000 0.0192 0.0274 ALCHDRUG 0.3713 0.0620 5.9900 0.0000 0.2498 0.4928 HVINV 0.5917 0.0539 10.9800 0.0000 0.6973 0.4861 MIDDLE_AGE 0.1431 0.0305 4.6900 0.0000 0.2028 0.0833 Cons 1.4436 0.1268 11.3800 0.0000 1.6922 1.1949 Model III: 3 j DAYLIGHT 0.1835 0.0577 3.1800 0.0010 0.2966 0.0705 GR_CUR 0.0734 0.0646 1.1400 0.2560 0.0532 0.2000 VIS_OBS 0.0900 0.0471 1.9100 0.0560 0.0024 0.1823 URBAN 0.5022 0.0658 7.6300 0.0000 0.6312 0.3733 FREEWAY 0.4522 0.0462 9.7800 0.0000 0.5428 0.3616 MAXSPEED 0.0233 0.0021 11. 0900 0.0000 0.0192 0.0274 ALCHDRUG 0.8945 0.0792 11.3000 0.0000 0.7393 1.0497 HVINV 0.3199 0.0815 3.9300 0.0000 0.4796 0.1603 MIDDLE_AGE 0.1431 0.0305 4.6900 0.0000 0.2028 0.0833 Cons 2.8041 0.1369 20.4800 0.0000 3.0724 2.5357 Model IV: 4 j DAYLIGHT 0.5151 0.1344 3.8300 0.0000 0.7785 0.2518 GR_CUR 0.5186 0.1260 4.1200 0.0000 0.2717 0.7655 VIS_OBS 0.0900 0.0471 1.9100 0.0560 0.0024 0.1823 URBAN 0.6882 0.1284 5.3600 0.0000 0.9399 0.4364 FREEWAY 0.4522 0.0462 9.7800 0.0000 0.5428 0.3616 MAXSPEED 0.0233 0.0021 11. 0900 0.0000 0.0192 0.0274 ALCHDRUG 1.8792 0.1393 13.4900 0.0000 1.6062 2.1522 HVINV 0.4900 0.1361 3.6000 0.0000 0.2233 0.7567 MIDDLE_AGE 0.1431 0.0305 4.6900 0.0000 0.2028 0.0833 Cons 4.9755 0.1961 25.3800 0.0000 5.3598 4.5913 40
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Table 4.8 Statistic Criteria for Assessing Partial Proportional Odds Regression Partial Proportional Odds Regression Number of obs = 16868 LR chi2(24) = 1087.66 Prob > chi2 = 0.0000 Log likelihood = 21229.217 Pseudo R2 = 0.0250 4.3.4 Interpretation The crash severity model estimated by th e ordinal logit regression has same slope coefficients across all K1 severity levels. For example, the coefficient for DAYLIGHT is 0.0883, which means that the presence of day light (DAYLIGHT=1) tends to reduce the injury severity of work zone crashes, and the odds ratio ( 9155 .0)0883.0exp( ) is same for all pairs of the comparisons: 2, 3, 4, 5 versus 1; 3, 4, 5 versus 1, 2; 4, 5 versus 1, 2, 3; and 5 versus 1, 2, 3, 4. The Table 4.10 gives the odds ratio for each explanatory variable in the ordinal logit models. Table 4.9 Odds Ratio of Explanatory Variables in the Ordinal Logit Models Model I Model II Model III Model IV Variable )1Pr( )1Pr( Y Y )2Pr( )2Pr( Y Y )3Pr( )3Pr( Y Y )4Pr( )5Pr( Y Y DAYLIGHT 0.9155 0.9155 0.9155 0.9155 GR_CUR 1.0887 1.0887 1.0887 1.0887 VIS_OBS 1.0936 1.0936 1.0936 1.0936 URBAN 0.7528 0.7528 0.7528 0.7528 FREEWAY 0.6446 0.6446 0.6446 0.6446 MAXSPEED 1.0230 1.0230 1.0230 1.0230 ALCHDRUG 1.3400 1.3400 1.3400 1.3400 HVINV 0.4621 0.4621 0.4621 0.4621 MIDDLE_AGE 0.8664 0.8664 0.8664 0.8664 Based on this table, some interpreta tions can be concluded as follows: (1) the presence of day light tends to re duce the crash severity of work zone crashes; 41
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(2) if the crash location is in urban area or in freeway, the injury severity of work zone crashes is also more likely to decrease; (3) if there is a curve or grade at the cr ash location, an increase in the injury severity of work zone crashes is expected more likely; (4) the presence of vision obstruction leads to a high probability of the occurrence of more severe work zone crashes; (5) a high speed limit tends to increase the crash severity of work zone crashes; (6) if alcohol or drug is involved, the work zone crash severity is more likely to increase; (7) the involvement of heavy vehicles te nds to reduce the work zone crash severity; and (8) young and old drivers (MIDDLE_AGE=0) tends to conduct more severe work zone crashes. In contrast to the ordinal models, some of the slope coefficients in the partial regression model are different acr oss severity levels. So the interpretation for coefficients in the partial proportional odds logit regression model is different to those in the ordinal logit model. The odds ratios of explanator y variables for the pa rtial proportional odds logit regression model are given in Table 4.11. 42
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Table 4.10 Odds Ratio of Explanatory Variables in the Partial Regression Models Model I Model II Model III Model IV Variable )1Pr( )1Pr( Y Y )2Pr( )2Pr( Y Y )3Pr( )3Pr( Y Y )4Pr( )5Pr( Y Y DAYLIGHT 0.8659 0.8324 0.5974 GR_CUR 1.1442 1.6797 VIS_OBS 1.0942 1.0942 1.0942 1.0942 URBAN 0.8664 0.7065 0.6052 0.5025 FREEWAY 0.6362 0.6362 0.6362 0.6362 MAXSPEED 1.0236 1.0236 1.0236 1.0236 ALCHDRUG 1.4496 2.4461 6.5483 HVINV 0.4199 0.5534 0.7262 1.6323 MIDDLE_AGE 0.8667 0.8667 0.8667 0.8667 Because VIS_OBS, FREEWAY, M AXSPEED, and MIDDLE_AGE do not violate the parallel regression a ssumption, the odds ratios for them are identical across the four models (Model I to Model IV). So the interpretations for these variables are similar to the corresponding ones in the ordinal logit models. The in terpretations are given as: (1) the presence of vision obstructions at crash location tends to increase the injury severity; (2) if crashes occurred in freeways rather th an surface roads, injury severity is likely to be reduced; (3) a higher speed limit tends to a higher injury severity; and (4) young and old drivers (MIDDLE_AGE=0) tends to increase the work zone crash severity. But for DAYLIGHT, GR_CUR, URBAN, ALC HDRUG, and HVINV, the interpretations are different across the four models. The inte rpretation for these variables is given as follows: (1) The presence of day light (DAYLIGHT=1) 43
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The factor in Model I has no significant influence on the crash severity (pvalue=0.2120>0.05). For other three models, this factor tends to reduce the crash severity (odds ratios are less than 1). But its effects on injury severity change in ascending order (associated odds ratios in descending order) as an increase of severity levels from possible injury to fa tality. The factor most tends to reduce the probability of fatality (Y=5) to no fatal ity (Y=1, 2, 3, and 4), followed by the probability ratio of more severe injury (Y= 4 and 5) to less severe injury (Y=1, 2, and 3). The factor least tends to reduce the probability ratio of injury ( Y =3, 4, and 5) to possible or no injury (Y =2 and 1). Figure 4.1 indi cates the variety of odds ratios. 0.8659 0.8324 0.59740 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pr(Y>1)/Pr(Y=1)Pr(Y>2)/Pr(Y 2)Pr(Y>3)/Pr(Y 3)Pr(Y=5)/Pr(Y 4) Partial Regression ModelsOdds Ratio Figure 4.1 Effects of Presence of Day Light (2) The crash location in urban area (URBAN=1) This factor is significant in all models. This factor has ascending tendency to reduce the injury severity of work z one crashes across the four models from I to IV as shown in Figure 4.2. 44
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0.8664 0.7065 0.6052 0.50250 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pr(Y>1)/Pr(Y=1)Pr(Y>2)/Pr(Y 2)Pr(Y>3)/Pr(Y 3)Pr(Y=5)/Pr(Y 4) Partial Regression ModelsOdds Ratio Figure 4.2 Effects of Urban Area (3) A curve or grade at the crash location (GR_CUR=1) This factor has significant influence in Model II and Model IV. That the odds for these two models are greater than 1 indicates that th e factor tends to increase the injury severity at ascending order from Model II to Model IV. From Figure 4.3, we know that the factor most tends to increa se the probability ratio of fatality to no fatality, followed by the one of injury to possible or no injury. 1.1442 1.67970 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Pr(Y>1)/Pr(Y=1)Pr(Y>2)/Pr(Y 2)Pr(Y>3)/Pr(Y 3)Pr(Y=5)/Pr(Y 4) Partial Regression ModelsOdds Ratio Figure 4.3 Effects of Curve or Grade 45
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(4) The involvement of alcohol or drugs (ALCHDRUG=1) This factor has no significant influence on the probability ratio of injury to no injury ( pvalue >0.05). But it tends to increase the injury severity across other severity levels. Its odds ratio for the fatal ity to no fatality model is highest, almost double greater than the second one. It can be concluded that the involvement of alcohol or drugs is a very important factor to conduct a fatal work zone crash. 1.4496 2.4461 6.54830 1 2 3 4 5 6 7 Pr(Y>1)/Pr(Y=1)Pr(Y>2)/Pr(Y 2)Pr(Y>3)/Pr(Y 3)Pr(Y=5)/Pr(Y 1) Partial Regression ModelsOdds Ratio Figure 4.4 Effects of Involve ment of Alcohol or Drugs (5) The involvement of H eavy Vehicle (HVINV=1) The factor tends to increase the probability ratio of fatality to no fatality. That means it is an important factor to introduce a work zone fatal crash. But for other severity levels, the factor te nds to reduce the cr ash severity. 46
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0.4199 0.5534 0.7262 1.63230 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Pr(Y>1)/Pr(Y=1)Pr(Y>2)/Pr(Y 2)Pr(Y>3)/Pr(Y 3)Pr(Y=5)/Pr(Y 1) Partial Regression ModelsOdds Ratio Figure 4.5 Effects of Invol vement of Heavy Vehicle 4.4 Crash Severity Model for Rearend Work Zone Crashes Figure 4.6 presents the distribution of wo rk zone crashes over crash types. The most dominant crash type is rearend with a percentage of 38%, followed by angle (12%) and side swipe (11%). In this section, the crash severity model for rearend work zone crashes was developed to investigate the infl uence of explanatory va riables on the injury severity of rearend work zone crashes. 38% 12% 11% 39% Rearend Angle Side Swipe Other Figure 4.6 Distribution of Crash Type 47
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4.4.1 Description of Rearend Dataset There are 6355 observations extracted from the original dataset for rearend crash analysis. To explore the rearend dataset, we found the number of fatal crashes was too small (0.6% of total crashes). For ensuring enough observations for each severity value, the severity levels 4 and 5 were combined. Th e updated description of injury severity of work zone rearend crashes is given in Tabl e 4.12. The cross tabula tions of categorical variables are shown in Table 4.13, while Table 4.14 presents the description of continuous variables. 48
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Table 4.11 Description of Response Variable for Rearend Dataset Value Description Frequency Distribution 1 No Injury 2523 39.7% 2 Possible Injury 2150 33.8% 3 NoCapacitating Injury 1251 19.7% 4 Incapacitating Injury or Fatal 431 6.8% Table 4.12 Cross Tabulations between Explanatory Variables and Crash Severity for Rearend Dataset Crash Severity Frequency Row % Value 1 2 3 4 Total DAYLIGHT 0 691 549 329 148 1717 40.2% 32.0% 19.2% 8.6% 100.0% 1 1832 1601 922 283 4638 39.5% 34.5% 19.9% 6.1% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% BDWTHER 0 1766 1417 864 294 4341 40.7% 32.6% 19.9% 6.8% 100.0% 1 757 733 387 137 2014 37.6% 36.4% 19.2% 6.8% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% SPEC_SEC 0 1494 1287 809 313 3903 38.3% 33.0% 20.7% 8.0% 100.0% 1 1029 863 442 118 2452 42.0% 35.2% 18.0% 4.8% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% SURF_DRY 0 344 318 181 58 901 38.2% 35.3% 20.1% 6.4% 100.0% 1 2179 1832 1070 373 5454 40.0% 33.6% 19.6% 6.8% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% GR_CUR 0 2025 1708 960 347 5040 40.2% 33.9% 19.0% 6.9% 100.0% 1 498 442 291 84 1315 37.9% 33.6% 22.1% 6.4% 100.0% Total 2523 2150 1251 431 6355 49
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Table 4.12 (Continued) Crash Severity Frequency Row % Value 1 2 3 4 Total TRAF_CONT 0 773 740 422 150 2085 37.1% 35.5% 20.2% 7.2% 100.0% 1 1750 1410 829 281 4270 41.0% 33.0% 19.4% 6.6% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% VIS_OBS 0 2381 2020 1152 402 5955 40.0% 33.9% 19.3% 6.8% 100.0% 1 142 130 99 29 400 35.5% 32.5% 24.8% 7.3% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% URBAN 0 303 226 199 85 813 37.3% 27.8% 24.5% 10.5% 100.0% 1 2220 1924 1052 346 5542 40.1% 34.7% 19.0% 6.2% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% FREEWAY 0 1265 1175 683 232 3355 37.7% 35.0% 20.4% 6.9% 100.0% 1 1258 975 568 199 3000 41.9% 32.5% 18.9% 6.6% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% HVINV 0 2224 1987 1150 354 5715 38.9% 34.8% 20.1% 6.2% 100.0% 1 299 163 101 77 640 46.7% 25.5% 15.8% 12.0% 100.0% Total 2523 2150 1251 431 6355 ALCHDRUG 0 2323 2034 1173 373 5903 39.4% 34.5% 19.9% 6.3% 100.0% 1 200 116 78 58 452 44.2% 25.7% 17.3% 12.8% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% 50
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Table 4.12 (Continued) Crash Severity Frequency Row % Value 1 2 3 4 Total AGE 0 639 565 353 100 1657 38.6% 34.1% 21.3% 6.0% 100.0% 1 1718 1424 780 292 4214 40.8% 33.8% 18.5% 6.9% 100.0% 2 166 161 118 39 484 34.3% 33.3% 24.4% 8.1% 100.0% Total 2523 2150 1251 431 6355 39.7% 33.8% 19.7% 6.8% 100.0% Table 4.13 Descriptive Statis tic of Continues Variables Variable N Minimum Maximum Range Mean Std. Deviation SURWIDTH 6355 10 88 78 29.58 9.298 MAXSPEED 6355 20 70 50 53.60 10.586 SECTADT 6355 1800 302000 300200 73032.64 55231.438 4.4.2 Estimation Results for Rearend Dataset As same as for the overall work zone cr ash dataset, an ordinal logit regression model was developed for rearend dataset using the STATA software. Three dummy variables (YOUNG_AGE, MIDDLE_AGE, and OL D_AGE) were also derived from AGE. Stepwise procedure was implemented to select explanatory variables which are significant to the response. The parallel regression assumption was examined by the Brant test, and the partia l proportional odds logit regression model was estimated. Because the injury severity for the rearend da taset has 4 levels rather than 5, 3 models (Model I, II, III) were estimated for both of th e two regressions. The estimation results of ordinal logit models are given in Tables 4.15. From the table, we know that overall or individual coefficients are sign ificantly not equal to zero. Ta ble 4.16 offers the result of Brant test. It indicates that the parallel regression assumption is violated for HVINV, FREEWAY, and MAXSPEED. 51
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Table 4.14 Estimation of Ordinal Logit Regression for Crash Severity Model (Rearend Dataset) Ordered logistic regression Number of obs. = 6355 LR chi2(11) = 134.97 Prob > chi2 = 0.0000 Log likelihood = 7786.3796 Pseudo R2 = 0.0086 ACCISEV Coef. Std. Err. z zp [95% Conf. Interval] SPEC_SECT 0.2824 0.0547 5.160 0 0.0000 0.3897 0.1751 HVINV 0.1679 0.0814 2.0600 0.0390 0.3275 0.0082 GR_CUR 0.1905 0.0582 3.2700 0.0010 0.0764 0.3046 TRAF_CONT 0.1401 0.0496 2.8200 0.0050 0.2373 0.0429 FREEWAY 0.6623 0.0710 9.3300 0.0000 0.8015 0.5232 MAXSPEED 0.0248 0.0033 7. 4700 0.0000 0.0183 0.0313 OLD_AGE 0.2064 0.0866 2.3800 0.0170 0.0367 0.3761 /cut1 (Model I) 0.4231 0.1651 0.0994 0.7467 /cut2 (Model II) 1.8874 0.1669 1.5604 2.2144 /cut3 (Model III) 3.5043 0.1730 3.1652 3.8434 Table 4.15 Results of Brant Test of Parallel Regression Assumption (Rearend Dataset) Binary Logistic Models 1 Y 2 Y 3 Y SPEC_SECT 0.2460 0.3262 0.5546 HVINV 0.3527 0.0185 0.6342 GR_CUR 0.1916 0.2265 0.0129 TRAF_CONT 0.1781 0.0982 0.0995 FREEWAY 0.5727 0.7765 0.8052 MAXSPEED 0.0179 0.0342 0.0329 OLD_AGE 0.1971 0.2445 0.1516 Cons 0.0682 2.3832 3.8827 Brant Test of Parallel Regression Assumption Variable ChiSquare pvalue DF All 97.3500 0.0000 14 SPEC_SECT 5.7800 0.0550 2 HVINV 51.6800 0.0000 2 GR_CUR 4.2000 0.1220 2 TRAF_CONT 1.7600 0.4150 2 FREEWAY 6.0600 0.0480 2 MAXSPEED 16.5400 0.0000 2 OLD_AGE 0.4900 0.7820 2 52
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Tables 4.17 and 4.18 show the estimation results of the partial proportional logit regression. Table 4.16 Estimation Results of Coefficients of Partial Proportional Odds Re gression (Rearend Dataset) ACCISEV Coef. Std. Err. z zp [95% Conf. Interval] Model I: 1 j SPEC_SECT 0.2878 0.0550 5.2300 0.0000 0.3956 0.1799 HVINV 0.3470 0.0854 4.0600 0.0000 0.5145 0.1796 GR_CUR 0.1880 0.0581 3.2300 0.0010 0.0741 0.3020 TRAF_CONT 0.1444 0.0497 2.9100 0.0040 0.2418 0.0470 FREEWAY 0.6607 0.0708 9.3400 0.0000 0.7994 0.5220 MAXSPEED 0.0201 0.0035 5. 7800 0.0000 0.0133 0.0269 OLD_AGE 0.2086 0.0868 2.4000 0.0160 0.0384 0.3787 Cons 0.1503 0.1753 0.8600 0.3910 0.4939 0.1933 Model II: 2 j SPEC_SECT 0.2878 0.0550 5.2300 0.0000 0.3956 0.1799 HVINV 0.0022 0.0951 0.0200 0.9810 0.1885 0.1841 GR_CUR 0.1880 0.0581 3.2300 0.0010 0.0741 0.3020 TRAF_CONT 0.1444 0.0497 2.9100 0.0040 0.2418 0.0470 FREEWAY 0.6607 0.0708 9.3400 0.0000 0.7994 0.5220 MAXSPEED 0.0318 0.0037 8. 4900 0.0000 0.0244 0.0391 OLD_AGE 0.2086 0.0868 2.4000 0.0160 0.0384 0.3787 Cons 2.2778 0.1918 11.8800 0.0000 2.6536 1.9020 Model III: 3 j SPEC_SECT 0.2878 0.0550 5.2300 0.0000 0.3956 0.1799 HVINV 0.6380 0.1363 4.6800 0.0000 0.3708 0.9052 GR_CUR 0.1880 0.0581 3.2300 0.0010 0.0741 0.3020 TRAF_CONT 0.1444 0.0497 2.9100 0.0040 0.2418 0.0470 FREEWAY 0.6607 0.0708 9.3400 0.0000 0.7994 0.5220 MAXSPEED 0.0340 0.0057 6. 0200 0.0000 0.0229 0.0451 OLD_AGE 0.2086 0.0868 2.4000 0.0160 0.0384 0.3787 Cons 4.1088 0.3054 13.4500 0.0000 4.7073 3.5102 Table 4.17 Statistic Criteria for Assessing Partial Proportional Odds Regression (Rearend Dataset) Partial Proportional Odds Regression Number of obs = 16868 LR chi2(24) = 206.70 Prob > chi2 = 0.0000 Log likelihood = 7750.5142 Pseudo R2 = 0.0132 53
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4.4.3 Interpretation The odds ratios for the ordinal logit models are given in Table 4.19, and those for the partial proportional o dds regression model are given in Table 4.20. Table 4.18 Odds Ratios for the Ordinal Logit Models (Rearend Dataset) Model I Model II Model III Variable )1Pr( )1Pr( Y Y )2Pr( )2Pr( Y Y )3Pr( )3Pr( Y Y SPEC_SECT 0.7540 0.7540 0.7540 HVINV 0.8454 0.8454 0.8454 GR_CUR 1.2099 1.2099 1.2099 TRAF_CONT 0.8693 0.8693 0.8693 FREEWAY 0.5157 0.5157 0.5157 MAXSPEED 1.0251 1.0251 1.0251 OLD_AGE 1.2292 1.2292 1.2292 Table 4.19 Odds Ratios for the Partial Regression Models (Rearend Dataset) Model I Model II Model III Variable )1Pr( )1Pr( Y Y )2Pr( )2Pr( Y Y )3Pr( )3Pr( Y Y SPEC_SECT 0.7499 0.7499 0.7499 HVINV 0.7068 1.8927 GR_CUR 1.2068 1.2068 1.2068 TRAF_CONT 0.8655 0.8655 0.8655 FREEWAY 0.5165 0.5165 0.5165 MAXSPEED 1.0203 1.0323 1.0346 OLD_AGE 1.2320 1.2320 1.2320 Since only HVINV and MAXSPEED violate the parallel regre ssion assumption, their coefficients are different across the in jury severity levels. Others without the violation have same coefficients. The interpre tations for the slope coefficients are given as follows: (1) The crash location under the influence of intersection, interchanges, or other special sections (SPEC_SECT=1) 54
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This factor is more likely to reduce the injury severity of work zone rearend crashes. (2) A curve or grade at the crash location (GR_CUR=1) This factor tends to increase the injury severity of work zone rearend crashes. (3) The presence of traffic control meas ure at crash location (TRAF_CONT=1) The injury severity of work zone rea rend crashes is more likely to be reduce due to this factor. (4) The crash location at freeway sections (FREEWAY=1) This factor is likely to reduce the in jury severity of work zone rearend crashes. (5) Old drivers (OLD_AGE=1) Old drivers tends to increase the injury se verity of work zone rearend crashes. (6) Heavy vehicle involvement (HVINV=1) This factor has no significant influe nce on the Model II. But its odds for Model III is greater than 1, in other words, the factor is likely to conduce fatal or incapacitating injury when a rearend crash occurs at work zone area. (7) Speed Limit (MAXSPEED) A higher speed limit is likely to result in a more severe rearend crash at work zone area. 4.5 Summary In this chapter, two kinds of logit regr ession models for overall work zone crash dataset and rearend crash dataset were de veloped respectively. The ordinal logit 55
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56 regression model has same slope coefficients across different severity levels. But the parallel regression assumption is violated for the two samp les. The partial proportional odds logit regression model has less restrictive on the assumption. In this model, some variables for which the assumption is not violated have same slope coefficients across crash severity levels, while some variables th at do not meet the assumption have different coefficients. And more specific interpretations are given to the variables that do not meet the assumption. By summarizing the estimation results of the partial proportional odds logit model, Table 4.12 indicates the significant influences of the variables on the work zone crash severity. indicates a variable is more likely to reduce the work zone crash severity if the variable adopts (for binary vari able) or increase by a positive value (for continuous variable). By contraries, denotes a variable tends to increase the work zone crash severity.
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Table 4.20 Summary of the Influence of the Explanatory Variables Overall Work Zone Crash Severity Model Rearend Work Zone Crash Severity Model Variable )1Pr( Pr( Y Y)1 )2Pr( Y)2Pr( Y )3Pr( Y)3Pr( Y )4Pr( )5 Pr(Y Y )1Pr( Y)1Pr( Y )2Pr( Y)2Pr( Y )3Pr( Y)3Pr( Y DAYLIGHT GR_CUR VIS_OBS URBAN FREEWAY MAXSPEED ALCHDRUG HVINV MIDDLE_AGE OLD_AGE SPEC_SECT TRAF_CONT 57
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Chapter Five Modeling Methodology for Work Zone Speed Profile Models 5.1 Introduction In this study, work zone speed profile is defined as the spee d distribution over the distance to the starting point of lane closure. Figure 5.1 sh ows a typical speed profile in open lanes at freeway work zones. When vehi cles are running at open lanes and start to close to a work zone, their speed may be redu ced due to the disturbance of lane changes from closed lanes or the backward queue formed by the capacity reduction. The speed continues to decrease until r eaching a steady low value. Afte r then, vehicles start to accelerate up to the normal speed. Apparen tly, the speed profile model is a nonlinear function of the position to the start point of lane closure. It is difficult to develop a uniform equation to describe the character istics of speed profile using traditional statistical methodologies, like linear regression. In this st udy, a new learning machine algorithm, Support Vector Regression, was im plemented to develop a uniform equation for describing the relationship between speed profile and various factors. 58
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0 10 20 30 40 50 6022,999 22,100 21,200 20,300 19,400 17,500 16,600 15,700 14,800 13,900 12,999 12,100 11,200 10,300 9,400 8,500 7,600 6,700 5,800 4,900 4,000 3,100 2,200 1,300 400 501 1,400 2,300Distance to Closure Point (feet)Mean Speed (m/h) Figure 5.1 Speed Profile at Work Zones (Open Lanes) 59
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5.2 Simulationbased Experiment Design A simulationbased experiment was designed for the data collection. Rather than field experiment, simulationbased experime nt has several advantages: (1) computer simulation could reduce the cost of data collection; (2) traffic factors are easy to be changed according to researchers needs; (3) measures of effectiveness could be handled automatically by programming. Especially for work zone study, lane closure scenarios are difficult found in field, the simulationba sed experiment provides a feasible method to generate various traffic scenarios so that the speed profile models can be constructed based on a more comprehensive dataset. But simulationbased experiment also has some limitations: (1) some factors cannot be realized in current simulation software; (2) even based on a calibrated model, the error between the simulation environment and the real world. The microsimulation software package CO RSIM 5.1 was selected to create the experiment in this study. This package, or iginally developed by FHWA, has been used and validated for traffic operations research in past 20 years. CORSIM has the ability to simulate the freeway section with the integrated FRESIM module. The lane closure can be realized in FRESIM module by simulating an incident on a la ne. A series of incidents are created along the lanes during a long peri od (greater than the simulation time), and the traffic on the same lanes is blocked from the range of the incidents. This method does not take into consideration of the taper section prior to the lane closure. 60
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61 5.2.1 Simulation Model In Figure 5.2, a 30,000 feet freeway sect ion was setup in CORSIM with FRESIM module for simulating a real work zone section. Because this study focused on the four divided lanes freeway, two lanes with one closed lane on one direction was configured in the simulation model. Along the open lane, 31 traffic detectors were installed at an 800 feet interval to collect the m easure of speed. An incident was simulated at the close lane to realize the lane closure. The closure point could be changed from A to G with different length of closure zone. 5.2.2 Model Calibration The goodness of the results of computerbas ed traffic micro simulation is based on a well calibrated model which makes the model could reflect the real world more accurately. In general, the calib ration configures internal factors related to traffic flow characteristics according to small size of obser ved values in field. Because this study did not aim at representing any real freeway segment or project, a calibrated simulation model developed in a previous research for freeway work zone was adopted. Park and Won (2006) developed a syst ematic procedure for microscopic simulation model calibration a nd validation, which was successfully applied to freeway work zone case studies. In the procedure, a genetic algorithm optimization program is implemented to find an optimal calibration parameter set from the feasible parameter ranges. The optimal calibration parameter set fo r freeway work zones, shown in Table 5.1, which was adopted in this study.
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Figure 5.2 Simulation Model 62
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Table 5.1 Calibration Parameters Parameter Default Value Altered Value Entry Vehicles Headway Distribution Uniform Enlarge Car following sensitivity Index 1 1 Pitt car following constant (ft) 10 3 Lag acceleration (sec) 0.3 1.2 Lag deceleration (sec) 0.3 0.5 Time to complete a lanechange maneuver (sec) 2.0 1.0 Gap acceptance parameter 3 4 Percent of drivers desiring to yield to merging vehicles (%) 20 20 Multiplier for desire to make a discretionary lane change 0.5 0.4 Advantage threshold for discreti onary lane change 0.4 0.8 Minimum separation for generation of vehicles (sec) 1.6 1.3 Distribution of free flow speed by driver type Index 1 2 5.2.3 Input Variables and Simulation Scenarios Through the review of past research, the variables listed in Table 5.2 were selected to form various simulation scenar ios. In the study, a typical work zone configuration was selected: twolane freeway (one direction) with one lane closed. The default value of the volume dist ribution over lanes, 50:50, was adopted in this study, and there is no difference between left lane closed and right lane closed. In this study, only right lane closure was considered. Free flow speed (FFS) is defined in HC M 2000 as the mean speed of passenger cars that could be accommodated under low to moderate flow rates on a uniform freeway segment under prevailing roadway and traffic conditions. A measure of FFS is the speed where the average headway is greater 4 se conds between two successive vehicles. The "highest" (ideal) type of basi c freeway section is one in which the freeflow speed is 70 mph or higher. But the maximum FFS value is 70mph in CORSIM. In this study, the 63
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levels of FFS in freeway were categorized as three types: 70mph, 65mph, and 55mph. Since the simulation time constraints, th e level of FFS 65mph was not presented. A survey (Kamyab and Maze, Et al. 2001) conducted in 1999 to the state transportation agencies and to ll authorities throughout the country showed that most participating agencies repor ted reducing speed limits by 10 mph below the normal posted speed during construction activiti es. In this study, based on the FFS in freeway sections, the reduction of FFS in work zone is fixed as 10mph. Work zone grade is another important f actor which affects the speed because of the presence of grades would exacerbate any fl ow constriction that w ould otherwise exist, particularly in the presence of heavy vehicles. In this study, 3 levels of work zone grade are selected: 5, 0, +5. Heavy vehicle occupy more space on th e roadway than passe nger cars. Moreover, heavy vehicles accelerate slowly and th eir presence makes other drivers more apprehensive, and they need more operation time to shift lane in freeway. These factors reduce the overall capacity of the work zone. In this study, percentage of heavy vehicle is categorized into four levels: 0%, 5%, and 15%. The entry volume for different scenarios should cover a wide range to evaluate the variable early merge comprehensively. Krammes and Lopez (1994) recommended that the shortterm work zone lane clos ure capacity is 1600 pcphpl. For estimating the speed profile under congested and uncongested conditions, the range of entry volume is adopted from 800 pcph to 4000 pcph (one approach, two lanes). For reducing the simulation time, the entry volume is selected at 6 levels. 64
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The length of lane closure is also selected as an i nput variable. A longer work zone would reduce the capacity of the freew ay, and conducted a backward queue to the upstream which affects the upstream speed profile. In this study, 7 levels of the length of work zone were selected. Table 5.2 Input Variables Factor Level Work Zone Configuration 2 lanes with one closed FFS 70mph, 65mph, 55mph Work Zone FFS Reduction 10mph Work Zone Grade 5,0,+5 Percentage of Heavy Vehicle 0,5%,15% Entry Volume (one direction) 800pcph, 16 00pcph, 2400pcph, 2800pcph,3200pcph,4000pcph Length of Lane Closure 2000feet, 2500feet, 3000feet, 3500feet, 4000feet, 4500feet, 7500feet Simulation scenarios were performed by the combinations of each level of the variables. In total, 3 (FFS) (Grade) (HV %) (Volume) (Lengt h of lane closure) = 1134 simulation scenarios were performed in this study. A Visual Basic.NET program was developed to generate these scenarios thr ough revise the CORSIM (.trf) input file. 5.2.4 Data Collection Because the CORSIM simulation is stoc hastic, the results from different simulations with a same input files will not be identical. To reduce the stochastic errors and get a stable result, it is necessary to run simulation for many times instead of only once. But too many runs will result in increa se in the simulation time and the amount of output data. So the default value of 10 run ti mes for each traffic scenario was adopted in this study, because it satisfie d the precision of results and did not increase the simulation time greatly. The analysis time period for each run was 15 minutes. 65
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The speed data was collected from 31 traffic detectors on th e open lane at a 1 minute time interval with each run. For each scenario, the sample size is 15 (sample size per run) 10 (run times) 31 (detectors) = 4650. A program was developed to read these data from the CORSIM (.out) output files, and calculate the mean speed value of each detector for each scenario. Finally, each scenario had 31 observations. 5.3 Support Vector Regression 5.3.1 Introduction to Learning Machine The classical regression stat istical techniques like linea r regression were based on the very strict assumption that probability distribution models or probabilitydensity functions are known. Unfortunately, in many practical situations, there is not enough information about the underlying distributions laws, and distributio nfree regression is needed that does not require knowledge of probability distributions. In practical world, there are some systems are very complicated. People can only observe input and the corresponding output, but do not understand the relationship inside. The relationship between input and output de duced by learning from experimental data (samples or observations) is expected not only to be good fit to the samples, but also to have good generalization ability This learning mechanism is called statistical learning machine, and its concept is shown in Figure 5. 3. System is the research object which generates output given inputy x the output of the learning machine, is the predicted value of The objective of the learning machine is to estimate the relationship between and yy y x to minimize the difference between and y y 66
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y y x Figure 5.3 Concept of Learning Machine Suppose we are given training data An approximating function which approximates of the underlying dependency between the input and output, minimizes the expected risk. is the vector of parameters of the approximating function. The ri sk function is calculated as )} ,()...,,(),,{(2211nnyyyxxxw),(wxf (5.3.1) ),())(,(),() ,(ydPfyLydPyyLfRxwx, x where is a joint probability distribution equal to is the loss function, which represents the measure of the error introduced by the In regression, is continues variable, two functio ns in use are the square error ( norm), ) ,(yPxy) ()( xxyPP)) (,( wx,fyL) ,( wxf2L (5.3.2) 2)),(()),(,( wx wxfy fyL and the absolution error ( norm) 1L ),()),(,(wx wxfyfyL (5.3.3) 5.3.2 Empirical Risk Minimization and Structural Risk Minimization Learning can be considered a prob lem of finding the best estimator using available data. However, the joint prob ability distribution is unknown, and the f 67
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distributionfree learning must be performed based only on the training data pairs. With the only source of information a data set, the classical learni ng algorithm adopts the principle of empirical ri sk minimization (ERM): n i ii empfyL n fR1)),(,( 1 ][ Min wx (5.3.4) According to the classical law of large numbers ensures that the empirical risk converges to the expected risk empR R as the number of data points tends to infinity: 0))()((lim fRfRemp n (5.3.5) Because ERM does not suggest how to find a constructive procedure for model design, the learning algorithms based on the principl e of ERM (like ANN) may conduct an overfitting problem and thus bad generalization properties. When the training data is finite, th e expected can be written as (): (5.3.6) )( fRfRempwhere is confidence interval which is a m onotonic decreasing function of the sample size over the complexity of the stru cture of the approximating function ( )( h n ). When tends toward infinity, the confidence inte rval is tends to zero, so the estimator by minimizing is converged to the true estimator by minimizing the And the more complex the approximating function is, the larger confidence interval is. According to Equation 5.3.6, let function set nempf ) ( fR ) ( fRempf ) w ,( x fS be divided into a sequence of nested subsets ranked by co rresponding confidence interval SSSSk 21 (5.3.7) 68
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Within each function subset, the confidence inte rval is same. And a superset has a lager than its subset. Structural risk minimization (SRM) is a novel inductive principle for learning from finite training data sets, and is show n in Figure 5.4. The basic idea of SRM is: (1) To choose, from the sequence of the nested subsets of models (approximating functions), a subset (2S) of the right complexity to describe the training data; (2) To decide the best model by minimizing th e empirical risk within the selected subset (2S). Confidence Interval Empirical Risk, )( fRempExpected Risk, )( fR 3S2S1S Overfitting Lackfitting Complexity of Models Risk Figure 5.4 Concept of Structural Risk Minimization 69
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5.3.3 Support Vector Regression The support vector regression (SVR) is a nonlinear learning machine based on the principle of SRM for functional approxima tion. The learning machine is given training data, from which it attempts to lear n the inputoutput relati onship (dependency or function) A training data set n) ( x f niRRyDd i,...,2,1 , ixn consists of pairs(, , where inputs n),11yx ),,(22yx) ,(nny x R x are ddimensional vectors, and the system responses R y are continuous values. The SV R considers the approximating functions of the general form: K j jjw f1)( )( x wx, (5.3.8) To introduce all relevant concepts of SVR in a gradual way, the linear form is considered first. (5.3.9) bxwwx, Tf ) ( where is the bias vector b R b. Rather than the square error ( norm) or the absolution error ( norm) (Equations 5.3.2 and 5.3.3), SVR adopts 2L1Lityinsensitiv function introduced as the loss function. This SVR form is also called as SVR. The ityinsensitiv function is given as otherwise )( )( 0 )())(,( wx, xw, wx, wx, fy fy fy fyL (5.3.10) The loss function is equal to zero if the difference between the predicted and the observation is less than ) (wx, f In order to perform SVR, a new empirical risk is introduced: 70
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n i empfy n fR1)( 1 )( wx, (5.3.11) In formulating an SV algorithm for regression, the objective is to minimize the expected risk )),(( 2 1 )(1 2n i i ifyC fRwx w (5.3.12) where w is the parameter vector norm which reflects the complexity of the model. From Equation 5.3.10 and Figure 5.5, it follows that for all training data outside an tube, )( wx,fy for data above an tube, *)(wx,fy for data below an tube. *xy )( w x, f Figure 5.5 tube Parameters used in SVR (linear kernel) Thus, minimizing the risk in 5.3.12 is equi valent to minimizing the risk (Vapnik 1995, 1998) n i i n i iC R1 1 2 *2 1 ),,( w w (5.3.13) 71
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subject to (5.3.14) ni y yii i i i T i i T i,..2,1 ,0,* bxw bxw where i and are slack variables. i For minimizing the risk a Lagrange function is constructed from the objective function in Equation 5.3.13 and the constraints in Equations 5.3.14, by introducing a dual set of variab les. The primal variables Lagrange function is given: ) ,,(*w R n i i T ii i n i i T iii n i n i iiiib y b y C L1 * 1 11 ** 2) ( ) ( ) ()( 2 1 xw xw w (5.3.15) where are Lagrange multipliers and equal to or greater than zero. The partial derivatives of with respect to the primal variables have to vanish for optimality. **,,,iiiiL 0 0)( 0)((*) (*) (*) 1 1 ii i n i iii n i iiC L x L b L w w (5.3.16) where refer to (*)(*) (*),,i i and ii and ii and respectively. Substituting Equation 5.3.16 into Equation 5.3.15 yields the dual optimization problem, i maximize n i n i iii ii n ji jijjiiy11 * 1, *)()( ,))(( 2 1 xx (5.3.17) 72
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subject to and n i ii1 *0)( Cii,0,* From equation 5.3.16, we have n i iii1 *)( x wThus b fn i iii 1 *,)()( xx wx, (5.3.18) wix can be completely described as a line ar combination of the training patterns The corresponding to are called as support vectors (SVs). In a sense, the complexity of a functions representation by SVs depends only on the number of SVs. ix 0)(*iiFor the general form of the approximating f unction, kernel function is introduced to substitute the dot product xx ,i. Thus, (5.3.19) bK fn i iii 1 *),()()( xx wx,Except for the linear kernel function, Gaussian radial basis function ( RBF) is also a very important kernel function ) exp(),(2j ixx K xx (5.3.20) 73
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5.3.4 Procedure to Apply SVR LIBSVM is an integrated software devel oped by Chang and Lin (the National Taiwan University) for support vect or classification, regression ( SVR) and distribution estimation. In this study, the software is used to estimate the approximate function and evaluate the effectiveness of the SVR. The proposed procedure to apply SVR using LIBSVM is given as follows (Hsu, Chang and Lin, 2008) (1) Transform data to the format of the LIBSVM software (2) Conduct simple scaling on the data (3) Consider the RBF kernel (4) Determine the parameter ,Cand (5) Perform the data training (6) Test the model with the test data LIBSVM requires that each data instance is represented as a vector of real numbers. The whole dataset is split into two parts: training dataset and testing dataset. The former is used for model training while the latter is used for model validation. Scaling data before applying SVR is very important (Sarle 1997, Part 2 of Neural Networks FAQ). The main advantage of scaling is to avoid attributes in greater numeric ranges dominate those in smaller numeric ranges. Another advantage is to avoid numerical difficulties during the calculation. Because kernel values usually depend on the inner products of feature vector s, large attribute values might cause numerical problems. Two most common linearly scal ing methods are given as: 74
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min max min 1,0 min max min 1,11 2 xx xx x xx xx xscaled scaled (5.3.21) Apparently, we have to use the same rule as training data to scale testing data before model validation. The RBF function is a reasonable first choice for the kernel function. The RBF function nonlinearly maps samples into a higher dimensional space can handle the case when the relation between class labels and at tributes is nonlinear. Furthermore, the RBF kernel has less numerical difficulties. There are three parameters while using RBF kernels: ,Cand The insensitivity decides the range of the ad missible error for model training. A small value will lead to a small empirical risk, but may result in overfit ting and increase the training time. In contrast, a big value could reduce the training cost, but may bring a low accuracy in data training and predicting. In general, the value is selected from 0.01 to 0.1. The penalty factor C affects the training accuracy and the predicting ability. As the increase of the approximating error decreases and the training cost increases. When the value of Creaches a certain big value, the approximating error may stop decreasing, even start increasing due to overfitting. The kernel parameter C is also a factor which has influence on the approximating error. A larger will result in a complex model, thus may lead to ove rfitting problem, while a small will reduce the flatness of approximating function curve, a nd the approximating error. The Cand are correlated. 75
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The best pair of Cand are needed to decide before m odel training. In this study, the pairs of exponentially growing sequences of Cand are tried to indentify a good pair. The model training is processed using LIBSVM with training dataset and the selected model parameters. A validation procedure is used with the testing data to evaluate the accuracy of th e trained model. In LIBSVM, the Mean Square Error ( MSE ) and Squared Correlation Coefficient is adopted as the accuracy criteria. ) (2R n i if n MSE1 2)( 1 xiy (5.3.22) ) SSE y fix SST ( SSR )( SSE SST SSE 1 SST SSR SST SSTn 1i 2 n 1i 2 n 1i 2 2y yf y Ri i ix (5.3.23) In statistics, the mean squared error or MSE of an estimator is one of many ways to quantify the amount by which an estimator differs from the true value of the quantity being estimated. An MSE of zero means that the predictions are perfect to approximate the observations. 2 R is a statistic that will give some information about the goodness of fit of a model. In regression, the 2 R coefficient of determination is a statistical measure of how well the regression line approxima tes the real data points. An 2 R of 1.0 indicates that the regression line perfectly fits the data. 76
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Chapter Six Experiment Results of Speed Profile Models 6.1 Data Preparation The data for analysis were collected from the output files of the simulation experiment and translated into SPSS softwa re for data reduction. In total, 31,031 observations for 1001 scenarios were selected as the dataset for model development. The variables included in the dataset are given in Ta ble 6.1. The values of the scenario factors are shown in Table 5.2. Another input variable is the location of detectors. Because the start point of lane closure is changed as th e variety of the closur e length, the original values were translated into relative valu es which are measured as the distance of detectors to the start point. Table 6.1 Definition of Variables for Speed Profile Model Level Variable Definition Type Response SPEED Mean speed at detector points Continuous GRADE Work zone grade Continuous CLOSELENGTH Length of closure zone Continuous VOLUME Upstream volume Continuous HV Heavy vehicle percentage Continuous Scenario FFS Free flow speed Continuous Space LOCATION The distance to the start point of closure lane Continuous 77
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The comparison table of LOCATION to CLOSELENGTH is shown in Table 6.2. A positive value means the corresponding detector is located before the start point of lane closure, while a negative value means the detector is located after the point. Table 6.2 Comparison Table of LOCATION to CLOSELENGTH LOCATION LOSELENGTH Min Max Number 2000feet 499feet 25499feet 31 2500feet 1feet 24999feet 31 3000feet 501feet 24499feet 31 3500feet 1001feet 23999feet 31 4000feet 2001feet 22999feet 31 7500feet 5001feet 22999feet 31 The dataset was split randomly into two parts: the training dataset was used for model training, and the testing dataset was used for model validation. The statistical descriptions of the two datasets are given in Tables 6.3 and 6.4 respectively. These input variable were both rescaled into [1, 1] a nd the output variable was rescaled to [0, 1] Table 6.3 Descriptive Statistics for Training Dataset Number Minimum Maximum Mean Std. Deviation Grade 22010 2.00 2.00 0.01 1.62 CloseLength 22010 0.00 5500.00 1859.86 1667.16 Volume 22010 800.00 4000.00 2453.52 1047.65 HV 22010 0.00 15.00 5.70 5.90 FFS 22010 55.00 70.00 62.46 6.12 Location 22010 5001.00 25499.00 10801.33 7580.99 Speed 22010 1.13 70.05 55.26 13.32 Table 6.4 Descriptive Statistics for Testing Dataset Number Minimum Maximum Mean Std. Deviation Grade 9021 2.00 2.00 0.08 1.65 CloseLength 9021 0.00 5500.00 1850.52 1725.43 Volume 9021 800.00 4000.00 2461.86 1018.39 HV 9021 0.00 15.00 5.45 5.71 FFS 9021 55.00 70.00 62.42 6.10 Location 9021 5001.00 25499.00 10810.68 7594.26 Speed 9021 5.21 70.05 55.50 13.21 78
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79 6.2 Analysis on Speed Profiles The speed profile (pattern) at work zone s is more complex than that at common freeway section. Figure 6.1 shows the speed pr ofile with different entry volumes. It can be known that when the entry volume was less than the capacity (1600 suggested in HCM 2000), the speed profile is similar and approximated the free flow speed. When the entry volume is obviously greater than the cap acity, the speed prof ile becomes different much to that at common freeway section. Inspecting the figure, the speed profiles are described as follows: (1) When the traffic flow is under unconge sted traffic conditi ons, the speed along the freeway is controlled by the FFS (sp eed limit). The difference between the FFS and measured speed is little. But when vehicles are entering in work zone, due to the FFS reduction at the closure zone, the speed prof ile has a descent within lane closure area. (2) Being far from the start point of lane cl osure, the traffic flow on the open lane is not disturbed by the lane changes from the closed lane. The speed profile in this section is almost the same as th at in normal traffic flow in freeway. (3) When the traffic flow is closing to the start point, it is disturbed by the vehicle lane shifting. The speed of the vehicles is descending up to a small value. The start point of speed descent is going far from the work zone as the increase of the volume. (4) When the speed reaches a small and steady value, the backward queue is formed. The larger the entry volume is, the longer the queue length becomes.
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0 10 20 30 40 50 6022,999 22,100 21,200 20,300 19,400 17,500 16,600 15,700 14,800 13,900 12,999 12,100 11,200 10,300 9,400 8,500 7,600 6,700 5,800 4,900 4,000 3,100 2,200 1,300 400 501 1,400 2,300Distance to Closure Point (feet) (GRADE=2, CLOSELENGTH=4500,HV=15,FFS=55)Mean Speed (m/h) Entry Volume=800 Entry Volume=2400 Entry Volume=3200 Entry Volume=4000 Figure 6.1 Speed Profile under Different Congestion Condition 80
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(5) After the start point of lane closure, ve hicles start to accele rate up to the work zone FFS. 6.3 Results of Modeling Training The model training was a timeconsuming process, and the prediction accuracy depended on the parameters selection. For reducing the training time, the parameters insensitivity factor, penalty factor C and kernel function parameter were selected from a limited set which was the combination of =0.1 or 0.01, C=1, 1000, 2000, or 3000, and =0.16667, 1, 2, or 3. All these combina tions were used for model training and testing, and the best parameter comb ination was determined by the minimum MSE value. The final values of the parameters are01. 0 C=3000, and =2. As a comparison, the model trained with the default parameters was also provided. The training results are given in Table 6.5. Table 6.5 Results of Model Training and Validation Final Model Default Model Definition Kernel Function RBF RBF 0.01 0.1 insensitivity factor C 3000 1 penalty factor 2 0.166667 kernel function parameter Parameter total_SV 9481 3368 number of support vectors rho 0.717976 0.649306 bias term Training Results MSE( rescaled) 0.00396214 0.0104952 mean squared error (rescaled) MSE (mile/h)2 18.82 49.85 mean squared error Validation Results 2 R 0.892287 0.731187 squared correlation coefficient 81
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The final model has more support vect ors than the default model since its tube is more narrow than that of the default model. The MSE of the final model is a small than that of default value (MSE is rescaled value). And its2 R is close to 1. That indicates the predicted values are good at f itting the observations; in other words, the final model has good prediction ability. The selected comparisons of the predic ted speed profile to the observed speed profile for various scenarios are given in Fi gure Tables 6.2 through 6.10. These scenarios were selected from the testing dataset. From these figures, it can be concluded that the final speed profile model can fit the observati ons perfectly for all s ections under different scenarios. But the model with the default parameters has acceptable approximating characteristics only for the sections where the traffic flow is normal. 82
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0 10 20 30 40 50 60 7024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point of Lane Closure (feet) (GRADE=2, CLOSELENGTH=2500, HV=0, FFS=55, VOLUME=2400)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.2 Comparison of Speed Profile Models to Observations (low FFS and low VOLUME) 83
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0 10 20 30 40 50 60 7024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point (feet) (GRADE=2, CLOSELENGTH=500, VOLUME=3200, HV=15, FFS=55)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.3 Comparison of Speed Profile Models to Observations (low FFS and medium VOLUME) 84
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0 10 20 30 40 50 6024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point (feet) (GRADE=2, CLOSELENGTH=500, VOLUME=4000, HV=15%, FFS=55)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.4 Comparison of Speed Profile Models to Observations (low FFS and high VOLUME) 85
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0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000 70.0000 80.000024499 22900 21300 18700 17100 15500 13900 12300 10700 9100 7500 5900 4300 2700 1100 501Distance to the Start Point (feet) (GRADE=0, CLOSELENGTH=1000, VOLUME=2400, HV=0, FFS=65)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.5 Comparison of Speed Profile Models to Observations (medium FFS and low VOLUME) 86
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0 10 20 30 40 50 60 70 8024499 22900 21300 18700 17100 15500 13900 12300 10700 9100 7500 5900 4300 2700 1100 501Distance to the Start Point (feet) (GRADE=2, CLOSELENGTH=1000, VOLUME=3200, HV=5%, FFS=65)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.6 Comparison of Speed Profile Models to Observations (medium FFS and medium VOLUME) 87
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0 10 20 30 40 50 60 70 8024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point (feet) (GRADE=2, CLOSELENGTH=500, VOLUME=4000, HV=15%, FFS=65)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.7 Comparison of Speed Profile Models to Observations (medium FFS and high VOLUME) 88
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0 10 20 30 40 50 60 70 8024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point (feet) (GRADE=2, CLOSELENGTH=0, VOLUME=2400, HV=5, FFS=70)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.8 Comparison of Speed Profile Models to Observations (high FFS and low VOLUME) 89
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0 10 20 30 40 50 60 70 8024499 22900 21300 18700 17100 15500 13900 12300 10700 9100 7500 5900 4300 2700 1100 501Distance to the Start Point (feet) (GRADE=0, CLOSELENGTH=1000, VOLUME=3200, HV=5, FFS=70)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.9 Comparison of Speed Pr ofile Models to Observations (high FFS and medium VOLUME) 90
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0 10 20 30 40 50 60 70 8024999 23400 21800 19200 17600 16000 14400 12800 11200 9600 8000 6400 4800 3200 1600 1Distance to the Start Point (feet) (GRADE=0, CLOSELENGTH=500, VOLUME=4000, HV=5, FFS=70)Mean Speed (miles/h) Observation Final Model Default Model Figure 6.10 Comparison of Speed Profile Models to Observations (high FFS and high VOLUME) 91
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Chapter Seven Conclusions and Discussions 7.1 Conclusions This dissertation focused on modeling cras h severity and speed profile at work zones. Crash severity is an important criteri on reflecting the cost of work zone crashes in social and economy, and affected by various fa ctors including driver s characteristics, vehicle characteristics, envir onmental factors, and roadwa y features. To understand the influence of these factors on the crash se verity can be used to select proper countermeasure to reduce the crash severity at work zones and decrease the loss of construction/maintenance on roadway. A ne w modeling regression for ordinal output, partial proportional odds logit regression, was used to estimate the crash severity models for two crash datasets: overall work zone cras hes and rearend work zone crashes. Based on the results of crash severity modeling and analysis, some conclusions can be obtained: (1) The parallel regression assumption is al ways violated when the ordinal logit regression is utilized to estimate the work zone crash severity model. The partial proportional odds logit regression which has less restrict to the assumption can given more accurate and more detailed explanation on the impacts of factors on the work zone crash severity. 92
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(2) For over all work zone crashes, the pr esence daylight, the location at urban area or at freeway is more likely to reduce the severity of work zone crashes, while grade or curve of roadway section, vision obstruction, high speed limit, alcohol involvement, and young or old driver s tends to increase the severity of work zone crashes. The involvement of heavy vehicle is likely increase the probability of fatal crashes at work zone s, but tends to reduce the severity of injury only work zone crashes. (3) For rearend work zone crashes, the fact ors that tend to reduce the work zone crash severity include traffic controls, th e influence of special roadway section, and the freeway section. The factors that have reversed impacts include old drivers, grade or curve at roadway section, and high speed limit. Heavy vehicle involvement is more likely increase the probability of fatality or incapacitating injury, while reduce the probabi lity of injury crashes rather than that of no injury crashes. Work zone speed profile (pattern) is the mean value of the distribution of vehicle speed over the distance to the start point of la ne closure at work zones. Predicting work zone operating speeds under va rious scenarios is a useful precursor to appropriate regulatory and design decisions for work z ones. The speed profile model for the open lane on twolane with onelane closed (one direction) freeway was developed with a new learning machine algorithm, Suppor t Vector Regression. Based on the results of analysis and model development, the conclusion can be summarized as: (1) The speed profile is a typical nonlinear complicate system which is difficult to be described by a linear regressi on. The SVR has great capability to 93
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provide a uniform model for expressi ng the complicate relationship between speed profile and various traffic factors. (2) Based on the validation results, predictions of the speed profile model with selected parameters approximate obs ervations perfectly under various scenarios. That means the SVR mode l has good generalization ability for work zone speed profile; in other words, the SVR model can predict accurately the work zone speed rather than the training data. 7.2 Contributions to the Field 7.2.1 Methodological Contribution On the crash severity analysis aspect, this dissertation is dedicated into utilizing the partial proportional odds regression, a new logit regression met hod for ordinal outputs, to address the relationship between crash sever ity and various factors. This regression can avoid the parallel regression assumption, and provide more detailed interpretations of the factor coefficients. The ability for explaini ng the factor impacts on crash severity is beneficial to understand the characteristics of traffic crashes. The partial proportional odds regression can be used to analyze other cr ash data rather than work zone crashes. On the speed profile modeling aspect, this dissertation is dedicated into utilizing the support vector regression al gorithm to estimate the spee d profile model. Except for the capability to describe the complication nonlinear system, SVR has excellent prediction ability. Due to the features of SVR, SVR is applicable to modeling traffic systems which are always nonlinear complicate systems. The conclusions of this 94
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dissertation can be used as the guidance fo r the application of SVR in transportation research field. 7.2.2 Practical Contribution The interpretations of work zone crash se verity model can be used to understand the impacts of factors on work zone safety. Th is understanding is be nefit of addressing safety problem at work zones and selecti ng proper countermeasures to reduce crash severity and improve work zone safety. Because the simulation experiment is ba sed on a calibrated CORSIM model, the speed profile model can be utilized as a reference for highway design and operational analysis at work zones. It also can be used to help traffic engineers to understand the speed profile at work zone area, and to implement proper traffi c control systems to improve the work zone safety and operational performance. 7.3 Future Research Direction It is far from the end to come up with a full understanding of the factor impacts on work zone crash severity. Due to the limitati on of crash data collection, some useful variables were missed, such as gender of drivers, work zone types, traffic control countermeasures at work zones, and so on. In feature, crash work zone severity models which integrate the missed variables can provide more accurate and powerful interpretations of the factor impacts on the work zone severity. In this dissertation, only rearend work zone crashes were analyzed. For provide more specific understanding of the characteristics of work zone crashes, other types of work zone crashes should be 95
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modeled and explained. In addi tion, the interpretation of some factors is different from common sense. For example, the involvement of heavy vehicle tends to reduce the severity for work zone injury only crashes. A deeper research should be conducted for giving a more accurate explanation on this phenomenon. The effectiveness of SVR training is based on the parameter selection. In this dissertation, the selection performed by a si mple method within a small range. Although the final result is good, the model developed in this dissertation is not guaranteed to be the best estimation. In feature study, an optimal parameter selection process for SVR should be developed. This process sh ould adopt a search algorithm for global optimization (like genetic algorithm) to find the best combination of parameters for SVR training. 96
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List of References AlKaisy, A., Zhou, M., and Hall, F. New insi ghts into freeway capacity at work zones: empirical case study. Transportation Resear ch Record 1710, Transportation Research Board, Washington, D.C., pp. 154., 2001. Bai, Y. and Li, Y. Determining Major Caus es of Highway Work Zone Accidents in Kansas. Publication KTRAN: KU051. Kans as Department of Transportation, 2004. Benekohal, R. F., Elzohairy, Y. M. and Saak J. E., A Comparison of Delay from HCS, Synchro, PASSER II, PASSER IV and CORSIM for an Urban Arterial, Transportation Research Board, National Research Council, Washington, D.C., 2002. Benekohal, R. F., KajaMohideen, A., and Chitturi, M., A Methodology for Estimating Operating Speed and Capacity in Work Zone s, Transportation Research Board, National Research Council, Washington, D.C., 2004. Benetohan, R., R. Orloski, and A. Hashni Drivers Opinion on Work Zone Traffic Blincoe, L. J. The Economic Costs of Mo tor Vehicle Crashes, 1994. National Highway Traffic Safety Administration, Washington, D.C., 1996. Bloomberg, L.., Swenson, M., and Haldors, B., Comparison of Simulation Models and the HCM, Transportation Research Board, National Research Council, Washington, D.C., 2003. Chambless, J., Chadiali, A. M., Lindly, J. K, and McFadden, J. Multistate Work zone Crash Characteristics. ITE Journal, Vol. 72, pp46 50., 2002. Chien, Steven IJy and Chowdhury, M. S., SimulationBased Estimates of Delays at Freeway Work Zones, Transportation Res earch Board, National Research Council, Washington, D.C., 2002. Clogg, C. C. and Shihadeh, E. S. Statistic al Models for Ordinal Variables. Thousand Oaks, CA., 1994. Cohen, S. L. An Approach to Calibration and Validation of Traffic Simulation Models, Transportation Research Board, National Research Council, Wa shington, D.C., 2004. 97
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Crowther, B. C., A Comparison of CORSIM and INTEGRATION for the Modeling of Stationary Bottlenecks. Master Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2001. Dixon, K. K., Hummer, J. E., and Rouphail, N. M., Comparison of Rural Freeway Work Zone Queue Length Estimation Techniques: A Case Study, Transportation Research Board, Washington, D. C, 1998. Fan R. E., Chen, P.H. and Lin, C.J. Working set selection using the second order information for training SVM. Journal of Machine Learning Research. No.6, 18891918, 2005. FHWA. Manual on Uniform Traffic Control Devices for Streets and Highways. 2003 Edition, Federal Highway Administration. U. S. Department of Transportation, 2003. Garber, N. J. and Zhao, M. Crash Characte ristics at Work Zones. Publication VTRC 02R12, Virginia Transportation Research Council, Charlottesville, Virginia, 2002. Ha, T. and Nemeth, Z. A. Detailed Study of Accident Experience in Construction and Maintenance Zones. Transportation Research Record, No. 1590, TRB, National Research Council, Washington, D.C., pp38 45, 1995. Hall, J. W. and Lorenz, V. M. Character istics of Construction Zone Crashes. Transportation Research Record No. 1230, TRB, National Research C ouncil, Washington, D.C., pp20 27., 1989. Hill, R. W. Statistical Analysis of Fatal Traffic Accident Data. Masters Thesis, Texas Tech University. 2003. Holdridge, J. M., Shankar, V. N. and Ulfarsson, G. F. The Crash Severity Impacts of Fixed Roadside Objects. Journal of Safety Research. No.2, 139147., 2005 Hosmer, D. W. and Lemeshow, S. Applied Logistic Regression, Second Edition, John Wiley and Sons, New York, 1998. Hsu, C., Chang, C. C., and Lin, C. J. A Pr actical Guide to Support Vector Classification. http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf ., 2008 Jiang, X. J., and Adeli, H. Freeway Work Zone Traffic Delay and Cost Optimization Model. Journal of Transportation Engineering. Vol. 129, No. 3. 230241., 2003. Jiang, Y. Traffic Capacity, Speed and Queu eDischarge Rate of Indianas FourLane Freeway Work Zones, Transportation Res earch Record No. 1657, Transportation Research Board, National Research Council, Washington D.C., 1999. 98
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Kamyab, A., Maze, T.H., Gent, S. and Schrock, S. Work Zone Speed Control and Management by State Transportation Agencies and Toll Authorities, Transportation Research Board, National Research Council, Washington, D.C., 2001. Kim, K. N., Richardson, J., and Li, L. Persona l and Behavioral Predictors of Automobile Crash and Injury Severity. Accident Analys is and Prevention, Vol. 27, No. 4, 469481., 1995 Krammes, R.A., and G. O. Lopez. Updated Capacity Values For ShortTerm Freeway Work Zone Lane Closures. Transportation Research Record No.1442, Transportation Research Board, National Research Council, Washington, D.C., 1994. Martineli, D. R., and Xu, D. Delay estimation and optimal length for fourlane divided freeway work zones. J. Transp. Engrg., ASCE, 122(2), 114., 1996. Maze, T. and Kamyab, A. Work Zone Simu lation Model, Companion Report for Traffic Management Strategies for Merge Areas in Rural Interstate Work Zones. Center for Transportation Research and Education, Iowa State University, September, 1999. Maze, T. Kamyab, A. and Schrock, S. Evaluation of Work Zone Speed Reduction Measures. Final Contract Report. Iowa Department of Transportation, IA, 2000. McFadden, J., Yang, W. T., and Durrans, S. R. Application of Artificial Neural Networks to Predict Speeds on TwoLane Rural Highways. Transportation Research Record. No. 1751, Transportation Research Board, Nati onal Research Council, Washington D.C., 2005. McCoy, P. T., and Pesti, G. Dynamic Late Merge Control Concept for Work Zones on Rural Freeways. Transportation Research Boar d, National Research Council, Washington, D.C., 2001. McCoy, P. T., Pang, M., and Post, E. R. Optimum length of twolane, twoway, nopassing traffic operation in construction and maintenan ce zones on rural fourlane divided highways. Transp. Res.Rec. 773, Transportation Research Board, Washington, D.C., 20., 1980. Memmott, J. L., and Dudek, C. L. Queue a nd cost evaluation of work zones (QUEWZ). Transportation Research Record. No.979, Tr ansportation Research Board, Washington, D.C., 12., 1984. Mercier, C. R., Shelley, M. C., Rimkus, J. B., and Mercier, J. M., Age and Gender as Predictors of Injury Severity in Headon Highway Vehicular Crashes. Transportation Research Record No. 1581, Transportation Re search Board, National Research Council, Washington D.C., 1997. 99
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Migletz, J. and Graham, J. L. Work Zone Speed Limit Procedure. 78th Annual Meeting of the Transportation Research Board CD ROM, Transportation Research Board, National Research Council, Washington, D.C., 1999. Migletz, J., and J.L. Graham. Work Zone Sp eed Control Procedures: Proceedings of the Symposium on Work Zone Tra ffic Control. Report FHWA TS91003. TurnerFairbank Highway Research Center, Mclean, VA, 1991. Mohan, S. B. and Gautam, P. Cost of Highway Work Zone Injuries. Practical Periodical on Structural Design and Construction. Vol. 7, No.2, 2002, pp68 73., 2002. Mousa, R.M., Rouphail, N.M. and Azadivar, F. Integrating Micros copic Simulation and Optimization: Application to Freeway Work Zone Traffic Control. Transportation Research Record 1254, 1990. Park, B. B. and Qi, H. Development and Evaluation of a Calibration and Validation Procedure for Microscopic Simulation Mode ls. Final Contract Report, Virginia Transportation Research Council, 2004. Peterson, B. and Harrell, F. E. Partial Pr oportional Odds Models for Ordinal Response Variables. Application Statistics. No.2. 205217., 1990. Pigman, J. G. and Agent, K. R. Highway Cr ashes in Construction and Maintenance Work Zones. Transportation Research Record, No. 1270, TRB, National Research Council, Washington, D.C., pp12 21., 1990. Richard, S. H., and Dudek, C. L. Implemen tation of workzone speed control measures. Transportation Research Record, No. 1086, Tr ansportation Research Board, Washington, D.C., 36., 1986. Rouphail, N.M., and Tiwari, G. Flow Characteristics at Freeway Lane Closures. Transportation Research Record No.1035, Transportation Research Board, National Research Council, Washington, D.C., 1985. Sarle, W.S. Part 2 of Neural Networks FAQ, ftp://ftp.sas.com/pub/neural/FAQ.html 1997 Sisiopiku, V. P., Lyles, R. W., Krunz, M., Yang, Q., Akin, D., and Abbasi, M. Study of Speed Patterns in Work Zones, Transporta tion Research Board, National Research Council, Washington, D.C., 1999. Spainhour, L. K. and Wootton, I. A. Modeli ng Fault in Fatal Pedestrian Crashes Using Various Data Sources. Presented at 86th A nnual Meeting of the Tr ansportation Research Board, Washington, D.C., 2007. 100
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Suresh, R., Analysis of Freeway Weaving Areas Using Corridor Simulator and Highway Capacity Manual, Master's Thesis, Master Thes is, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1997. Talyor, D. R., Muthiah, S., Kulakowski, B. T., Mahoney, K. M. and Porter, R. J. Artificial Neural Network Speed Profile Model for Construction Work Zone on HighSpeed Highways. Journal of Transportation Engineering. Vol.133, No.3. 198204., 2007. Tarko, A., Kainpakapatman, S., and Wass on, J. Modeling and Optimization of the Indiana Lane Merge Control System on Approaches to Freeway Work Zones. Final Report, FHWA/IN/JTRP97/12. Purdue Un iversity, West Lafayette, Iniana., 1998. Thomas, G.B. Optimal Detector Location on Arterial Streets for Advanced Traveler Information Systems. Doctoral Dissertation, Arizona State University, Tempe, Arizona, Dec. 1998. Tian, Z., Urbanik, T., Engelbrecht, R.J., and Balke, K.N. Variations in Capacity and Delay Estimates from Microscopic Traffic Simulations Models. Transportation Research Board, National Research Council, Washington, D.C., 2002. Transportation Research Board, Highway Capacity Manual, 4th edition, National Research Council, Washington, D.C., 2000. Transportation Research Board. Nationa l Cooperative Highway Research Program (NCHRP) Report No. 350, Transportation Rese arch Board, National Research Council, 1993. Ullman, G. L., Finley, M. D., and Ullman B. R. Analysis of Crash at Active Night Work Zone in Texas. Presented at 85th Annual Mee ting of the Transporta tion Research Board, Washington, D.C., 2006. Wang, J., Hughes, W. E., Council, F. M., and Paniati, J. F. Investigation of Highway Work Zone Crashes: What We Know a nd What We Dont Know. Transportation Research Record, No.1529, Transportation Research Bo ard, National Research Council, Washington, D.C., 1996. 101
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Appendices 102
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Appedix A: Variables and Codes of Work Zone Crash Table A1 Variable of Work Zone Fatal Crash Variable Description Type YEAR The year of work zone fatal crash Nominal TIME The time of work zone fatal crash Nominal AGE The age of driver at fault Ordinal VEHMOVEMENT The movement of vehicle at fault before accident Nominal CRASHTYPE The type of crash Nominal VEHICLETYPE Heavy vehicle involved? Nominal FUNCLASS The function of roads Nominal TRWAYCHR Road Characteristics (level / curve?) Nominal MAXSPEED The speed limit Continue SECTADT The AADT of the section of work zones Continue TYPESUR The type of road surface Nominal SITELOCA Site Location Nominal LIGHTCONDITION Light condition Nominal WEATHERCONDITION Weather condition Nominal ROADSURFACE Road surface condition Nominal VISION Vision Obstructed Nominal RDACCESS Access control type Nominal SURWIDTH The width of roads Continue CONTRIBUTINGFACTORS The c ontributing factors Nominal TRAFCONT Traffic Control Nominal 103
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Appendix A (Continued) Table A2 Codes for TIME Codes Description 1 6:0010:00 2 10:0016:00 3 16:0020:00 4 20:006:00 Table A3 Codes for AGE Codes Description 1 <19 2 2024 3 2534 4 3544 5 4554 6 5564 7 >65 Table A4 Codes for VEHMOVEMENT Codes Description 01 STRAIGHT AHEAD 02 SLOWING/STOPPED/STALLED 03 MAKING LEFT TURN 04 BACKING 05 MAKING RIGHT TURN 06 CHANGING LANES 07 ENTERING/LEAVING PARKING SPACE 08 PROPERLY PARKED 09 IMPROPERLY PARKED 10 MAKING UTURN 11 PASSING 12 DRIVERLESS OR RUNAWAY VEH. 77 ALL OTHERS 88 UNKNOWN 104
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Appendix A (Continued) Table A5 Codes for CRASHTYPE Codes Description 01 COLL. W/MV IN TRANS. REAREND 02 COLL. W/MV IN TRANS. HEADON 03 COLL. W/MV IN TRANS. ANGLE 04 COLL. W/MV IN TRANS. LFTTURN 05 COLL. W/MV IN TRANS. RGTTURN 06 COLL. W/MV IN TRANS. SIDESWIP 07 COLL. W/MV IN TRANS. BAKD INTO 08 COLL. W/PARKED CAR 09 COLLISION WITH MV ON ROADWAY 10 COLL. W/ PEDESTRIAN 11 COLL. W/ BICYCLE 12 COLL. W/ BICYCLE (BIKE LANE) 13 COLL. W/ MOPED 14 COLL. W/ TRAIN 15 COLL. W/ ANIMAL 16 MV HIT SIGN/SIGN POST 17 MV HIT UTILITY POLE/LIGHT POLE 18 MV HIT GUARDRAIL 19 MV HIT FENCE 20 MV HIT CONCRETE BARRIER WALL 21 MV HIT BRDGE/PIER/ABUTMNT/RAIL 22 MV HIT TREE/SHRUBBERY 23 COLL. W/CONSTRCTN BARRICDE/SGN 24 COLL. W/TRAFFIC GATE 25 COLL. W/CRASH ATTENUATORS 26 COLL. W/FIXED OBJCT ABOVE ROAD 27 MV HIT OTHER FIXED OBJECT 28 COLL. W/MOVEABLE OBJCT ON ROAD 29 MV RAN INTO DITCH/CULVERT 30 RAN OFF ROAD INTO WATER 31 OVERTURNED 32 OCCUPANT FELL FROM VEHICLE 33 TRACTOR/TRAILER JACKNIFED 34 FIRE 35 EXPLOSION 36 DOWNHILL RUNAWAY 37 CARGO LOSS OR SHIFT 38 SEPARATION OF UNITS 39 MEDIAN CROSSOVER 77 ALL OTHER (EXPLAIN) 105
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Appendix A (Continued) Table A6 Codes for VEHICLETYPE Codes Description 00 UNKNOWN/NOT CODED 01 AUTOMOBILE 02 PASSENGER VAN 03 PICKUP/LIGHT TRUCK (2 REAR TIR) 04 MEDIUM TRUCK (4 REAR TIRES) 05 HEAVY TRUCK (2 OR MORE REAR AX) 06 TRUCK TRACTOR (CAB) 07 MOTOR HOME (RV) 08 BUS (DRIVER + 9 15 PASS) 09 BUS (DRIVER + > 15 PASS) 10 BICYCLE 11 MOTORCYCLE 12 MOPED 13 ALL TERRAIN VEHICLE 14 TRAIN 15 LOW SPEED VEHICLE 77 OTHER 88 PEDESTRIAN NO VEHICLE Table A7 Codes for TRWAYCHR Codes Description 1 STRAIGHTLEVEL 2 STRAIGHTUPGRADE/DOWNGRADE 3 CURVELEVEL 4 CURVEUPGRADE/DOWNGRADE Table A8 Codes for TYPESUR Codes Description 01 SLAG/GRAVEL/STONE 02 BLACKTOP 03 BRICK/BLOCK 04 CONCRETE 05 DIRT 77 ALL OTHER 106
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Appendix A (Continued) Table A9 Codes for SITELOCA Codes Description 01 NOT AT INTERSECTION/RRX/BRIDGE 02 AT INTERSECTION 03 INFLUENCED BY INTERSECTION 04 DRIVEWAY ACCESS 05 RAILROAD CROSSING 06 BRIDGE 07 ENTRANCE RAMP 08 EXIT RAMP 09 PARKING LOT/TRAFFIC WAY 10 PARKING LOT AISLE OR STALL 11 PRIVATE PROPERTY 12 TOLL BOOTH 13 PUBLIC BUS STOP ZONE 77 ALL OTHER Table A10 Codes for LIGHTCONDITION Codes Description 01 DAYLIGHT 02 DUSK 03 DAWN 04 DARK (STREET LIGHT) 05 DARK (NO STREET LIGHT) 88 UNKNOWN Table A11 Codes for WEATHERCONDITION Codes Description 01 CLEAR 02 CLOUDY 03 RAIN 04 FOG 77 ALL OTHER 88 UNKNOWN 107
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Appendix A (Continued) Table A12 Codes for ROADSURFACE Codes Description 01 DRY 02 WET 03 SLIPPERY 04 ICY 77 ALL OTHER 88 UNKNOWN Table A13 Codes for VISION Codes Description 01 VISION NOT OBSCURED 02 INCLEMENT WEATHER 03 PARKED/STOPPED VEHICLE 04 TREES/CROPS/BUSHES 05 LOAD ON VEHICLE 06 BUILDING/FIXED OBJECT 07 SIGNS/BILLBOARDS 08 FOG 09 SMOKE 10 GLARE 77 ALL OTHER (EXPLAIN) Table A14 Codes for RDACCESS Codes Description 1 FULL 2 PARTIAL 3 NONE 108
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Appendix A (Continued) Table A15 Codes for CONTRIBUTINGFACTORS Codes Description 01 NO IMPROPER DRIVING/ACTION 02 CARELESS DRIVING 03 FAILED TO YEILD RIGHT OF WAY 04 IMPROPER BACKING 05 IMPROPER LANE CHANGE 06 IMPROPER TURN 07 ALCOHOLUNDER INFLUENCE 08 DRUGSUNDER INFLUENCE 09 ALCOHOL DRUGSUNDER INFLUENCE 10 FOLLOWED TOO CLOSELY 11 DISREGARDED TRAFFIC SIGNAL 12 EXCEEDED SAFE SPEED LIMIT 13 DISREGARDED STOP SIGN 14 FAILED TO MAINTAIN EQUIP/VEHIC 15 IMPROPER PASSING 16 DROVE LEFT OF CENTER 17 EXCEEDED STATED SPEED LIMIT 18 OBSTRUCTING TRAFFIC 19 IMPROPER LOAD 20 DISREGARDED OTHER TRAFFIC CONT 21 DRIVING WRONG SIDE/WAY 22 FLEEING POLICE 23 VEHICLE MODIFIED 24 DRIVER DISTRACTION 77 ALL OTHER (EXPLAIN) Table A16 Codes for TRAFCONT Codes Description 01 NO CONTROL 02 SPECIAL SPEED ZONE 03 SPEED CONTROL SIGN 04 SCHOOL ZONE 05 TRAFFIC SIGNAL 06 STOP SIGN 07 YIELD SIGN 08 FLASHING LIGHT 09 RAILROAD SIGNAL 10 OFFICER/GUARD/FLAGMAN 11 POSTED NO UTURN 12 NO PASSING ZONE 77 ALL OTHER 109
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Appedix B: Sample of CORSIM Input File Created by TSIS Wed Sep 26 14:26:18 2007 from TNO Vers ion 61 Work Zone Simulation 0 12345678 1 2345678 2 2345678 3 2345678 4 2345678 5 2345678 6 2345678 7 234567 Zhenyu Wang 6 202007USF 0 1 1 1 1 10 9927 0000 22 81419 8219 24007 2 900 3 60 4 0 0 0 0 0 0 0 0 0 0 0 5 94 86before 10 94 86 85 30000 2 1 19 86 85 84 5000 2 1 19 85 84 83 5000 2 1 19 84 83 82 5000 2 1 19 83 82 81 5000 2 1 19 82 81 80 5000 2 1 19 81 80 50 20000 2 1 19 93 94 86 50000 2 1 19 92 93 94 50000 2 1 19 91 92 93 50000 2 1 19 90 91 92 40000 2 1 19 8001 90 91 0 2 1 19 80 508002 2000 2 1 19 94 86 0 0 0 11055 100 20 86 85 0 0 0 11055 100 20 85 84 0 0 0 11055 100 20 84 83 0 0 0 11055 100 20 83 82 0 0 0 11055 100 20 82 81 0 0 0 11055 100 20 81 80 0 0 0 11045 100 20 93 94 0 0 0 11055 100 20 92 93 0 0 0 11055 100 20 91 92 0 0 0 11055 100 20 90 91 0 0 0 11055 100 20 8001 90 0 0 0 11055 20 80 50 0 0 0 11055 100 20 94 86 85 100 25 86 85 84 100 25 85 84 83 100 25 84 83 82 100 25 83 82 81 100 25 82 81 80 100 25 81 80 50 100 25 110
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Appendix B (Continued) 93 94 86 100 25 92 93 94 100 25 91 92 93 100 25 90 91 92 100 25 8001 90 91 100 25 80 508002 100 25 94 86 2 1 0 94 28 94 86 1 1 0 94 28 94 86 2 100 0 94 28 94 86 1 100 0 94 28 94 86 2 200 0 94 28 94 86 1 200 0 94 28 94 86 2 300 0 94 28 94 86 1 300 0 94 28 94 86 2 400 0 94 28 94 86 1 400 0 94 28 94 86 2 500 0 94 28 94 86 1 500 0 94 28 94 86 2 600 0 94 28 94 86 1 600 0 94 28 94 86 2 700 0 94 28 94 86 1 700 0 94 28 94 86 2 800 0 94 28 94 86 1 800 0 94 28 94 86 2 900 0 94 28 94 86 1 900 0 94 28 94 86 21000 0 94 28 94 86 11000 0 94 28 94 86 21100 0 94 28 94 86 11100 0 94 28 94 86 21200 0 94 28 94 86 11200 0 94 28 94 86 21300 0 94 28 94 86 11300 0 94 28 94 86 21400 0 94 28 94 86 11400 0 94 28 94 86 21500 0 94 28 94 86 11500 0 94 28 94 86 21600 0 94 28 94 86 11600 0 94 28 94 86 21700 0 94 28 94 86 11700 0 94 28 94 86 21800 0 94 28 94 86 11800 0 94 28 111
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Appendix B (Continued) 94 86 21900 0 94 28 94 86 11900 0 94 28 94 86 22000 0 94 28 94 86 12000 0 94 28 94 86 22100 0 94 28 94 86 12100 0 94 28 94 86 22200 0 94 28 94 86 12200 0 94 28 94 86 22300 0 94 28 94 86 12300 0 94 28 94 86 22400 0 94 28 94 86 12400 0 94 28 94 86 22500 0 94 28 94 86 12500 0 94 28 94 86 22600 0 94 28 94 86 12600 0 94 28 94 86 22700 0 94 28 94 86 12700 0 94 28 94 86 22800 0 94 28 94 86 12800 0 94 28 94 86 22900 0 94 28 94 86 12900 0 94 28 86 85 2 1 0 86 28 86 85 1 1 0 86 28 86 85 2 100 0 86 28 86 85 1 100 0 86 28 86 85 2 200 0 86 28 86 85 1 200 0 86 28 86 85 2 300 0 86 28 86 85 1 300 0 86 28 86 85 2 400 0 86 28 86 85 1 400 0 86 28 85 84 2 1 0 85 28 85 84 1 1 0 85 28 85 84 2 100 0 85 28 85 84 1 100 0 85 28 85 84 2 200 0 85 28 85 84 1 200 0 85 28 85 84 2 300 0 85 28 85 84 1 300 0 85 28 85 84 2 400 0 85 28 85 84 1 400 0 85 28 84 83 2 1 0 84 28 84 83 1 1 0 84 28 112
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Appendix B (Continued) 84 83 2 100 0 84 28 84 83 1 100 0 84 28 84 83 2 200 0 84 28 84 83 1 200 0 84 28 84 83 2 300 0 84 28 84 83 1 300 0 84 28 84 83 2 400 0 84 28 84 83 1 400 0 84 28 83 82 2 1 0 83 28 83 82 1 1 0 83 28 83 82 2 100 0 83 28 83 82 1 100 0 83 28 83 82 2 200 0 83 28 83 82 1 200 0 83 28 83 82 2 300 0 83 28 83 82 1 300 0 83 28 83 82 2 400 0 83 28 83 82 1 400 0 83 28 82 81 2 1 0 82 28 82 81 1 1 0 82 28 82 81 2 100 0 82 28 82 81 1 100 0 82 28 82 81 2 200 0 82 28 82 81 1 200 0 82 28 82 81 2 300 0 82 28 82 81 1 300 0 82 28 82 81 2 400 0 82 28 82 81 1 400 0 82 28 81 80 2 1 0 28 81 80 1 1 0 28 81 80 2 100 0 28 81 80 1 100 0 28 81 80 2 200 0 28 81 80 1 200 0 28 81 80 2 300 0 28 81 80 1 300 0 28 81 80 2 400 0 28 81 80 1 400 0 28 81 80 2 500 0 28 81 80 1 500 0 28 81 80 2 600 0 28 81 80 1 600 0 28 81 80 2 700 0 28 81 80 1 700 0 28 113
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Appendix B (Continued) 81 80 2 800 0 28 81 80 1 800 0 28 81 80 2 900 0 28 81 80 1 900 0 28 81 80 21000 0 28 81 80 11000 0 28 81 80 21100 0 28 81 80 11100 0 28 81 80 21200 0 28 81 80 11200 0 28 81 80 21300 0 28 81 80 11300 0 28 81 80 21400 0 28 81 80 11400 0 28 81 80 21500 0 28 81 80 11500 0 28 81 80 21600 0 28 81 80 11600 0 28 81 80 21700 0 28 81 80 11700 0 28 81 80 21800 0 28 81 80 11800 0 28 81 80 21900 0 28 81 80 11900 0 28 93 94 2 1 0 93 28 93 94 1 1 0 93 28 93 94 2 100 0 93 28 93 94 1 100 0 93 28 93 94 2 200 0 93 28 93 94 1 200 0 93 28 93 94 2 300 0 93 28 93 94 1 300 0 93 28 93 94 2 400 0 93 28 93 94 1 400 0 93 28 93 94 2 500 0 93 28 93 94 1 500 0 93 28 93 94 2 600 0 93 28 93 94 1 600 0 93 28 93 94 2 700 0 93 28 93 94 1 700 0 93 28 93 94 2 800 0 93 28 93 94 1 800 0 93 28 93 94 2 900 0 93 28 93 94 1 900 0 93 28 114
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Appendix B (Continued) 93 94 21000 0 93 28 93 94 11000 0 93 28 93 94 21100 0 93 28 93 94 11100 0 93 28 93 94 21200 0 93 28 93 94 11200 0 93 28 93 94 21300 0 93 28 93 94 11300 0 93 28 93 94 21400 0 93 28 93 94 11400 0 93 28 93 94 21500 0 93 28 93 94 11500 0 93 28 93 94 21600 0 93 28 93 94 11600 0 93 28 93 94 21700 0 93 28 93 94 11700 0 93 28 93 94 21800 0 93 28 93 94 11800 0 93 28 93 94 21900 0 93 28 93 94 11900 0 93 28 93 94 22000 0 93 28 93 94 12000 0 93 28 93 94 22100 0 93 28 93 94 12100 0 93 28 93 94 22200 0 93 28 93 94 12200 0 93 28 93 94 22300 0 93 28 93 94 12300 0 93 28 93 94 22400 0 93 28 93 94 12400 0 93 28 93 94 22500 0 93 28 93 94 12500 0 93 28 93 94 22600 0 93 28 93 94 12600 0 93 28 93 94 22700 0 93 28 93 94 12700 0 93 28 93 94 22800 0 93 28 93 94 12800 0 93 28 93 94 22900 0 93 28 93 94 12900 0 93 28 93 94 23000 0 93 28 93 94 13000 0 93 28 93 94 23100 0 93 28 93 94 13100 0 93 28 115
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Appendix B (Continued) 93 94 23200 0 93 28 93 94 13200 0 93 28 93 94 23300 0 93 28 93 94 13300 0 93 28 93 94 23400 0 93 28 93 94 13400 0 93 28 93 94 23500 0 93 28 93 94 13500 0 93 28 93 94 23600 0 93 28 93 94 13600 0 93 28 93 94 23700 0 93 28 93 94 13700 0 93 28 93 94 23800 0 93 28 93 94 13800 0 93 28 93 94 23900 0 93 28 93 94 13900 0 93 28 93 94 24000 0 93 28 93 94 14000 0 93 28 93 94 24100 0 93 28 93 94 14100 0 93 28 93 94 24200 0 93 28 93 94 14200 0 93 28 93 94 24300 0 93 28 93 94 14300 0 93 28 93 94 24400 0 93 28 93 94 14400 0 93 28 93 94 24500 0 93 28 93 94 14500 0 93 28 93 94 24600 0 93 28 93 94 14600 0 93 28 93 94 24700 0 93 28 93 94 14700 0 93 28 93 94 24800 0 93 28 93 94 14800 0 93 28 93 94 24900 0 93 28 93 94 14900 0 93 28 92 93 2 1 0 92 28 92 93 1 1 0 92 28 92 93 2 100 0 92 28 92 93 1 100 0 92 28 92 93 2 200 0 92 28 92 93 1 200 0 92 28 92 93 2 300 0 92 28 92 93 1 300 0 92 28 116
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Appendix B (Continued) 92 93 2 400 0 92 28 92 93 1 400 0 92 28 92 93 2 500 0 92 28 92 93 1 500 0 92 28 92 93 2 600 0 92 28 92 93 1 600 0 92 28 92 93 2 700 0 92 28 92 93 1 700 0 92 28 92 93 2 800 0 92 28 92 93 1 800 0 92 28 92 93 2 900 0 92 28 92 93 1 900 0 92 28 92 93 21000 0 92 28 92 93 11000 0 92 28 92 93 21100 0 92 28 92 93 11100 0 92 28 92 93 21200 0 92 28 92 93 11200 0 92 28 92 93 21300 0 92 28 92 93 11300 0 92 28 92 93 21400 0 92 28 92 93 11400 0 92 28 92 93 21500 0 92 28 92 93 11500 0 92 28 92 93 21600 0 92 28 92 93 11600 0 92 28 92 93 21700 0 92 28 92 93 11700 0 92 28 92 93 21800 0 92 28 92 93 11800 0 92 28 92 93 21900 0 92 28 92 93 11900 0 92 28 92 93 22000 0 92 28 92 93 12000 0 92 28 92 93 22100 0 92 28 92 93 12100 0 92 28 92 93 22200 0 92 28 92 93 12200 0 92 28 92 93 22300 0 92 28 92 93 12300 0 92 28 92 93 22400 0 92 28 92 93 12400 0 92 28 92 93 22500 0 92 28 92 93 12500 0 92 28 117
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Appendix B (Continued) 92 93 22600 0 92 28 92 93 12600 0 92 28 92 93 22700 0 92 28 92 93 12700 0 92 28 92 93 22800 0 92 28 92 93 12800 0 92 28 92 93 22900 0 92 28 92 93 12900 0 92 28 92 93 23000 0 92 28 92 93 13000 0 92 28 92 93 23100 0 92 28 92 93 13100 0 92 28 92 93 23200 0 92 28 92 93 13200 0 92 28 92 93 23300 0 92 28 92 93 13300 0 92 28 92 93 23400 0 92 28 92 93 13400 0 92 28 92 93 23500 0 92 28 92 93 13500 0 92 28 92 93 23600 0 92 28 92 93 13600 0 92 28 92 93 23700 0 92 28 92 93 13700 0 92 28 92 93 23800 0 92 28 92 93 13800 0 92 28 92 93 23900 0 92 28 92 93 13900 0 92 28 92 93 24000 0 92 28 92 93 14000 0 92 28 92 93 24100 0 92 28 92 93 14100 0 92 28 92 93 24200 0 92 28 92 93 14200 0 92 28 92 93 24300 0 92 28 92 93 14300 0 92 28 92 93 24400 0 92 28 92 93 14400 0 92 28 92 93 24500 0 92 28 92 93 14500 0 92 28 92 93 24600 0 92 28 92 93 14600 0 92 28 92 93 24700 0 92 28 92 93 14700 0 92 28 118
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Appendix B (Continued) 92 93 24800 0 92 28 92 93 14800 0 92 28 92 93 24900 0 92 28 92 93 14900 0 92 28 91 92 2 1 0 91 28 91 92 1 1 0 91 28 91 92 2 100 0 91 28 91 92 1 100 0 91 28 91 92 2 200 0 91 28 91 92 1 200 0 91 28 91 92 2 300 0 91 28 91 92 1 300 0 91 28 91 92 2 400 0 91 28 91 92 1 400 0 91 28 91 92 2 500 0 91 28 91 92 1 500 0 91 28 91 92 2 600 0 91 28 91 92 1 600 0 91 28 91 92 2 700 0 91 28 91 92 1 700 0 91 28 91 92 2 800 0 91 28 91 92 1 800 0 91 28 91 92 2 900 0 91 28 91 92 1 900 0 91 28 91 92 21000 0 91 28 91 92 11000 0 91 28 91 92 21100 0 91 28 91 92 11100 0 91 28 91 92 21200 0 91 28 91 92 11200 0 91 28 91 92 21300 0 91 28 91 92 11300 0 91 28 91 92 21400 0 91 28 91 92 11400 0 91 28 91 92 21500 0 91 28 91 92 11500 0 91 28 91 92 21600 0 91 28 91 92 11600 0 91 28 91 92 21700 0 91 28 91 92 11700 0 91 28 91 92 21800 0 91 28 91 92 11800 0 91 28 91 92 21900 0 91 28 91 92 11900 0 91 28 119
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Appendix B (Continued) 91 92 22000 0 91 28 91 92 12000 0 91 28 91 92 22100 0 91 28 91 92 12100 0 91 28 91 92 22200 0 91 28 91 92 12200 0 91 28 91 92 22300 0 91 28 91 92 12300 0 91 28 91 92 22400 0 91 28 91 92 12400 0 91 28 91 92 22500 0 91 28 91 92 12500 0 91 28 91 92 22600 0 91 28 91 92 12600 0 91 28 91 92 22700 0 91 28 91 92 12700 0 91 28 91 92 22800 0 91 28 91 92 12800 0 91 28 91 92 22900 0 91 28 91 92 12900 0 91 28 91 92 23000 0 91 28 91 92 13000 0 91 28 91 92 23100 0 91 28 91 92 13100 0 91 28 91 92 23200 0 91 28 91 92 13200 0 91 28 91 92 23300 0 91 28 91 92 13300 0 91 28 91 92 23400 0 91 28 91 92 13400 0 91 28 91 92 23500 0 91 28 91 92 13500 0 91 28 91 92 23600 0 91 28 91 92 13600 0 91 28 91 92 23700 0 91 28 91 92 13700 0 91 28 91 92 23800 0 91 28 91 92 13800 0 91 28 91 92 23900 0 91 28 91 92 13900 0 91 28 91 92 24000 0 91 28 91 92 14000 0 91 28 91 92 24100 0 91 28 91 92 14100 0 91 28 120
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Appendix B (Continued) 91 92 24200 0 91 28 91 92 14200 0 91 28 91 92 24300 0 91 28 91 92 14300 0 91 28 91 92 24400 0 91 28 91 92 14400 0 91 28 91 92 24500 0 91 28 91 92 14500 0 91 28 91 92 24600 0 91 28 91 92 14600 0 91 28 91 92 24700 0 91 28 91 92 14700 0 91 28 91 92 24800 0 91 28 91 92 14800 0 91 28 91 92 24900 0 91 28 91 92 14900 0 91 28 90 91 2 1 0 90 28 90 91 1 1 0 90 28 90 91 2 100 0 90 28 90 91 1 100 0 90 28 90 91 2 200 0 90 28 90 91 1 200 0 90 28 90 91 2 300 0 90 28 90 91 1 300 0 90 28 90 91 2 400 0 90 28 90 91 1 400 0 90 28 90 91 2 500 0 90 28 90 91 1 500 0 90 28 90 91 2 600 0 90 28 90 91 1 600 0 90 28 90 91 2 700 0 90 28 90 91 1 700 0 90 28 90 91 2 800 0 90 28 90 91 1 800 0 90 28 90 91 2 900 0 90 28 90 91 1 900 0 90 28 90 91 21000 0 90 28 90 91 11000 0 90 28 90 91 21100 0 90 28 90 91 11100 0 90 28 90 91 21200 0 90 28 90 91 11200 0 90 28 90 91 21300 0 90 28 90 91 11300 0 90 28 121
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Appendix B (Continued) 90 91 21400 0 90 28 90 91 11400 0 90 28 90 91 21500 0 90 28 90 91 11500 0 90 28 90 91 21600 0 90 28 90 91 11600 0 90 28 90 91 21700 0 90 28 90 91 11700 0 90 28 90 91 21800 0 90 28 90 91 11800 0 90 28 90 91 21900 0 90 28 90 91 11900 0 90 28 90 91 22000 0 90 28 90 91 12000 0 90 28 90 91 22100 0 90 28 90 91 12100 0 90 28 90 91 22200 0 90 28 90 91 12200 0 90 28 90 91 22300 0 90 28 90 91 12300 0 90 28 90 91 22400 0 90 28 90 91 12400 0 90 28 90 91 22500 0 90 28 90 91 12500 0 90 28 90 91 22600 0 90 28 90 91 12600 0 90 28 90 91 22700 0 90 28 90 91 12700 0 90 28 90 91 22800 0 90 28 90 91 12800 0 90 28 90 91 22900 0 90 28 90 91 12900 0 90 28 90 91 23000 0 90 28 90 91 13000 0 90 28 90 91 23100 0 90 28 90 91 13100 0 90 28 90 91 23200 0 90 28 90 91 13200 0 90 28 90 91 23300 0 90 28 90 91 13300 0 90 28 90 91 23400 0 90 28 90 91 13400 0 90 28 90 91 23500 0 90 28 90 91 13500 0 90 28 122
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123 Appendix B (Continued) 90 91 23600 0 90 28 90 91 13600 0 90 28 90 91 23700 0 90 28 90 91 13700 0 90 28 90 91 23800 0 90 28 90 91 13800 0 90 28 90 91 23900 0 90 28 90 91 13900 0 90 28 81 80 2 0 2000 0 2000 001200 29 8001 900800 00 0 100 50 50 50 1 30 20 1 64 82838485869091929394 67 125 115 105 95 85 75 65 55 45 35 3 68 16 16 16 16 12 5 69 10 13 4 20 4 8 80 80 80 80 80 80 80 80 80 100 15 70 90 93 95 98 99 101 102 105 107 110 147 0 170 8001 0 0 195 8002 5846 0 195 50 5700 0 195 80 5500 0 195 81 5100 0 195 82 5000 0 195 83 4900 0 195 84 4800 0 195 85 4700 0 195 86 4600 0 195 90 200 0 195 91 1000 0 195 92 2000 0 195 93 3000 0 195 94 4000 0 195 1 0 0 210
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About the Author Zhenyu Wang received a Bachelors De gree in Electronic Engineering from Taiyuai University of Technology, Taiyuan, China in 1996 and a M.S. degree in Civil Engineering from ChangAn University in 1999. He continued to study for a Ph.D. degree in Transportation Systems of Civil Engi neering at the University of South Florida in 2003. While in the Ph.D. program at the Univ ersity of South Florida, Mr. Ye was very active in transportation research. He has comple ted several research projects and authored one journal publication.
