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PAGE 1 Effects of TwoWay LeftTurn Lane on Roadway Safety by Haolei Peng A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Jian John Lu, Ph.D. Ram Pendyala, Ph.D. Manjriker Gunaratne, Ph.D. Date of Approval: March 22, 2004 Keywords: average number of crashes, dist ribution, prediction m odel, access density, posted speed, ADT, number of lanes, critical section Copyright 2004 Haolei Peng PAGE 2 ACKNOWLEDGEMENTS It is of great pride that I had a chance to work with the brilliant minds affiliated to the Department of Civil and Environmental Engineer ing, University of South Florida. First, I would like to thank Dr. Jian John Lu for hi s continued support and able guidance in my research efforts. I would also like to thank Dr. Ram Pendyala and Dr. Manjriker Gunaratne for serving on my committee and provid ing their valuable suggestions. And I would like to acknowledge the Florida Depa rtment of Transportation for providing funding for the research. In part icular, I would like to thank Juan Pernia and Jingjing Fan for their help and suggestions throughout the research. Finally, I would like to dedicate my thesis effort to my parents Mr. Guoxiong Peng and Ms. Peifen Zhuo. PAGE 3 i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES v ABSTRACT viii CHAPTER 1: INTRODUCTION 1 1.1 Background 1 1.2 Research Statement 4 1.3 Research Purposes and Objectives 5 1.4 Outline of the Report 5 CHAPTER 2: LITERATURE REVIEW 7 2.1 Characteristics 7 2.2 Existing Guideline 8 2.3 Regression Model 9 CHAPTER 3: METHODOLOGY 11 3.1 Crash Frequency 11 3.2 Distributing Fitting 12 3.3 Chisquare Test 13 3.4 Crash Prediction Model 14 3.4.1 General 14 3.4.2 Poisson Model and Negative Binomial Model 15 3.4.3 Prediction Model Procedure 16 3.4.4 Evaluation of GoodnessofFit 17 CHAPTER 4: DATA COLLECTION 20 4.1 Analysis Time Period 20 4.2 Settingup the Crash Database 20 4.2.1 Extracting the Original Database 21 4.2.2 Sorting the Dataset 22 4.2.3 Converting the Crashbased Databa se to Sectionbase Database 24 4.3 Obtaining the Access Density 26 4.4 Database Summary 27 PAGE 4 ii CHAPTER 5: RESULTS FOR STATISTICAL MODELING 29 5.1 Crash Data Analysis 29 5.1.1 Crash Distribution for Average Number of Crashes 29 5.1.2 Distributing Fitting for Average Number of Crashes 30 5.2 Crash Predictive Model 35 5.2.1 Predictor Variables 35 5.2.2 Models for Average Number of Crashes 37 5.2.3 GoodnessofFit of Model 41 CHAPTER 6: APPLICATION OF STATISTICAL MODEL 43 6.1 Distribution Fitting 43 6.2 the 85th Percentile Value of Crashes 44 6.3 Estimation of the Critical Value 45 6.4 Identification of the Critical Sections 47 CHAPTER 7: SUMMARY AND CONCLUSIONS 49 7.1 Summary 49 7.2 Conclusions 50 REFERENCES 53 APPENDICES 55 Appendix A. Distribution Fitting for Six Categories 56 Appendix B. Critical ADT Value Corresponding to the 85th Percentile Value of Average Number for Six Categories 65 Appendix C. Critical ADT Value Corresponding to Selected Percentile Value for Six Categories 68 Appendix D. Identified Critical TWLTL Sections in Florida 74 PAGE 5 iii LIST OF TABLES Table 4.1 Description of Record Type 22 Table 4.2 Description of the Select ed Variables 23 Table 4.3 Variables Included in TW LTL Sections List from FDOT 26 Table 4.4 Sample Crash Database for Analysis 28 Table 5.1 Mean and Variance of Average Number of Crashes 30 Table 5.2 Chisquare Test for Poisson Distribution Fitted for Average Number of Crashes 31 Table 5.3 Chisquare Test for Negative Binomial Distribution Fitted for Average Number of Crashes 32 Table 5.4 Chisquare Test for Lognormal Di stribution Fitted for Average Number of Crashes 33 Table 5.5 Descriptive Statisti cs for the Variable ADT 36 Table 5.6 Descriptive Statistics for the Variable Access Density 36 Table 5.7 Descriptive Statistics for the Number of Lanes 36 Table 5.8 Descriptive Statistics for the Posted Speed 36 Table 5.9 Description of Categories for Analysis 37 Table 5.10 Estimated Parameters of the Negative Binomial Model 38 Table 5.11 Explanations of Contents of the Results 39 Table 5.12 Criteria for A ssessing the GoodnessofFit 42 Table 6.1 Chisquare Test for Po isson, Negative Binomial and Lognormal Distribution Fitting 44 PAGE 6 iv Table 6.2 85th Percentile Value for Average Crashes Distribution for Each Category 44 Table 6.3 85th Percentile Value for Average Crashes Distribution for Each Category after Linear Regression 45 Table 6.4 Results of Evaluation of ADT 46 Table 6.5 TWLTL Sections Identified as Critical for District 7 48 Table C.1 Critical ADT Values for Higher Speed and Twoway 2lane Sections 68 Table C.2 Critical ADT Values for Higher Speed and Twoway 4lane Sections 69 Table C.3 Critical ADT Values for Higher Speed and Twoway 6lane Sections 70 Table C.4 Critical ADT Values for Lower Speed and Twoway 2lane Sections 71 Table C.5 Critical ADT Values for Lower Speed and Twoway 4lane Sections 72 Table C.6 Critical ADT Values for Lower Speed and Twoway 6lane Sections 73 Table D.1 Critical TWLTL Sections for District 1 in Florida 74 Table D.2 Critical TWLTL Sections for District 2 in Florida 75 Table D.3 Critical TWLTL Sections for District 3 in Florida 77 Table D.4 Critical TWLTL Sections for District 4 in Florida 78 Table D.5 Critical TWLTL Sections for District 5 in Florida 79 Table D.6 Critical TWLTL Sections for District 6 in Florida 82 Table D.7 Critical TWLTL Sections for District 7 in Florida 83 PAGE 7 v LIST OF FIGURES Figure 1.1 Basic Concept of Twoway Leftturn Lane 1 Figure 1.2 Conflicts Occurring on TWLTL Roadways 3 Figure 5.1 Average Number of Crashes 29 Figure 5.2 Poisson Distribution of Average Number of Crashes 34 Figure 5.3 Negative Binomial Distributi on of Average Number of Crashes 35 Figure 5.4 Lognormal Distribution of Average Number of Crashes 35 Figure 5.5 The Model Curve of Higher Sp eed and Twoway 4lane Sections 40 Figure 6.1 The 85% Percentile Value of the Average Crashes for Higher Speed and Twoway 4lane Sections 45 Figure 6.2 Evaluation of ADT According to 85th Percentile Value 46 Figure A.1 Poisson Distribution Fitting for Higher Speed and Twoway 2lane Sections 56 Figure A.2 Negative Binomial Distribution Fitting for Higher Speed and Twoway 2lane Sections 56 Figure A.3 Lognormal Distribution Fitting for Higher Speed and Twoway 2lane Sections 57 Figure A.4 Poisson Distribution Fitting for Higher Speed and Twoway 4lane Sections 57 Figure A.5 Negative Binomial Distribution Fitting for Higher Speed and Twoway 4lane Sections 58 Figure A.6 Lognormal Distribution Fitting for Higher Speed and Twoway 4lane Sections 58 PAGE 8 vi Figure A.7 Poisson Distribution Fitting fo r Higher Speed and Twoway 6lane Sections 59 Figure A.8 Negative Binomial Distribution Fitting for Higher Speed and Twoway 6lane Sections 59 Figure A.9 Lognormal Distribution Fitting for Higher Speed and Twoway 6lane Sections 60 Figure A.10 Poisson Distribution Fitting for Lower Speed and Twoway 2lane Sections 60 Figure A.11 Negative Binomial Distribution F itting for Lower Speed and Twoway 2lane Sections 61 Figure A.12 Lognormal Distribution Fitting for Lower Speed and Twoway 2lane Sections 61 Figure A.13 Poisson Distribution Fitting for Lower Speed and Twoway 4lane Sections 62 Figure A.14 Negative Binomial Distribution F itting for Lower Speed and Twoway 4lane Sections 62 Figure A.15 Lognormal Distribution Fitting for Lower Speed and Twoway 4lane Sections 63 Figure A.16 Poisson Distribution Fitting for Lower Speed and Twoway 6lane Sections 63 Figure A.17 Negative Binomial Distribution F itting for Lower Speed and Twoway 6lane Sections 64 Figure A.18 Lognormal Distribution Fitting for Lower Speed and Twoway 6lane Sections 64 Figure B.1 Critical ADT Value for Higher Sp eed and Twoway 2lane Sections 65 Figure B.2 Critical ADT Value for Higher Speed and Twoway 4lane Sections 65 Figure B.3 Critical ADT Value for Higher Sp eed and Twoway 6lane Sections 66 Figure B.4 Critical ADT Value for Lower Sp eed and Twoway 2lane Sections 66 PAGE 9 vii Figure B.5 Critical ADT Value for Lower Sp eed and Twoway 4lane Sections 67 Figure B.6 Critical ADT Value for Lower Sp eed and Twoway 6lane Sections 67 PAGE 10 viii EFFECTS OF TWOWAY LEFTTURN LANE ON ROADWAY SAFETY Haolei Peng ABSTRACT Twoway leftturn lane (TWLTL) is one of the common median treatments on the roadway. It is found that a number of crashes reported in Florida State are related to TWLTLs. This research focused on evaluating the effect of TWLTLs on these crashes by using the statistical crash prediction model th at can estimate the expected number of crashes on TWLTLs. The crash database for an alysis was extracted from the Florida Traffic Crash Database based on the TW LTL section list provided by FDOT and combined with some traffic characteristics. It consisted of totally 1688 sample sections within a threeyear period from 1996 to 1998. Based on the crash database, distribut ion fittings for Poisson, Negative Binomial and Lognormal regression were conducted for averag e number of crashes. According to the results, statistical crash predictive model was developed to estimate the average number of crashes. Negative Binomial regression wa s applied with four variables, ADT, access density, posted speed and number of lane s for the TWLTL sections. The regression parameters were estimated by using maximum likelihood method with st atistical software. The findings of the analysis indicated that a ll of the variables adopt ed in the predictive model significantly affect the occurrence of cr ashes. And the average number of crashes increases with the increase of ADT, access dens ity and number of lanes, while with the PAGE 11 ix decrease of posted speed. After that, th e goodnessoffit of developed model was performed in term of Pearsons Rsquare and likelihood ratio inde x. The results showed that the Negative Binomial regression model could explain the relationship between the variables and the crash occurrence In the third part, an approach was developed to identify the TWLTL sections with safety concern. For an undivided roadway, the ap proach can be carried out to judge if the TWLTL is appropriate to be selected as th e median treatment. During the process, the whole database was divided into six categor ies according to the posted speed and number of lanes. By adopting the selected percenti le value from the distribution of average number of crashes for each category in the predictive model, the critical ADT values according to specific access density, number of lane and posted speed level for each category were calculated and tabulated. W ith the comparison of the actual ADT value and the critical ADT value, if the actual ADT is higher than the critical value, the TWLTL section is determined as the critical section, which means the TWLTL is not appropriate to be selected as the medi an treatment in this roadway section. PAGE 12 1CHAPTER 1 INTRODUCTION 1.1 Background A twoway leftturn lane (TWLTL) is a lane in the center of a road that is designed for left turn movements by both direc tions of traffic. It is commonly used as the median treatment on roadways. Figure 1.1 showed the basic concept of TWLTL. By decreasing the conflicts between throughand midblock leftturn traffic, TWLTL is considered to solve the safety and operational problems on roadways. Figure 1.1 Basic Concept of Twoway Leftturn Lane PAGE 13 2 From the 1950s through the 1970s, many arterial and collector roads and streets were constructed with either two lanes or four lanes and no turn lanes or medians. Since all lanes served both through traffic and turning traffic, the accident rate caused by the conflicts between through and leftturning vehicles grew. When those roads with unmanaged development and access experience a considerable amount of turning traffic, congestion delays and crashes increase. Types of crashes most associated with turning vehicles include rearend and leftturn collisions. Considering that TWLTLs separate leftturning traffic from through traffic, they can help solve some of these problems. But the operation of a TWLTL also allows vehicles to make some other conflicting movements (See Figure 1.2). The conflicts involve 1) motorists trying to cross the arterial from a driveway to a driveway or street to street; 2) making a left turn off the arterial to a driveway or side street; 3) using the leftturn lane to pass stopped vehicles in the main thru lanes; 4) allowing uncontrolled Uturns across two thru lanes; 5) making a left turn from a side street or driveway onto the arterial; 6) accelerating in TWLTL to merge right; and 7) headon accidents in the TWLTL. [7] All of these conflicts are potential traffic accidents. These conflicts would be highlighted by the very high traffic volumes on the roadway. Previous studies have indicated that TWLTLs should generally not be used in situations where the through traffic vol ume is substantial. When the ADT on a street is very high, a TWLTL road may start to become ineffective. The main reason is that if a leftturning vehicle might not be able enter the TWLTL as soon as PAGE 14 3possible, it might decelerate or even stop in the inside through lane, creating delay to through traffic and a loss of capacity and efficiency. Heavy volumes on multiple through lanes may prevent a leftturning vehicle from finding a safe, acceptable gap for an extended period of time. If more leftturning vehicles queue up behind the first, its driver may feel under pressure to acce pt an unsafe gap. So if the number of movements made in a TWLTL becomes too large, there will be a resultant increase in accidents or near accidents. Figure 1.2 Conflicts Occurring on TWLTL Roadways Many traffic engineering and highway designers have been concerned about whether or not TWLTLs are appropriate under certain conditions. Some of the states had some kind of guidelines for the selecting TWLTLs as the median treatment. But PAGE 15 4using data from deferent source will get deferent results. The models and procedures of the existing state of art are not applicable to all cases and locations. So this analysis was carried out by using the crash database of the state of Florida. 1.2 Research Statement From above, its concluded that the volume of the roadway is a very significant factor that should be taken into consideration in the decision. The book A Policy on Geometric Design of Highways and Streets, published by the American Association of State Highway and Transportation Officials (AASHTO), makes a few specific comments about the use of a TWLTL, which includes: [TWLTL] works well where the speed on the arterial highway is relatively low and there are no heavy concentrations of leftturn traffic, and [TWLTL] should be used only in an urban setting where there are no more than two through lanes in each direction. In a report prepared for the Federal Highway Administration (FHWA), Azzeh et al, presented the results of a comparative analysis on the safety aspects of a raised median and TWLTL. The authors found that when driveway density was high, a raised median was safer than a TWLTL. In this research, three factors, traffic volume, access density and post speed, were used in the analysis. And some other related factors, such as number of lanes, were also considered. And mathematical methodology was applied to develop the models to estimating accidents for roads with a TWLTL. From the model, the critical traffic volume was calculated responding to selected critical percentile value of the PAGE 16 5crash distribution. Compared with the actual road characteristics, recommendations of appropriate use of TWLTL median treatment were addressed. Detailed studies will be stated in the following chapters. 1.3 Research Purposes and Objectives The primary purpose of this rese arch was to analyze the factors that are influential in the safety experience of TWLTLs and develop recommendations concerning when TWLTLs may be appropriate based on these factors. The specific objectives of the study were: 1) To review the available literature and other projects in relation with the factors that were to be evaluated and analyzed; 2) To obtain the information of the related factors from the Florida Department of Transportation; 3) To conduct a detailed crash data analys is related to concerns to verify the influence of the factors on crash occurrence; 4) To develop mathematical models to identify various factors that are influential in selecting TWLTL as the median treatment; 5) To apply the approach to identify the TWLTL sections which have safety concerns; 6) To write a final report. PAGE 17 61.4 Outline of the Report This report on the crash data analysis of TWLTLs consists of seven chapters. Chapter 1 provides an overview of the research project with some backgrounds in this subject area. Chapter 2 describes the brief summary of the previous studies done in selecting TWLTLs as the median treatment. Chapter 3 explains the methodology employed in achieving the previously mentioned objectives. Chapter 4 presents the data performing process, which was obtained from the FDOT Crash Database and other data resource. Analysis results and findings of the study are given in Chapter 5, it consisted of statistical analysis and prediction modeling. Chapter 6 introduced the procedure of the identification of critical TWLTL sections and advanced practical recommendation for the existed TWLTL treatment. The final chapter Chapter 7 provides the summary and conclusion of this study. PAGE 18 7CHAPTER 2 LITERATURE REVIEW 2.1 Characteristics Towway leftturn lane and raised median are two common median treatments on the roadway. Most business sector and the motoring public prefer the TWLTL to raisedmedian designs. In 1978, a research of TWLTLs by Ohio State University listed the general characteristics of TWLTLs. Advantages of TWLTL over Raised Medians: 1) Removal of leftturning vehicles from through traffic while still providing maximum leftturning access; 2) Reduction of delay to leftturning vehicles; 3) Direct access to adjoining property; 4) Flexibility in roadway use, as for a detour lane, a path for emergency vehicles, refuge for disabled vehicles. However, there are also some disadvantages of TWLTL compared with Raised Medians: 1) No refuge area for pedestrians crossing wide arterial; 2) Unsafe operation where sight distance is inadequate (such as where a TWLTL goes over a steep hill); PAGE 19 83) Visibility problem of painted median (on rainy nights); 4) More traffic conflict points, especially at driveways; 5) Possible misuse as a passing lane or even a travel lane; 6) Burden of instructing public in proper use. Some motorists do not know that the solid yellow line prohibits passing. Harwood and St. John also list so me characteristics and appropriate use of raised medians and TWLTLs. They found TWLTLs decrease travel time for drivers who wish to turn left and reduce deay to leftturning vehicles comparing with where median openings are not provided. They also reduce operational flexibility, such as allowing for emergency vehicle operation, lane closures, and work zones. 2.2 Existing Guideline In the past decade, there have been many studies regarding median treatment selection. They focused on operational a nd safety effects of TWLTLs and other median treatment. And they addressed the situation where the median types could be appropriately used. Parkers research, 1983, was based on a fourlane road. It presented a series of expected value tables, which indicated that in a ADT range from 10,000 to 30,000, when the driveways per mile is lower than 30 and the streets per mile is lower than 5, the number of accident per mile of TWLTL is relatively lower. FHWA conducted a study of the accidentrate of TWLTLs and raised medians for a fourlane highway. They measured the accident rate reduction of these two median types from a previously undivided roadway. The study was carried out in PAGE 20 9three ADT levels, less than 5,000,5,000to 15,000 and more than 15,000 vehicles per day. From the comparison of the results, for all ADT ranges, TWLTLs were expected to be safer in the areas with several concentrated sources of traffic and fewer than 60 commercial lowvolume driveways per mile. And for the areas with no highvolume driveways and a large number of lowvolume driveways, raised medians are safer. The report also gave some comments about each median treatment. They found A TWLTL should be used when there were frequent rearend conflicts caused by leftturning vehicles and on moderate to high volume highways that have few cross streets and many driveways. However the book, A Policy on Geometric Design of Highways and Street, does not present a comparative analysis of medians and TWLTLs. It made a few specific comments about the use of a TWLTL, which said TWLTL works well where the speed on the arterial highway is relatively low (25 miles per hour to 45 miles per hour) and there is no large amount of the movements of leftturn traffic. And TWLTL should be used only in an urban area where there are no more than two through lanes in each direction. 2.3 Regression Model Previous researches developed statistic models to predict the expect accident frequency for a roadway. These models have some typical independent variables, such as traffic volume, driveway density, number of arterial traffic lanes, signalized intersection density and unsignalized appr oach density. Finally, regression model equations were produced for the accident occurrence of different median types. PAGE 21 10There are some studies comparing the alternative median treatments and presenting the procedures for estimating accidents for roads. Parker used data collected in Virginia to develop the equation, which is as follows: Accidents/Mile/Year for Traversable Median (mostly TWLTL) = 5.432 Signal/Mile + 0.00173 ADT +2.157 Street/Mile + 0.0000058 Population 28.797 Squires and Parsonson got the equation with the data in Georgia. Their equation for accidents are as follows: Accidents/Mile/Year for TWLTL = 0.0038777 ADT +22.68622 Signal/Mile 8.85380 Approaches/Mile 21.86862 In the existing accident prediction models, it is found that all models predict an increase in accident frequency with increasing daily traffic demand. Bonneson and McCoy used the models to identify common trends related to median type. They used a large number of independent variables in each model. The combination of variables was established an d used to calculate the accident frequency predicted by each model given a range of daily traffic demand. PAGE 22 11CHAPTER 3 METHODOLOGY 3.1 Crash Frequency Crash frequency was calculated in this study. Crash frequency is the actual number of reported crashes that has occurred at a certain location, which could either be a roadway section or an intersection. The number of crashes at each of the sections with TWLTLs considered in the study was obtained by using the Florida Traffic Crash Database. The primary virtues of using cras h frequency are that it is simple and it makes intuitive sense. By ranking the number of reported crashes, safety analysis can identify crashprone locations. The dist ribution curve of crash frequency could provide a basic concept of the TWLTLs and the results are easily understood by the general public. The average number of crashes, which is the arithmetic mean of number of crashes, was calculated for each TWLTL section. In statistical inference, the mean is generally the most efficient estimator of the central tendency of the population characteristics being studied. The average nu mber of crashes for section i is defined as: L Y n Ni i PAGE 23 12Where, Ni = average number of crashes for section i, ni = number of crashes at section i, Y = the number of years when ni crashes occurred, L = the length of section i (mile). 3.2 Distribution Fitting The average number of crashes was calculated for each section with the use of SPSS. Details of this procedure to obtain da ta will be explained in the next chapter. The estimated values are then plotted into histograms, where the independent variable (xaxis) is the average number of crashes for each section and the dependent variable (yaxis) is the number of sections. Poisson, Negative Binomial and Lognormal distribution are used to fit the frequency of crash data for higher and lower speed sections using the observed mean and variance. Subsequently, the Chisquare goodnessoffit test was used to test the hypothesis whether the average number of crashes follows a particular probability distribution. The following presents a brief introduction to Poisson, Negative Binomial and Lognormal distribution. The definition of Poisson distribution is: if the mean number of counts ( ) in the interval is greater than zero ( the random variable X that equals the number of counts in the interval has a Poisson distribution with parameter and the probability mass function of X is PAGE 24 13 ) ( x e x fx Where, observed mean value of the crash frequency In regard to the negative binomial distribution, the probability function of X is: r x rp p r x x f ) 1 ( 1 1 ) ( Where, r, p two parameters calculated from observed mean and variance. The mean and variance of this distribution of crash counts can be expressed in terms of parameter p and r as follows: Mean=p r x E / ) ( Variance=2/ ) 1 ( ) ( p p r Y Var The Lognormal distribution is the continuous probability distribution of a random variable whose logarithm follows the normal distribution. The random variable x has the range space of Rx={x:0 PAGE 25 143.3 ChiSquare Test The Chisquare goodnessof fit test is used to test the hypothesis whether the average number of crashes follows a particular probability distribution. The test procedure requires a set of randomly chosen samples of size n from X, whose probability density function is unknown. These n observations are then plotted into a frequency histogram of k class interviews. Oi represents the observed frequency in the ith class interval. The expected frequency in the ith class interval denoted Ei could be calculated from the hypothesized probability distribution. The test statistic is, )] /( ) [(2 2 i i iE E O SUM Where, Oi observed frequency in the class interval i. Ei expected frequency in the class interval i. It can be shown that, if the population follows the hypothesized distribution, 0 2 has, approximately a Chisquare distribution with kp1 degrees of freedom, where p represents the number of parameters of the hypothesized distribution estimated by sample statistics. This appr oximation improves as n increases. If the calculated value of the test statistic 0 2> a,kp1 2, the hypothesis that the distribution of the population is the hypothesized distribution would be rejected. a=0.05. PAGE 26 153.4 Crash Prediction Models 3.4.1 General Developing crash prediction models is a means of summarizing the complicated interactive effect of these crash related factors on the basis of information contained in the data, as well as engineering judgment (e.g. the selection of independent variables), and analytical assumptions about the crash process (e.g. which probability law will be relatively appropriate to apply to the crash study). This approach relates safety to site characteristics. The models use crash frequency as the dependent variable together with various s ite characteristics for a large number of sites over an extended period of time. Th e modeling approach finds a relationship between crash frequency, traffic characterist ics (such as volume and speed), and road geometry (such as segment length and la ne width). A crash prediction model with good quality should estimate the occurrence of crash accurately at a specific statistical confidence level; meanwhile, the model shall make good engineering sense. Many types of statistical regression mo dels have been used to develop crash prediction models in the past 30 years. Tw o general types of regression models have been considered to apply to the crash da ta: (1) conventional linear regression model; and (2) generalized linear model, negative binomial regression models. 3.4.2 Poisson Model and Negative Binomial Model Conventional regression models are proved to be inappropriate to model the traffic crash data, which are nonnegative, ra ndom, discrete and sporadic in nature. PAGE 27 16As alternatives, generalized linear models were explored and adopted in recent crash studies due to their advantages over c onventional linear regression models. The regression models adopted in this study are based on observed crash frequency distributions. Based on crash frequency di stributions and previous studies, Poisson regression and Negative Binomial regressi on were chosen to estimate the model parameters. Both in the two regressions, th e regression parameters were estimated by maximum likelihood method. Generally, Poisson regressions can be us ed to build the relationships between crash frequencies and a set of predictor variables under assumptions that crash frequencies are Poisson distributed. However, the inability of the Poisson model to handle overdispersed data is a major concern with regard to studying crash frequencies. This inability is caused by th e major limitation of the Poisson regression model, which requires the variance of the data to be equal to the mean. The variance of most crash count data will be significantly greater than the mean, so the crash data are likely to be overdispersed. When the mean and the variance of the data are not approximately equal, the variances of the estimated Poisson model coefficients tend to be understand and the coefficients themselves are biased. The Negative Binomial regression model is an extension of Poiss on regression model. This restraint can be overcome by Negative Binomial regressions which assume crash frequencies are negative binomial distributed. PAGE 28 173.4.3 Prediction Modeling Procedure The crash modeling consists of seven major tasks: (1) to obtain and process the crash data; (2) to determine the safety measures that were adopted as dependent variables in the modeling, and find appropria te probability functions to describe the random variation of crash frequencies; (3 ) to select and analyze the predictor variables; (4) to determine an appropria te functional form and parameterization, f(., ), to describe the effects of predictor variables on expected crash frequencies; (5) to estimate the regression parameter in f(., ) using appropriate statistical algorithm based on crash data and probability assumptions; (6) to assess the quality of developed models, and make sure that the models make good engineering sense in addition to fulfilling statistical goodnes soffit criteria; and (7) to apply the developed models, and convert the modeling results to tables for use. The tasks are briefly presented in the following paragraphs. The modeling database was created from the Florida crash database maintained by FDOT, which consists of a ll crashes occurred on state roadways for a certain period of time. The TWLTL secti ons included in the modeling database contained safety related characteristic s and crash counts occurred within the influence area of those TWLTLs. The process of generating the modeling database will be presented in detail later. Another important issue was to determine which TWLTL section characteristics should be used as predictor variables in the model. The principle to select the predictor variables was to include the factors that have distribution to the PAGE 29 18roadway safety. Totally four characteristics including ADT on the roadway, access density on the roadway, posted speed on the roadway and number of lanes on the roadway. The predictor variables used in the model were easy to obtain by FDOT traffic engineers when applying the models. Once each variable parameters of crash predictive model were estimated, the average number of crashes can be estimated by replacing the regression parameter, 0, 1, 2, , q, with the estimated values, and the variables Xi1, Xi2, , Xiq, with the corresponding values of the section ch aracteristics. If a predictor variable is insignificant and was excluded from the final model, the variable would be omitted in the linear equation. However, the estimated average number of crashes will only provide a statistic of the safety measure either for an infinite number of sections with the same characteristics or a section in an infinite time period with every characteristic unchanged. 3.4.4 Evaluation of Goodnessoffit So far there is no commonly acceptable measure that can give an absolute assessment of goodnessoffit for generali zed linear models. Therefore, several measures are selected and calculated, and jointly will give a relatively accurate evaluation of the models. First, deviance is defined as minus twice the logarithm of the ratio of the maximum likelihood under current model and the maximum likelihood under saturated model. Thus, deviance describes lack of fit, greater deviance indicates poorer fit. Secondly, the Pearsons chisquare is asymptotic to the chisquare distribution with np1 degrees of freedom for large sample sizes and PAGE 30 19exact for normally distributed error struct ures. Therefore, for a model, similar to deviance, the greater the Pearsons chisquare, the poorer the fit. In traditional least square regression, the coefficient of determination, R2, is frequently used to assess the goodnessoffit of a model. It represents the proportion of variation in the data that is explained by the model. However, it was shown that R2 is not an appropriate measure to asse ss the goodnessoffit of crash prediction models due to their nonnormal and nonlinear nature. As a variation, a measure based on the standardized residuals, Pearsons R2, can be calculated for each model to give some indication of the goodnessoffit. n i i n i i i i py y y y R1 2 1 2 2) ( ) ( 1 Where, 2pR Pearsons Rsquare statistic; iy observed number of crash at ith section during a time period; i estimated average number of crashes during a time period; y average crash counts at all sections of interest. In addition, as the counterpart of R2 in nonlinear regression, a measure of overall statistical fit, the likelihood ratio index can be computed as, ) 0 ( ) ( 12L L PAGE 31 20Where, ) ( L Loglikelihood at convergence; ) 0 (L restricted loglikelihood (all parameters are se t to zero except for the intercept). The value of 0.200 is quite satisfactory considering the variance in the data, and values tend to be generally lower than typical R2 values. PAGE 32 21CHAPTER 4 DATA COLLECTION The purpose of the chapter is to describe the process of the data collection effort in this research. This chapter address the time period, the FDOT crash database, system for identify the roadway sections, the procedures for gathering relevant crash data and creating a specific crash database for the research. 4.1 Analysis Time Period In this study, crash data of three consecutive years, from 1996 through 1998, were used for the analysis process. It is commonly believed that three years will usually provide a sufficient number of crashes for analysis while reducing the possibility of extraneous factors influencing the crash data. Changes that have occurred at the site during the analysis period can result in changes to the crash characteristics. These include changes in the surrounding land use in addition to changes at the site itself. These changes have a higher probability of occurring, as the analysis period becomes longer. A time frame of three years is the most common choice as it is a good tradeoff between the desire for larger samples and the desire that conditions have not changed much within the time frame. PAGE 33 224.2 Settingup of the Crash Database This section provides the genera l information about the creation of the crash database for the purpose of this project. The data set creation was conducted using the Florida Traffic Crash database, which was obtained from the State Data Program of the National Highway Traffic Safety Administration established under the U.S. Department of Transportation. (NHTSA, 1998). 4.2.1 Extracting the Original Database The crash data of a 3year period from 1996 to 1998 was used in this study. Corresponding to each year, there is one data file consisting of all crashes occurred on state roads during that year. For each crash, several record types containing specific information related to the crash are included. Table 4.1 lists the different record types for each crash. All files, stor ed in ASCII format, have the same database structure. A SAS (Statistical Analysis System) program was written and used in order to change the ASCII format to SAS format. SAS program uses Structured Query Language (SQL) to gather all of crash data needed for the files. First of all, based on the possible contribution to crash occurrence, 168 variables were selected for the original database for the research. These variables were selected from five of the twelve record types, which included the factors that were considered having effect on the safety of TWLTLs. The record types selected were record 00 (Time a nd Location), record 01 (Characteristics), 09 (RCIFeaturesI), record 10 (RCIFeature sII), and record 11 (RCIPoint). In PAGE 34 23order to put the 168 variables in one file, these files with record type 00, 01, 09, 10 and 11 were merged into one merged file for each year. As explained above, only the data of three consecutive years, from 1996 to 1998, were used for the further analysis. Table 4.1 Description of Record Type Record TypeDescription 00 Time and location 01 Characteristics 02 Vehicle 03 Towed 04 Driver 05 Passenger 06 Pedestrian 07 Property Damage Amount 08 Reserved for future use 09 RCIFeaturesI 10 RCIFeaturesII 11 RCIPoint 12 RCITotal 4.2.2 Sorting the Data Set A statistical package software pr ogram SPSS was used to handle the large data sets.. SPSS and SAS are the two most popular statistical programs in the social sciences, but SPSS is much easier to use. Wi th SPSS software, the data files of three years were merged into one file. Each data record consists of a number of variables. In order to make the database smaller and easier to manipulate, it is necessary to PAGE 35 24select some variables that are useful for the study. Table 4.2 addresses the description of the selected variables. As the safetyrelated characteristics, the variables, Average Daily Traffic (ADT), posted speed (POSTSPED), and number of lanes (NUMBLANE), were would be medaled in further analysis. Table 4.2 Description of the Selected Variables Variable Name Description DISTID District ID COUNTYID County ID SECID Section ID SUBSECID Subsection ID MILEPOST Milepost ADT Average Daily Traffic POSTSPED Posted Speed on the roadway NUMBLANE Number of lanes considering both sides of the roadway ACCNUMB Accident number SITELOC Site location Additionally, some other variables, district ID (DISTID), county ID (COUNTYID), section ID (SECID), subsection ID (SUBSECID), milepost (MILEPOST), accident number (ACCNUMB) and site location (SITELOC) were also remained. The first five variables, district ID, county ID, section ID, subsection ID, milepost were used to identify the sections related to TWLTLs, which was described next. In FDOT database, a certain accident number corresponds to one crash record. If there are more than one vehicle involved in the crash, some characteristics variables, such as vehicle movement, may have several different values. Thus in the PAGE 36 25crash database, there can be several crash records indicating just he same accident because of different values of some vari ables. Therefore, in order to avoid the analysis bias of the crash counts, duplicate crashes were taken out from the data set according to the accident number. Based on the variable of site location, it could be judged if the crashes in the section were related to TWLTLs. Some accident locations are found very close to an intersection, it is possible that the accident is not influenced by the TWLTLs but by the nearest intersection, like the conflicts caused by impropriate signal circle The code 02 and 03 of the site location i ndicate at intersection and influenced by intersection. So with the criteria, the records with these two codes of site location were taken out of the data set. Then the database is prepared for the further analysis. 4.2.3 Converting the Crashbased Da tabase to Sectionbased Database After the database based on crashes was all set, the next step is to convert it to sectionbased database. In the secti onbased modeling database, a record should correspond to a section. The procedure to obtain the sectionbased database involved the selection of three types of variables for a threeyear period for each TWLTL section. Three types of variables were included in the modeling database, (1) TWLTL section ID, (2) section characteristics variables, and (3) crash counts variables. FDOT provided a list of 3535 sections with TWLTLs in the 7 districts of Florida State. Each section was identified by roadway ID, begin milepost and end milepost. The roadway ID is an eightdigi t code consisting of county number, section PAGE 37 26number, and a subsection number. The first two digits correspond to the county number; the next three numbers are the actual section number of the roadway. And the last three numbers are known as the s ubsection number. The breakpoints of the TWLTL on a roadway are indicated by mileposts (begin/end milepost). The mileposts are used to describe the interacting points of TWLTL on the roadway. Each crash has its own milepost of location. T hose crashes, of which the mileposts were within one of the ranges of begin milepost and end milepost on the list, were grouped in one section record. The secti ons studied in this research were summarized based on the element, District ID, County ID, section ID subsection ID, begin milepost and end milepost of the list sent by FDOT. The list is an EXEL file that includes all the TWLTL sections found in Florida State. Table 4.3 gives the variables included in the section list. If the TWLTL section obtained from the original crash database was not found in the list, these sections were taken out considering that the median treatment was changed in the time period. Crash data for a section in three years could be zero, one of more crashes. This possibility of having different average number of crashes also means that it could be zero, one or more crash records re lated to this section in the sectionbased database. During data manipulation, the average number of crashes of each section was easily to determine by summing up the crash counts for one TWLTL section. But one problem encountered was that if there were more than one crash in the section, inconsistency of the data among the crash records could be possible. It was important to calculate or select a value for each variable. For the number of lanes, all PAGE 38 27records had the same value. So that value would be taken for the variable in this section. For posted speed the values are different, the value that appeared most frequently for a variable was chosen to present that variable in the section. For ADT, it could be as many values as the number of crash record. Average ADT was calculated by averaging the ADT values of all the crashes in the section. If there was zero crash or no crash in the section, the average number of crashes was recorded as 0. While the values of all the variables were missing. The values of number of lanes and posted sp eed were obtained from the TWLTL section list mentioned above, which include the variables of ADT, Posted speed and number of lanes. Table 4.3 shows the variables listed in the TWLTL section list. Meanwhile, with this information, these two variables obtained during the previous procedure could be double checked to make sure the variables of the database and the spreadsheet were compatible. If there were difference between them, the values from the TWLTL section list by FDOT were used, which were more reliable. The missing ADT were obtained from a computer disk of Florida Traffic Information prepared by FDOT. The FTI system contains the main characteristics information including ADT. The program was easy to operate. After inputting the district number and the eightdigit road ID, the road was highlighted on a map of that area. Clicking any point of the road, the ADT of that section was shown on the screen. Thus ADT of the zero crash section were obtained by using of the system. Finally, the dataset of zero crash section was combined with the previous dataset. The final database consisted of reliable information which is required for analysis. PAGE 39 28Table 4.3 Variables Included in TWLTL Section List from FDOT Variables District Roadway ID Begin Point End Point Net Length (miles) Local Name Median Type Median Width Speed Limit Left & Right Number of Lanes Left & Right Width of Lanes Right Number of Lanes Right Width of Lanes Left Number of Lanes Left Width of Lanes 4.3 Obtaining the Access Density As present in Chapter 2, the access density is also a significant factor that should be considered in the analysis. But this variable was unavailable in the FDOT Crash Database. Obtaining the information of access was the most timeconsuming part of this research. FDOT provided a hard drive containing review software and a large amount of images reflecting the roadways in Florida State. These images were recorded by video camera and saved as *.jpg format files. When the road ID, begin milepost and end milepost were input, the images would keep going when click the play button. While reviewing the video record according to the TWLTL section list obtained above, the number of driveways along the roadway with TWLTLs was counted and recorded. The same method was applied on the opposite direction of the movement of the images. After that, the two numbers were added up as the number PAGE 40 29of the driveways in this section. Then th e access density was calculated as following: Access Density = number of driveways (i n both directions)/ length of section During the procedure, it was found some sections dont have TWLTLs, probably due to the change of the conditions of the roadways after that time period. Thus these sections were taken out of the database. Finally, 1688 sections with access density were available. Combining the data set of access density with the database extracted from the original database, the specific sectionbased database for this research was completed with all the information required. 4.4 Database Summary Once the steps choosing time frames for crash analysis, identifying sections related crashes, selecting variables for the database, and gathering the missing information were completed, the database was set up to perform the statistical analysis for the further analysis. Figure 4.1 shows part of the sample database that includes all the variables for developing the crash occurrence predictive model. Table 4.4 Sample Crash Database for Analysis Road ID Begin Milepost End Milepost Section Length Access Density ADT Posted speed Number of lanes Average Number of Crashes 101050000 6.448 6.980 .53 3.76 11200.00 55 2 1.00 101050000 7.727 9.096 1.37 6.57 10500.00 55 2 .00 101050000 9.096 9.515 .42 14.32 16004.00 50 2 1.00 101050000 12.799 13.347 .55 3.65 16004.00 45 2 1.00 101060000 9.244 10.311 1.07 54.36 20172.73 45 4 7.00 103001000 6.101 6.267 .17 6.02 21500.00 45 2 .00 103010000 21.798 22.067 .27 3.72 4600.00 60 2 .00 103010000 28.256 28.755 .50 2.00 4100.00 60 2 .00 PAGE 41 30Table 4.4 Sample Crash Data base for Analysis (Cont) 103030001 16.470 16.704 .23 4.27 42000.00 45 4 .00 103080000 35.064 35.679 .62 3.25 7800.00 45 2 .00 103080000 37.856 38.888 1.03 34.88 13200.00 45 2 4.00 103080000 38.888 39.761 .87 29.78 8240.00 45 2 2.00 104020000 2.065 2.257 .19 10.42 4900.00 60 2 .00 104020000 13.693 13.775 .08 85.37 12700.00 35 2 8.00 104020000 13.775 14.315 .54 83.33 11500.00 35 2 1.00 104040000 15.018 15.469 .45 4.43 7500.00 45 2 .00 105020000 13.180 13.402 .22 9.01 4200.00 50 2 .00 105090000 .000 .364 .36 5.49 4800.00 50 2 .00 106010000 13.221 13.831 .61 47.54 12488.89 45 2 5.00 106010000 14.992 15.231 .24 87.87 16600.00 45 4 .00 106010000 15.231 15.556 .32 43.08 17500.00 55 4 2.00 106030000 11.973 12.338 .36 5.48 6100.00 60 2 .00 107010000 7.790 8.260 .47 10.64 9950.00 45 4 1.00 107010000 8.260 8.608 .35 8.62 11950.00 45 4 2.00 107010000 8.608 8.710 .10 78.43 11500.00 40 4 3.00 107010000 8.734 9.279 .55 89.91 11940.00 35 4 3.00 107010000 9.514 9.630 .12 34.48 11800.00 35 4 .00 107010000 9.630 10.000 .37 37.84 11800.00 45 4 .00 107010000 10.000 10.071 .07 28.17 9300.00 50 4 .00 107010000 10.071 10.181 .11 27.27 9300.00 50 2 .00 107010000 12.251 12.574 .32 6.19 9300.00 60 2 .00 107010000 14.270 14.522 .25 7.94 9300.00 60 2 .00 107010000 18.228 18.470 .24 8.26 6000.00 60 2 .00 107030000 2.280 2.345 .07 61.54 20000.00 50 4 5.00 107030000 2.345 3.518 1.17 84.40 17040.00 35 4 3.00 107060000 15.922 16.716 .79 61.71 6880.00 45 2 2.00 107060000 16.716 16.944 .23 78.95 6700.00 35 2 6.00 107060000 17.008 17.486 .48 69.04 10530.00 35 2 7.00 107060000 18.397 18.498 .10 19.80 14900.00 50 2 .00 109030001 .396 .722 .33 70.55 13600.00 35 2 3.00 109030001 .722 1.058 .34 29.76 13000.00 35 2 4.00 109040000 .877 1.049 .17 23.26 10300.00 30 2 .00 109040000 3.408 3.769 .36 5.54 5600.00 55 4 .00 109080000 .936 1.194 .26 7.75 10300.00 60 2 .00 109080000 2.877 2.996 .12 50.42 10300.00 45 2 .00 109080000 2.996 3.082 .09 69.77 10300.00 35 2 .00 109110000 2.846 2.968 .12 16.39 3600.00 55 2 .00 109110000 3.292 3.572 .28 7.14 3600.00 55 2 .00 109110000 6.476 6.807 .33 6.04 3600.00 55 2 .00 109110000 10.512 10.712 .20 25.00 3600.00 45 2 .00 PAGE 42 31CHAPTER 5 RESULTS FOR STATISTICAL MODELING 5.1 Crash Data Analysis 5.1.1 Crash Distribution for Average Number of Crashes The dependent variable adopted in the modeling process was average number of crashes, which was defined as number of crashes per mile per year in each TWLTL section. Prior to the statistical modeling, the general shape of average number of crashes was assessed in order to provide the basis for crash distribution assumptions for modeling. The number of those TWLTL sections that have the same average number of crashes were plotted as data points on the frequency distribution curve. When all the points, number of sections, on one distribution curve were cumulated, the number would always equal to the to tal sample sections. Figure 5.1 shows the statistical results for average crashes. In the figure, it is clearly that a large number of TWLTL sections had no or low crash experience. And the distribution seems to follow the Poisson distribution. PAGE 43 32 0 100 200 300 400 500 6000 2 4 6 8 10 12 14 16 18 20 22 24Average Number of CrashesNumber of Sections Figure 5.1 Average Number of Crashes 5.1.2 Distribution Fitting fo r Average Number of Crashes Based on the frequency distribution and cumulative probability for average number of crashes, the mean and variance were calc ulated for the distribution fitting. Table 5.1 shows the procedure to get the mean and variance for number of crashes per mile per year. The mean or expected value of the discrete random variable X, denoted as E(x), and the variance of x, denoted as V(x), are calculated as ) ( ) (x f x x Ex ) ( )) ( ( ) (2x f x E x x Vx Where, f ( x ) = the probability of each random variable x. Table 5.1 Mean and Variance of Average Number of Crashes x FrequencyF(x)Cumulative PercentXf(x)(xE(x))2 0 512 16.016.0 0.00 3.69 1 122 3.8 19.8 0.04 0.55 2 129 4.0 23.8 0.08 0.32 3 130 4.1 27.9 0.12 0.13 4 98 3.1 30.9 0.12 0.02 5 86 2.7 33.6 0.13 0.00 PAGE 44 33Table 5.1 Mean and Variance of Average Number of Crashes (Cont) 6 66 2.1 35.7 0.12 0.03 7 57 1.8 37.4 0.12 0.09 8 57 1.8 39.2 0.14 0.18 9 50 1.6 40.8 0.14 0.27 10 51 1.6 42.4 0.16 0.43 11 33 1.0 43.4 0.11 0.39 12 30 0.9 44.3 0.11 0.48 13 29 0.9 45.2 0.12 0.61 14 16 0.5 45.7 0.07 0.42 15 17 0.5 46.3 0.08 0.55 16 19 0.6 46.8 0.09 0.74 17 18 0.6 47.4 0.10 0.83 18 14 0.4 47.8 0.08 0.76 19 13 0.4 48.3 0.08 0.82 20 16 0.5 48.8 0.10 1.15 21 10 0.3 49.1 0.07 0.82 22 10 0.3 49.4 0.07 0.92 23 11 0.3 49.7 0.08 1.14 24 9 0.3 50.0 0.07 1.03 E(x)=2.40 V(x)=16.39 Using the observed mean and variance, the Poisson, Negative Binomial, and Lognormal distribution models were revi ewed and tested to determine which one best fit the crash distribution. Table 5.2 through 5.4 demonstrates that the Chisquare test for Poisson distribution, Negative Binomial distribution, and lognormal distribution fitted for average number of crashes in the TWLTL sections. Table 5.2 Chisquare Test for Poisson Distribution Fitted for Average Number of Crashes x f(i) f(x)poissionf(I)f(x)(f(I)f(x))^2(f(I)f(x))^2/f(x) 0 31.9 0.09072 0.228680.05230 0.576468 1 7.6 0.21772 0.141620.02006 0.092113 2 8.0 0.26127 0.180790.03269 0.125107 3 8.1 0.20901 0.127920.01636 0.078284 4 6.1 0.12541 0.064270.00413 0.032941 5 5.4 0.06020 0.006550.00004 0.000712 PAGE 45 34Table 5.2 Chisquare Test for Poisson Distribution Fitted for Average Number of Crashes (Cont) 6 4.1 0.02408 0.017090.00029 0.012136 7 3.6 0.00826 0.027300.00075 0.090297 8 3.6 0.00248 0.033080.00109 0.441889 9 3.1 0.00066 0.030530.00093 1.411409 10 3.2 0.00016 0.031660.00100 6.322554 11 2.1 0.00003 0.020550.00042 12.21348 12 1.9 0.00001 0.018710.00035 50.60148 13 1.8 0.00000 0.018090.00033 256.2764 14 1.0 0.00000 0.009980.00010 455.105 15 1.1 0.00000 0.010610.00011 3211.188 16 1.2 0.00000 0.011850.00014 26741.53 17 1.1 0.00000 0.011230.00013 170005.1 18 0.9 0.00000 0.008730.00008 771319.7 19 0.8 0.00000 0.008110.00007 5265110 20 1.0 0.00000 0.009980.00010 66462926 21 0.6 0.00000 0.006240.00004 2.27E+08 22 0.6 0.00000 0.006240.00004 2.08E+09 23 0.7 0.00000 0.006860.00005 2.41E+10 24 0.6 0.00000 0.005610.00003 1.62E+11 Chi2=1.88E+11 Table 5.3 Chisquare Test for Negative Binomial Distribution Fitted for Average Number of Crashes x f(i) f(x)NegBino m f(i)f(x)(f(i)f(x))^2(f(i)f(x))^2/f(x) 0 31.9 0.15 0.17300.0299190.2043 1 7.6 0.12 0.04890.0023890.0191 2 8.0 0.11 0.02620.0006870.0064 3 8.1 0.09 0.01009.93E05 0.0011 4 6.1 0.08 0.01660.0002750.0035 5 5.4 0.07 0.01270.0001610.0024 6 4.1 0.06 0.01550.0002390.0042 7 3.6 0.05 0.01280.0001630.0034 8 3.6 0.04 0.00573.25E05 0.0008 9 3.1 0.04 0.00401.62E05 0.0005 10 3.2 0.03 0.00183.07E06 0.0001 11 2.1 0.03 0.00512.57E05 0.0010 12 1.9 0.02 0.00321.02E05 0.0005 PAGE 46 35Table 5.3 Chisquare Test for Negative Binomial Distribution Fitted for Average Number of Crashes (Cont) 13 1.8 0.02 0.00063.65E070.0000 14 1.0 0.02 0.00603.57E050.0022 15 1.1 0.01 0.00309.1E06 0.0007 16 1.2 0.01 0.00025.12E080.0000 17 1.1 0.01 0.00131.7E06 0.0002 18 0.9 0.01 0.00036.9E08 0.0000 19 0.8 0.01 0.00097.73E070.0001 20 1.0 0.01 0.00381.45E050.0024 21 0.6 0.01 0.00109.41E070.0002 22 0.6 0.00 0.00173.03E060.0007 23 0.7 0.00 0.00309.14E060.0024 24 0.6 0.00 0.00235.47E060.0017 Chi2=0.2578 Table 5.4 Chisquare Test for Lognormal Distribution Fitted for Average Number of Crashes x f(i) f(x)Logf(i)f(x) (f(i) f(x))^2(f(i)f(x))^2/f(x) 0 31.9 0 0.3194010.102017* 1 7.6 0.3381260.262020.0686540.203042 2 8.0 0.1569430.076470.0058470.037258 3 8.1 0.0849050.003811.45E05 0.000171 4 6.1 0.050990.0101450.0001030.002019 5 5.4 0.0329110.0207390.00043 0.013068 6 4.1 0.022390.0187820.0003530.015756 7 3.6 0.0158590.0197 0.0003880.024471 8 3.6 0.0115960.0239620.0005740.049515 9 3.1 0.0087020.0224890.0005060.058121 10 3.2 0.0066730.0251430.0006320.094739 11 2.1 0.0052110.0153760.0002360.045373 12 1.9 0.0041330.0145820.0002130.051447 13 1.8 0.0033230.0147680.0002180.065627 14 1.0 0.0027040.0072775.3E05 0.019584 15 1.1 0.0022240.0083817.02E05 0.031591 16 1.2 0.0018460.0100070.0001 0.054246 17 1.1 0.0015450.0096849.38E05 0.060675 18 0.9 0.0013040.007435.52E05 0.04234 19 0.8 0.0011080.0070024.9E05 0.044267 PAGE 47 36Table 5.4 Chisquare Test for Lognormal Distribution Fitted for Average Number of Crashes (Cont) 20 1.0 0.0009470.0090348.16E05 0.08619 21 0.6 0.0008140.0054242.94E05 0.036126 22 0.6 0.0007040.0055343.06E05 0.0435 23 0.7 0.0006120.006253.91E05 0.063859 24 0.6 0.0005340.005082.58E05 0.048334 Chi2=1.191321 The Chisquare calculation value obtained from the distribution fitted for the crashes was calculated with: k ix f x f i f1 2 2 0) ( / )) ( ) ( ( The value estimated of 2 0 is 1.8811, which is much bigger than the Chisquare test value obtained from the Negative Binomial distribution fitting, 0.2578, and the value from the Lognormal distribution fitting, 1.1913. Between the Chisquare test value of Negative Binomial distribution and Lognormal distribution, the one obtained from Negative Binomial is bigger. And the Chisquare from the Negative Binomial distribution fitting 2 0=0.2578. This value is smaller than the Chisquare table value, which indicates that the hypothesis that the distribution of the average number of crashes is hypothesized Negative Binomial distribution will not be rejected. It could be concluded that the Negative Binomial distribution is better to fit the distribution of average number of crashes for TWLTL sections from the Chisquare test comparison. Figure 5.2 through 5.4 present the graphs of frequency distributions, which illustrate the respective distribution fitting of the average number of crashes. Therefore, the Negative Binomial distribution was selected as the fitted distribution to fit the average number of crashes. PAGE 48 37 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00 3 6 9 1 2 15 18 21 24Average Number of CrashesNumber of Sections Real Poisson Figure 5.2 Poisson Distribution of Average Number of Crashes 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00 4 8 12 16 20 24Average Number of CrashesNumber of Sections Real NB Figure 5.3 Negative Binomial Distribution of Average Number of Crashes PAGE 49 38 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.00 3 6 9 1 2 15 18 2 1 24Average Number of CrashesNumber of Sections Real Logn Figure 5.4 Lognormal Distribution of Average Number of Crashes 5.2 Crash Predictive Model 5.2.1 Predictor Variables After the modeling database was built, all the variables were available for the development of the model. Table 5.5 through 5.8 show the summary descriptive statistics for these independent variables Table 5.5 Descriptive Statistics for the Variable ADT Statistics ADT Mean 20110 Standard Deviation11534 Minim 1800 Maxim 78722 PAGE 50 39Table 5.6 Descriptive Statistics for the Variable Access Density Statistics Access Density Mean 32.86 Standard Deviation25.26 Minim 0.5 Maxim 149 Table 5.7 Descriptive Statistics for the Number of Lanes Number of LanesFrequencyPercentage 2 722 42.8 4 833 49.3 6 133 7.9 Table 5.8 Descriptive Statistics for the Posted Speed Posted SpeedFrequency Percentage 25 18 1.1 30 124 7.3 35 410 24.3 40 296 17.5 45 583 34.5 50 77 4.6 55 141 8.4 60 39 2.4 It was found for the variables, ADT and access density, the maxim values were much higher than the median values. The higher values may be a result of particular reasons under abnormal traffic c onditions. In the modeling process, these sections were taken out from the data set. And since all the ADT values are so big PAGE 51 40that the evaluated parameter for this variable may be much small than other parameter, the weight of ADT is determined as 1/10000 vph. Based on the distribution, posted speed has two levels, less than 45 mph and equal to or greater than 45 mph. And the variable of posted speed was transformed from continuous to discrete value because the results of models will be tabulated for application so that traffic engineers c ould easily apply the level of posted speed (lower and higher) to the model. And the values used in the model were 0 and 1. Thus the data set was divided to two ca tegories by the posted speed of 45 mph. Also, the number of lanes has three common values, 2, 4 and 6. The two posted speed categories could be divided into six groups with 2 lanes, 4 lanes, and 6 lanes considering both sides of the road. Thus the sample sections could be divided into six categories. The categories are described as below. Table 5.9 Description of Categories for Analysis Category Description 1 Higher speed & Twoway 2lane Sections 2 Higher speed & Twoway 4lane Sections 3 Higher speed & Twoway 6lane Sections 4 Lower speed & Twoway 2lane Sections 5 Lower speed & Twoway 4lane Sections 6 Lower speed & Twoway 6lane Sections 5.2.2 Models for the Average Number of Crashes The effect of TWLTLs on roadway accident frequency could be studied with statistics models. The following section presents summary of modeling process. Previous research has shown that conven tional linear regression is not appropriate PAGE 52 41for estimating the relationships among the accident frequency and roadway characteristics. Poisson or negative binomial regression is a more proper analysis approach. The regressionbased test for over dispersion can determine the selection between Negative Binomial regression model and Poisson regression model. The over dispersion parameter is statistically significant ( =6.72), indicating the appropriateness of the Negative Binomial regression model rather than Poisson regression model to estimate model coefficients. The Negative Binomial regression model is an extension of Poisson regression model and can overcome the limitation of Poisson regression, which does not require the variance of dependent variable to be equal to its mean. Therefore, Negative Binomial regression model was adopted to develop the predictive model of the crash occurrence of the TWLTLs. The parameters estimations were carried out with LIMDEP software package. The results of the negative binomial regression are presented in Table 5.9. The explanations of the contents of Table 5.10 are listed on Table 5.11. Table 5.10 Estimated Parameters of the Negative Binomial Model Variable Coefficient Estimate Standard Error Relative Effect ChiSquare Pr>Chisq Constant 0.0082 0.1045 0.0343 0.8532 Access Density 0.0193 0.0013 1.0082 39.7870 <0.0001 Average ADT 0.5253 0.0389 1.6910 182.3541 <0.0001 Posted Speed 0.3039 0.0633 0.7379 23.0491 <0.0001 Number of Lanes 0.1124 0.0348 1.1190 10.4622 0.0012 PAGE 53 42Table 5.11 Explanations of Contents of the Results Column Explanation Coefficient Estimate Estimated parameters. Standard Error Estimated standard deviat ion associated with each parameter. Relative Effect Exponent of the estimated parameter of the variable. Chisquare Chisquare test statistic for testing that the parameter is 0. This was computed as the square of the ratio of the parameter estimate divided by its standard error. Pr>ChiSq The probability of obtaining a Chisquare statistic greater than that observed given that the true parameter is 0 From the table, it was found the significance of the variables was all under 0.05. That demonstrated the variables adopted in the model, ADT, access density, posted speed and number of lanes are significant at 5% confidence level. While the estimated constant is 0.0193, with pvalue equal to 0.8593, which means that the effect of constant is extremely insignificant. The Negative Binomial regression was run again after the constant was removed from the regression equation. The results showed that removing constant from the model had very few effects on other variables. Among the four variables, ADT, Access Density and number of lanes had a positive effect on the safety of TWLTLs. These findings suggested that the increase of their values increase the likelihood of accident. For example, Figure 5.5 shows the intuitional relationship between the dependent and independents for the category of higher speed and twoway 4lane sections. For ADT, its the common sense that the higher traffic volume the more accidents occurred. And the higher access density PAGE 54 43also leads to potential accidents. If there is a business area along the roadway with TWLTL, it results in a great number of leftturn movements by motorist, which could cause the probability of accident occurrence. For the same reason, the more lanes in one direction on the roadway, the more chance for the motorists to change lane in order to make leftturn, which is associated with rearend accidents. On the other hand, the sign of the parameters of posted speed was negative. It was also demonstrated that the relative effect for posted speed is 0.74, which means that sections with posted speed more than or equal to 45 mph would have 26% fewer average crashes than similar sections with posted speed less than 45 mph. Even though, this result may not be as expected. The common engineering knowledge is that high speed more likely results in severe crashes. However, drivers tend to travel at speeds in which they feel comfortable given the prevailing conditions. Therefore, this finding could be because lower posted speed more likely promotes speed differential that is generally more closely associated with crashes. 0 50 100 150 200 2501800 6 800 11 8 00 16 8 00 218 0 0 268 00 318 00 368 00 418 00 468 00 518 00 5 68 00 6 18 00 66800 718 0 0 Average ADTAverage Number of Crashes Density=40 Density=80 Density=120 Figure 5.5 The Model Curve of Higher Speed and Twoway 4lane Sections PAGE 55 445.2.3 Goodnessof fit of Model The following step is to asse ss the goodnessoffit of the model. Four statistics, including deviance, Pearsons Ch isquare, and likelihood ratio index, were adopted. The deviance is defined as minus twice the logarithm of the ratio of the maximum likelihood under current model and the maximum likelihood under saturated model. Thus, deviance describes lack of fit, greate r deviance indicates poorer fit. Secondly, in traditional leas t square regression, the coefficient of determination, R2, is frequently used to assess the goodnessoffit of a model. It represents the proportion of variation in the data that is explained by the model. However, it was shown that R2 is not an appropriate measure to assess the goodnessoffit of models due to their nonnormal and nonlinear nature. As a variation, a measure based on the standardized residuals, Pearsons 2, can be calculated to give some indication of the goodnessoffit. The Pearsons 2 is asymptotic to the 2 distribution with np1 degrees of freedom for large sample sizes and exact for normally distributed error stru ctures. Therefore, for a model similar to deviance, the greater the Pearsons 2, the poorer the fit. However, this statistic is not well defined in terms of minimum sample size when applied to nonnormal distributions. Therefore, it should not be used as an absolute measure of model significance. In addition, as the counterpart of R2 in nonlinear regression, a measure of overall statistical fit, the likelihood ratio index can be computed. Table 5.12 presents the four statistics for the Negative Binomial model of the average crashes. PAGE 56 45Table 5.12 Criteria for Assessing the GoodnessofFit Item Value Number of Observations 1688 Number of Variables in Model 4 Number of Parameters in Model4 Degree of Freedom 1684 Loglikelihood Function 4513.050 Restricted Log likelihood 8273.891 Deviance 2323.92 Deviance/DOF 1.38 Pearson Chisquare 2237.23 Pearson Chisquare/DOF 1.33 Pearson Rsquare 31.81% Likelihood Ratio Index 45.45% Both the mean deviance and Pearsons Chisquare ratio are over one, and the Pearsons Rsquare and the likelihood are around 30% and 40%. The statistics indicate that the developed model has satisfactory capability in fitting the data and explaining the variation of the data. PAGE 57 46CHAPTER 6 APPLICATION OF STATISTICS MODEL ADT is known as the most significant factor contributing to crash occurrence on the TWLTL sections and most traffic engineers will first consider it in their roadway design. In this chapter, an approach to identify the unsafe TWLTL sections regarding the traffic volume was explored. The approach employed distribution fitting results and critical value, like the 85th percentile value to obtain the critical value of average crash frequency. Then by using the predictive model developed above, the critical value of ADT could be evaluated for a TWLTL section with specific traffic characteristics, posted speed, access density and number of lanes. Thus, with the comparison of the actual ADT value and th e critical ADT value, the critical TWLTL section could be determined. 6.1 Distribution Fitting The method used for average number of crashes distribution fitting was also applied for each category. The categories were described in Table 5.9. If all the distribution were not rejected by the Chisquare test ( 0 2), the distribution with smaller Chisquare calculation value was selected as the fitted distribution. If the Chisquare value of the three distributions were close, the Chisquare value with big difference from the critical Chisquare value, was selected. Table 6.1 exhibits the Chisquar PAGE 58 47tests for fitting Poisson, Negative Binomial and Lognormal distributions for each category. Three of them were fitted to Negative Binomial Distribution, the rest of them was fitted to Lognormal distribution. Table 6.1 Chisquare Test for Poisson, Negative Binomial and Lognormal Distribution Fitting Poisson Negative Binomial Lognormal Category Chisquare Calculation 0 2 Chisquare Table Value a,kp1 2 Chisquare Calculation 0 2 Chisquare Table Value a,kp1 2 Chisquare Calculation 0 2 Chisquare Table Value a,kp1 2 Distribution Selected 1 21623860.35 26.2962 0.98 24.9958 0.26 24.9958 NB 2 10010.42 33.9244 0.88 32.6705 0.27 33.9244 NB 3 2421.98 41.3372 3.35 40.1133 0.58 40.1133 Lognormal 4 7385.36 26.2962 0.20 24.9958 0.36 24.9958 NB 5 593.15 36.4151 7.71 35.1752 0.23 35.1752 Lognormal 6 279.78 35.1752 1.89 33.9244 0.80 33.9244 Lognormal 6.2 The 85th Percentile Value of Crashes Based on the distribution, the 85th percentile values of each crash distribution were obtained. The 85th percentile is the point where 85 percent of the crashes in a section will occur either at or below this measurement. This value is often used in engineering analysis because the data in the top 15 percent, considered the top portion of the population, is not targeted in design. The application of the two values is described in further section. Table 6.2 presents the 85th percentile values for average number of crashes for each category, respectively. And Table 6.3 presents the 85th percentile values after the linear regression for the previous values. PAGE 59 48Table 6.2 85th Percentile Value for Average Cras hes Distribution for Each Category Number of lanesHigher Speed Lower Speed 2 8.85 6.84 4 14.00 10.91 6 19.20 14.98 Table 6.3 85th Percentile Value for Average Cras hes Distribution for Each Category after Linear Regression Number of lanesHigher Speed Lower Speed 2 8.11 6.72 4 15.5 11.16 6 18.46 14.86 6.3 Estimation of the Critical Value After obtaining the 85th percentile value, the respective critical ADT values for each category were evaluated by using the predictive model. To calculate the ADT value, the other characteristics were given for the equation. Figure 6.1 and 6.2 show the example procedure of the evaluation of ADT. Table 6.4 presented the results of the evaluations according to some given conditions. PAGE 60 49 Higher Speed & Twoway 4lane Sections 0 20 40 60 80 100 024681012141618202224 Average Number of CrashesCumulative % 15.5 85% Figure 6.1 The 85% Percentile Value of the Average Crashes for Higher Speed and Twoway 4lane Sections Higher Speed & Twoway 4lane Sections (85%) 0 5 10 15 20 25 30 3526000 2 8 0 0 0 3 0 0 0 0 32000 3 4 0 0 0 36000 38000 4 0 0 0 0 42000Average ADTAverage Number of Crashes density=40 density=80 density=120 85% point 14.0 29203.4 35447.5 41691.55 Figure 6.2 Evaluation of ADT According to 85th Percentile Value PAGE 61 50Table 6.4 Results of Evaluation of ADT Percentile 85% 40 accesses per mile 36505.2 80 accesses per mile 30261.2 2lane 120 accesses per mile24017.0 40 accesses per mile 40956.7 80 accesses per mile 34712.7 4lane 120 accesses per mile28468.6 40 accesses per mile 42690.0 80 accesses per mile 36446.0 High Speed 6lane 120 accesses per mile30202.0 40 accesses per mile 25712.7 80 accesses per mile 19469.6 2lane 120 accesses per mile13224.6 40 accesses per mile 30321.3 80 accesses per mile 24077.3 4lane 120 accesses per mile17833.2 40 accesses per mile 32077.2 80 accesses per mile 25833.2 Low Speed 6lane 120 accesses per mile19589.1 * means the ADT in this situation was not available from the figure. The results presented a general range of traffic volume within which the TWLTL could be used on the roadway. The conditions for each category were similar, including the posted speed level, number of lanes and access density of the roadway. According to the statistics analysis of the access density, three levels were selected to give a basic concept of the traffic volume. The three levels were 40 accesses per mile, 80 accesses per mile and 120 accesses per mile. PAGE 62 516.4 Identification of the Critical Sections To identify the critical TWLTL sections that present safety concerns, the next step is to compare the actual ADT to the critical ADT value listed in the table. If the actual ADT value of the section is higher than the estimated critical ADT value, the TWLTL section is identified as critical. To apply this method, the first issu e is to select a percentile value of average number of crashes. For example, if the 85th percentile value is selected, this means that 85% of the TWLTL sections of a group with similar characteristics have an average number of crashes equal to or lower than the 85th percentile value of average number of crashes obtained from crash distribution. Those TWLTL sections that were identified as critical were exhibited in tables. Table 6.5 shows the critical sections in District 7 in Florida State. It is a reference for traffic engineers to further study of improving the roadways which is using TWLTLs as the median treatment. PAGE 63 52Table 6.5 TWLTL Sections Identified as Critical for District 7 Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 7101300004.5 4.796 44 41,036 45 15.77 4 7151200005.65 5.723 27 53,500 50 9.13 7100300001.554 1.697 112 43,125 45 9.32 7100300001.798 2.166 76 43,040 45 22.64 7100300002.36 3.014 73 42,771 45 17.84 7101300008.827 8.926 61 49,375 45 13.47 7101300009.596 9.789 78 64,984 45 55.27 7101600000.265 0.646 63 74,224 45 25.37 7101600000.899 1.24 62 78,722 45 17.6 7101600001.24 1.939 44 77,500 45 0 7150400004.693 4.843 13 50,833 45 6.67 7150400004.947 5.541 71 52,850 45 16.84 Higher Speed 6 7150400005.841 5.911 43 52,167 45 14.29 Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 7150200000 1.073 79 21,692 30 4.04 7150200003.67 4.952 83 25,167 40 1.56 2 7150200007.571 9.23 33 28,174 40 4.62 7150070003.544 3.798 83 28,100 40 6.56 7150400000.803 1.034 82 25,700 35 14.43 7150900001.254 2.227 99 24,709 35 3.77 4 7150900002.227 2.338 117 29,667 40 9.01 70200000014.203 14.545 99 26,450 40 9.75 7100300000.052 0.449 86 41,568 40 36.94 Lower Speed 6 7100300000.545 0.9 79 41,688 40 30.05 PAGE 64 53CHAPTER 7 SUMMARY AND CONCLUSIONS 7.1 Summary This research was conducted to evaluate the safety impact of TWLTLs on the roadway crashes. This paper consists of thre e major parts (1) setting up a database for analysis, (2) establishing statistical model to explain the relationship between traffic characteristics and accident occurrence, and (3) developing the criteria to determine the improvement of TWLTL treatment. First, the database was built by use of SPSS and SAS package. There were some issues for the data collection (1) selec ting useful variables for data analysis, (2) taking out the crashes which are not related to TWLTL, (3) aggregating the crashes occurring in a certain TWLTL section in order to transfer the crashbased database into sectionbased database, (4) obtaining the missing data for the variables from the data source by FDOT, (5) discarding some section samples whose value of the variables indicated abnormal traffic situation. Finally, a threeyear crash history database including totally 1688 TWLTL sections and four major variables all over Florida State was used in this research. For the modeling part, distribution fitting analysis for the Poisson, negative binomial and lognormal distribution were first performed for the crash data. The results of comparing the Chisquare of each distribution helped to decide which PAGE 65 54distribution model the crash data set best fit. Based on this statistics result, crash prediction model was developed to estimate the average number of crashes by four variables, ADT, posted speed, access density and number of lanes. Negative binomial regression model was applied since the crash data showed overdispersion. The regression parameters were estimated by using the maximum likelihood method with LIMDEP program. The goodnessoffit for the developed models were evaluated with Pearsons Rsquare and likelihood ratio index. After that, an approach for the appropriate use of TWLTLs was carried out by using the model developed above. First, based on the distribution of the four variables, the whole database was divided into six categories according to the posted speed level and number of lanes. For each category, the selected percentile values of the average number of crash were obtained from the distribution fitting curve. With the employment of these critical values and some specific characteristics into the predictive model, the traffic volume on the TWLTLs was calculated, called critical ADT value. Thus, a list of critical ADT value responding to different posted speed level, different number of lanes, different access density and average number of crashes according to selected percentile value. If the actual ADT value is higher than the critical value, the TWLTL section was regarded as a critical section which needs improvement for the median treatment. 7.2 Conclusions The distribution fitting test for the average number of crashes showed it follows a negative binomial regression distribution. The predictive model indicates PAGE 66 55the relationship between the independents, ADT, posted speed, access density and number of lanes, and the dependents, average number of crashes. From the results, the predictor variables are all significant at 5% confidence level, which means they do affect the occurrence of accidents in TWLTL sections. With the growth of traffic volume, number of lane, and access density, the number of crashes grows up, which can be understood by common traffic engi neer sense. The three variables could increase the movements of leftturn which cause the accidents frequently on the roadway. The model also indicated posted speed has a negative effect on the frequency of crash. This is because of the difference speed generated by the motorist to drive comfortably, which is the main cause of the accidents. To apply the predictive model, the TWLTL sections were divided into six categories, high posted speed and twoway 2lane sections, high posted speed and twoway 4lane sections, high posted speed and twoway 6lane sections, low posted speed and twoway 2lane sections, low posted speed and twoway 4lane sections, and low posted speed and twoway 6lane sections. For each category, with the use of the predictor model, ADT value can be calculated corresponding to specific access density. In order to control the crash frequency at a certain level, the value of the roadway characteristics should be controlled. Though the average daily traffic volume is random and discrete, there must be a range of ADT within which the roadway is appropriate to install TWLTs as the treatment, which means the crash frequency should under a distribution percentile level. The critical ADT values for different PAGE 67 56percentile value of average number of crashes are tabulated in Appendix C. Once the critical percentile is determined, according to the posted speed value, number of lanes and access density, the critical ADT value can be obtained from the table. Then the critical TWLTL sections can be identified based on the critical ADT value. The TWLTL sections identified as critical in seven districts of Florida State are tabulated in Appendix D, which presents the need of improving the existing TWLTL sections. While for a future roadway the median type of which is not determined yet, once the percentile considered critical for roadway safety is decided, the respective critical ADT value can be obtained from the table. If the actual traffic volume is higher than the critical ADT value, this section is regarded not appropriate to use TWLTL as the median treatment. This approach is easy for traffic engineering to get the basic concept of the safety effect of TWLTLs on roadway and consider in highway design. PAGE 68 57REFERENCE 1. Nemeth, Z. A., Twoway LeftTurn Lanes: A StateoftheArt Overview and an Implementation Guide, Ohio State University, Research Record 681, Transportation Research Record, 1978 2. D.W. Harwood and A.D. St. John. Passing Lanes and Other Operational Improvements on Twolane Highways. Report FHWARD85.028. FHWA, U.S. Department of Transpostation, 1985 3. J.A. Bonneson and P.T. McCoy. Capacity and Operational Effects of Midblock Leftturn Lanes. NCHRP Report 395, TRB Transportation Research Record, National Research Council, Washington D.C. 1997 4. J.A. Azzeh, B.A. Thorson, J. J.Valenta, J. C. Glennon. And C.J. Wilton, Evaluation of Techniques for the Control of Direct Access to Arterial Highways. Report FHWARD7687, FHWA, U.S. Department of Transportation, 1975 5. M.R. Parker. Jr. Design Guidelines for Raised and Traversable Medians in Urban Areas. Virginia Highway and Transportation Research Council, Charlottesville, 1983 6. Harwood, D.W. Multilane Design Alternatives for Improving Suberban Highways. National Cooperative Highway Research Program Report No. 282, TRB Transportation Research Record, Washington D.C. 1986 7. Peter S. Parsonson. Development of Policies and Guidelines Governing Median Selection. School of Civil Engineering, Georgia Institute of Technology, Georgia Tech Sponsored Research Project No. E20841, 1990 8. Christopher A. Squires and Peter S. Parsonson. Accident Comparison of Raised Median and Twoway Leftturn Lane Median Treatments. TRB Transportation Research Record 1239, Washington D.C. 1989 9. Henry C. Brown and Andrzej P. Tarko, Effects of Access Control on Safety on Urban Arterial Streets, TRB Transportation Research Record 1665, Washington D.C. 1999 PAGE 69 5810. Patrick T. McCoy, John L. Ballard, Duane S. Eitel, and Walter E. Witt Twoway Leftturn Lane Guidelines for Urban Fourlane Roadways. TRB Transportation Research Record 1195, Washington D.C. 11. Kay Fitzpatrick and Kevin Balke. Evaluation of Flush Medians and Twoway Leftturn Lanes on Fourlane Rural Highways. TRB Transportation Research Record 1500, Washington D.C. 12. Gary Long, ChengTin Gan and Bradley S. Morrison. Safety Impacts of Selected Median and Access Design and Access Design Features. Transportation Research Center, Department of Civil Engineering, University of Florida (Project Account No. 4910 4504 347 12) 13. Development of Models to Quantify the Impacts of Signalization on Intersection Crashes, Department of Civil and Environment Engineering, for Florida Department of Transportation, 2002 PAGE 70 59 APPENDICES PAGE 71 60Appendix A. Distribution Fitting for Six Categories Higher Speed & Twoway 2lane Sections 0.0 10.0 20.0 30.0 40.0 50.0 60.00 3 6 9 1 2 15 18Average Number of CrashesProbability Real Poisson Figure A.1 Poisson Distribution Fitting for Higher Speed and Twoway 2lane Sections Higher Speed & Twoway 2lane Sections 0.0 10.0 20.0 30.0 40.0 50.0 60.00 3 6 9 1 2 1 5 1 8Average Number of CrashesProbability Real NB Figure A.2 Negative Binomial Distribution Fitting for Higher Speed and Twoway 2lane Sections PAGE 72 61Appendix A (Continued) Higher Speed & Twoway 2lane Sections 0.0 10.0 20.0 30.0 40.0 50.0 60.00 3 6 9 12 15 1 8Average Number of CrashesProbability Real Logn FigureA.3 Lognormal Distribution Fitting for Higher Speed and Twoway 2lane Sections Higher Speed & Twoway 4lane Sections0.0 5.0 10.0 15.0 20.00 3 6 9 12 15 18 2 1 24Average Number of CrashesProbability Real Poisson Figure A.4 Poisson Distribution Fitting for Higher Speed and Twoway 4lane Sections PAGE 73 62Appendix A (Continued) Higher Speed & Twoway 4lane Sections0.0 5.0 10.0 15.0 20.00 3 6 9 1 2 15 18 21 24Average Number of CrashesProbability Real NB Figure A.5 Negative Binomial Distribution Fitting for Higher Speed and Twoway 4lane Sections Higher Speed & Twoway 4lane Sections0.0 5.0 10.0 15.0 20.00 3 6 9 12 1 5 18 21 24Average Number of CrashesProbability Real Logn Figure A.6 Lognormal Distribution Fitting for Higher Speed and Twoway 4lane Sections PAGE 74 63Appendix A (Continued) Higher Speed & Twoway 6lane Sections 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00 4 8 12 1 6 20 24 28Average Number of CrashesProbability Real Poisson Figure A.7 Poisson Distribution Fitting for Higher Speed and Twoway 6lane Sections Higher Speed & Twoway 6lane Sections0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00 4 8 12 16 20 24 28Average Number of CrashesProbability Real NB Figure A.8 Negative Binomial Distribution Fitting for Higher Speed and Twoway 6lane Sections PAGE 75 64Appendix A (Continued) Higher Speed & Twoway 6lane Sections0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00 4 8 12 16 20 24 28Average Number of CrashesProbability Real Logn Figure A.9 Lognormal Distribution Fitting for Higher Speed and Twoway 6lane Sections Lower Speed & Twoway 2lane Sections0.0 10.0 20.0 30.0 40.0 50.00 3 6 9 12 15 18Average Number of CrashesProbability Real Poisson Figure A.10 Poisson Distribution Fitting for Lower Speed and Twoway 2lane Sections PAGE 76 65Appendix A (Continued) Lower Speed & Twoway 2lane Sections0 10 20 30 40 500 3 6 9 12 15 18Average Number of CrashesProbability Real NB Figure A.11 Negative Binomial Distribution Fitting for Lower Speed and Twoway 2lane Sections Lower Speed & Twoway 2lane Sections0.0 10.0 20.0 30.0 40.0 50.00 3 6 9 12 15 18Average Number of CrashesProbability Real Logn Figure A.12 Lognormal Distribution Fitting for Lower Speed and Twoway 2lane Sections PAGE 77 66Appendix A (Continued) Lower Speed & Twoway 4lane Sections 0.0 5.0 10.0 15.0 20.00 4 8 1 2 1 6 2 0 2 4Average Number of CrashesProbability Real Poisson Figure A.13 Poisson Distribution Fitting for Lower Speed and Twoway 4lane Sections Lower Speed & Twoway 4lane Sections0 5 10 15 200 4 8 12 16 20 24Average Number of CrashesProbability Real NB Figure A.14 Negative Binomial Distribution Fitting for Lower Speed and Twoway 4lane Sections PAGE 78 67Appendix A (Continued) Lower Speed & Twoway 4lane Sections0.0 5.0 10.0 15.0 20.00 4 8 12 1 6 20 24Average Number of CrashesProbability Real Logn Figure A.15 Lognormal Distribution Fitting for Lower Speed and Twoway 4lane Sections Lower Speed & Twoway 6lane Sections 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00 4 8 12 16 20 24Average Number of CrashesProbability Real Poisson Figure A.16 Poisson Distribution Fitting for Lower Speed and Twoway 6lane Sections PAGE 79 68Appendix A (Continued) Lower Speed & Twoway 6lane Sections0.0 2.0 4.0 6.0 8.0 10.0 12.00 3 6 9 12 15 18 21 24Average Number of CrashesProbability Real NB Figure A.17 Negative Binomial Distribution Fitting for Lower Speed and Twoway 6lane Sections Lower Speed & Twoway 6lane Sections0.0 2.0 4.0 6.0 8.0 10.0 12.00 3 6 9 12 1 5 18 21 24Average Number of CrashesProbability Real Logn Figure A.18 Lognormal Distribution Fitting for Lower Speed and Twoway 6lane Sections PAGE 80 69Appendix B. Critical ADT Value Corresponding to the 85th Percentile Value of Average Number of Crashes for Six Categories Higher Speed & Twoway 2lane Sections (85%) 0 2 4 6 8 10 12 14 16 18 202 2 0 0 0 24000 2 6 0 0 0 28000 300 0 0 3 2 0 00 34000 3 6 0 0 0 38000Average ADTAverage Number of Crashes density=40 density=80 density=120 85% point 885 24017.08 30261.14 36505.19 Figure B.1 Critical ADT Value for Higher Speed and Twoway 2lane Sections Higher Speed & Twoway 4lane Sections (85%) 0 5 10 15 20 25 30 352 6 0 0 0 28000 30000 3 2 0 0 0 340 0 0 36000 3 8 0 00 4 0 0 0 0 42000Average ADTAverage Number of Crashes density=40 density=80 density=120 85% point 140 28468.6 34712.7 40956.74 Figure B.2 Critical ADT Value for Higher Speed and Twoway 4lane Sections PAGE 81 70Appendix B (Continued) Higher Speed & Twoway 6lane Sections (85%) 0 5 10 15 20 25 30 35 40 452 8 0 0 0 31000 3 4 0 0 0 3 7 0 00 40000 4 3 0 0 0Average ADTAverage Number of Crashes density=40 density=80 density=120 85% point 19.2 30201.99 36446.04 42690.09 Figure B.3 Critical ADT Value for Higher Speed and Twoway 6lane Sections Lower Speed & Twoway 2lane Sections (85%) 0 2 4 6 8 10 12 14 16 18120 00 1400 0 16000 1 8000 20 000 2200 0 24000 26000 2 8000Average ADT Average Number of Crashes density=40 density=80 density=120 1 3 224. 6 1 9 4 68 6 4 2 57 12. 7 85% point 6.84 Figure B.4 Critical ADT Value for Lower Speed and Twoway 2lane Sections PAGE 82 71Appendix B (Continued) Lower Speed & Twoway 4lane Sections (85%) 0 5 10 15 20 25 301 6 0 0 0 19000 2 2 0 0 0 25000 2 8 0 00 3 1 0 0 0Average ADTAverage Number of Crashes density=40 density=80 density=120 85% point 10.91 17833.23 24077.29 30321.34 Figure B.5 Critical ADT Value for Lower Speed and Twoway 4lane Sections Lower Speed & Twoway 6lane Sections (85%) 0 5 10 15 20 25 30 35 40180 00 2 1000 2 4000 27000 30000 3300 0Average ADTAverage Number of Crashes density=40 density=60 density=120 85% point 14.98 19589.11 25833.16 32077.21 Figure B.6 Critical ADT Value for Lower Speed and Twoway 6lane Sections PAGE 83 72Appendix C. Critical ADT Value Corresponding to Selected Percentile Value for Six Categories Table C.1 Critical ADT Value for Higher Speed and Twoway 2lane Sections 50%75%80%85%90% 95% Access Density 2.14 6.33 7.44 8.85 10.95 14.01 10 14163.44634808.68537884.46341188.22545241.566 49932.826 20 12602.43333247.67236323.4539627.21243680.553 48371.813 30 11041.42131686.6634762.43838066.19942119.54 46810.801 40 9480.407930125.64733201.42536505.18740558.528 45249.788 50 7919.395228564.63431640.41234944.17438997.515 43688.775 60 6358.382427003.62130079.39933383.16137436.502 42127.762 70 4797.369725442.60928518.38731822.14835875.489 40566.75 80 3236.356923881.59626957.37430261.13634314.477 39005.737 90 1675.344222320.58325396.36128700.12332753.464 37444.724 100 114.3314120759.5723835.34827139.1131192.451 35883.711 110 1446.681319198.55822274.33625578.09729631.438 34322.699 120 3007.694117637.54520713.32324017.08528070.426 32761.686 130 4568.706916076.53219152.3122456.07226509.413 31200.673 140 6129.719614515.51917591.29720895.05924948.4 29639.66 PAGE 84 73Appendix C (Continued) Table C.2 Critical ADT Value for Higher Speed and Twoway 4lane Sections 50%75%80%85%90% 95% Access Density 6.18 10.75 12.18 14 16.29 21.15 10 30072.68740611.18942988.67845639.77448523.728 53494.002 20 28511.67539050.17641427.66544078.76146962.715 51932.989 30 26950.66237489.16339866.65342517.74945401.702 50371.976 40 25389.64935928.15138305.6440956.73643840.69 48810.963 50 23828.63634367.13836744.62739395.72342279.677 47249.951 60 22267.62432806.12535183.61437834.7140718.664 45688.938 70 20706.61131245.11233622.60236273.69739157.651 44127.925 80 19145.59829684.132061.58934712.68537596.639 42566.912 90 17584.58528123.08730500.57633151.67236035.626 41005.9 100 16023.57326562.07428939.56331590.65934474.613 39444.887 110 14462.5625001.06127378.55130029.64632913.6 37883.874 120 12901.54723440.04925817.53828468.63431352.588 36322.861 130 11340.53421879.03624256.52526907.62129791.575 34761.849 140 9779.521620318.02322695.51225346.60828230.562 33200.836 PAGE 85 74Appendix C (Continued) Table C.3 Critical ADT Value for Higher Speed and Twoway 6lane Sections 50%75%80%85%90% 95% Access Density 9.62 15.16 16.92 19.2 21.63 28.29 10 34217.48142875.69744966.61647373.12549641.752 54751.73 20 32656.46841314.68543405.60445812.11348080.739 53190.717 30 31095.45539753.67241844.59144251.146519.727 51629.705 40 29534.44338192.65940283.57842690.08744958.714 50068.692 50 27973.4336631.64638722.56541129.07443397.701 48507.679 60 26412.41735070.63437161.55339568.06241836.688 46946.666 70 24851.40433509.62135600.5438007.04940275.676 45385.654 80 23290.39131948.60834039.52736446.03638714.663 43824.641 90 21729.37930387.59532478.51434885.02337153.65 42263.628 100 20168.36628826.58330917.50233324.01135592.637 40702.615 110 18607.35327265.5729356.48931762.99834031.625 39141.603 120 17046.3425704.55727795.47630201.98532470.612 37580.59 130 15485.32824143.54426234.46328640.97230909.599 36019.577 140 13924.31522582.53224673.4527079.9629348.586 34458.564 PAGE 86 75Appendix C (Continued) Table C.4 Critical ADT Value for Lower Speed and Twoway 2lane Sections 50%75%80%85%90% 95% Access Density 1.88 4.7 5.64 6.84 8.58 11.62 10 5809.47623252.66526723.47430395.73134710.335 40484.062 20 4248.463321691.65325162.46128834.71833149.323 38923.049 30 2687.450520130.6423601.44827273.70531588.31 37362.036 40 1126.437818569.62722040.43525712.69230027.297 35801.023 50 434.5749717008.61420479.42324151.6828466.284 34240.01 60 1995.587715447.60218918.4122590.66726905.272 32678.998 70 3556.600513886.58917357.39721029.65425344.259 31117.985 80 5117.613212325.57615796.38419468.64123783.246 29556.972 90 6678.62610764.56314235.37217907.62922222.233 27995.959 100 8239.63879203.550512674.35916346.61620661.221 26434.947 110 9800.65157642.537811113.34614785.60319100.208 24873.934 120 11361.6646081.5259552.333213224.5917539.195 23312.921 130 12922.6774520.51237991.320511663.57815978.182 21751.908 140 14483.692959.49956430.307710102.56514417.169 20190.896 PAGE 87 76Appendix C (Continued) Table C.5 Critical ADT Value for Lower Speed and Twoway 4lane Sections 50%75%80%85%90% 95% Access Density 4.65 8.21 9.38 10.91 13.16 17.22 10 18769.60329591.71832127.92235004.37538573.804 43692.585 20 17208.5928030.70530566.9133443.36237012.791 42131.572 30 15647.57726469.69229005.89731882.34935451.779 40570.56 40 14086.56424908.67927444.88430321.33633890.766 39009.547 50 12525.55123347.66725883.87128760.32432329.753 37448.534 60 10964.53921786.65424322.85927199.31130768.74 35887.521 70 9403.52620225.64122761.84625638.29829207.728 34326.509 80 7842.513218664.62821200.83324077.28527646.715 32765.496 90 6281.500517103.61619639.8222516.27326085.702 31204.483 100 4720.487715542.60318078.80820955.2624524.689 29643.47 110 3159.47513981.5916517.79519394.24722963.676 28082.458 120 1598.462212420.57714956.78217833.23421402.664 26521.445 130 37.4494510859.56513395.76916272.22219841.651 24960.432 140 1523.56339298.551811834.75714711.20918280.638 23399.419 PAGE 88 77Appendix C (Continued) Table C.6 Critical ADT Value for Lower Speed and Twoway 6lane Sections 50%75%80%85%90% 95% Access Density 7.42 11.72 13.12 14.98 17.74 22.82 10 23386.23832088.26934236.39436760.25139979.478 44773.222 20 21825.22530527.25732675.38135199.23838418.465 43212.209 30 20264.21228966.24431114.36933638.22536857.452 41651.196 40 18703.19927405.23129553.35632077.21335296.44 40090.184 50 17142.18725844.21827992.34330516.233735.427 38529.171 60 15581.17424283.20526431.3328955.18732174.414 36968.158 70 14020.16122722.19324870.31827394.17430613.401 35407.145 80 12459.14821161.1823309.30525833.16229052.389 33846.133 90 10898.13519600.16721748.29224272.14927491.376 32285.12 100 9337.122718039.15420187.27922711.13625930.363 30724.107 110 7776.1116478.14218626.26721150.12324369.35 29163.094 120 6215.097214917.12917065.25419589.11122808.338 27602.082 130 4654.084513356.11615504.24118028.09821247.325 26041.069 140 3093.071711795.10313943.22816467.08519686.312 24480.056 PAGE 89 78Appendix D Identified Critical TWLTL Sections in Florida Table D.1 Critical TWLTL Sections for District 1 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 4 113010000 0 0.133 38 44,500 50 0 113010000 2.137 2.383 61 43,900 45 33.88 113010000 3.005 4.215 67 43,364 45 33.33 113010000 2.383 3.005 84 43,063 45 17.15 113010000 4.215 5.085 71 42,376 45 35.63 Higher Speed 6 117020000 15.14 16.37 56 50,477 45 17.34 2 112040000 5.658 5.898 58 24,167 40 4.17 113010000 5.369 5.455 116 29,688 40 31.01 113150000 6.586 8.171 76 37,977 40 9.25 113150000 8.171 8.305 37 36,500 40 19.9 116030000 27.773 27.886 53 32,500 40 0 116250000 25.749 27.348 91 36,398 40 12.3 116250000 27.348 27.499 112 26,500 30 8.83 116250000 27.499 28.647 85 25,293 30 8.13 116300000 0.598 0.672 81 28,000 40 13.51 116300000 0.672 0.758 81 30,500 35 15.5 117020000 18.689 19.003 57 34,625 40 12.74 117120000 0.13 0.557 73 32,732 35 21.86 117120000 0.557 1.148 64 36,652 35 12.97 4 191070000 9.628 9.842 84 29,063 35 12.46 112010000 21.045 23.375 84 43,259 40 16.6 112010000 23.375 23.459 36 44,429 40 27.78 117020000 16.37 16.983 68 51,592 40 41.33 117020000 16.983 17.31 34 52,196 35 23.45 Lower Speed 6 117040000 0.65 0.988 74 35,000 40 1.97 PAGE 90 79Appendix D (Continued) Table D.2 Critical TWLTL Sections for District 2 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 272230000 0.978 1.21 34 47,000 45 10.06 4 272230000 1.21 1.36 53 48,833 45 13.33 272100000 6.472 7.575 59 58,210 45 43.82 Higher Speed 6 272230000 0.444 0.978 58 44,422 45 19.98 226070000 18.538 18.711 46 27,600 35 9.63 229010000 6.338 6.58 99 26,643 35 9.64 272110000 0.241 0.576 69 34,000 40 17.91 2 272110000 0.576 1.592 78 28,625 35 5.25 226010000 13.623 14.623 64 36,175 30 26.67 226010000 14.623 15.331 62 34,319 35 22.13 226010000 15.348 15.808 72 37,451 35 29.71 226070000 19.416 20.017 75 29,892 30 33.28 228010000 7.545 8.068 69 27,357 30 17.85 272014000 1.124 1.736 49 43,441 35 21.24 272014000 2.31 4.148 68 39,176 40 28.29 272014000 4.325 4.595 11 35,500 40 0 272014000 4.716 5.06 32 33,000 40 0 272014000 5.06 5.29 48 33,000 35 0 272014000 5.29 5.431 64 33,000 35 0 272014000 5.431 5.493 97 27,833 35 16.13 272014000 5.563 5.955 38 33,000 35 0 272015000 1.084 2.116 27 35,052 40 15.5 272015000 2.116 2.3 33 38,077 40 23.55 272015000 2.3 2.373 27 36,500 40 9.13 272028000 1.42 1.912 4 36,500 35 0 272100000 3.199 3.282 84 41,233 40 60.24 272100000 3.282 5.565 56 40,118 40 18.54 272150000 2.14 2.996 35 31,991 35 21.81 272170000 4.838 5.845 55 35,735 35 22.51 272190000 0.498 3.198 50 31,266 40 15.06 272190000 13.7 14.771 74 28,255 35 9.65 Lower Speed 4 272291000 2.902 3.244 79 28,417 35 11.7 PAGE 91 80Appendix D (Continued) Table D.2 Critical TWLTL Sections for District 2 in Florida (Contd.) Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 229010000 8.111 9.076 71 40,345 35 14.51 272014000 1.736 1.946 105 50,960 40 39.68 272014000 1.946 2.253 26 48,000 40 0 Lower Speed 6 272018000 5.998 6.804 61 35,412 35 35.15 PAGE 92 81Appendix D (Continued) Table D.3 Critical TWLTL Sections for District 3 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 4 346020000 0.748 1.149 2 53,328 45 30.76 Higher Speed 6 346010000 16.178 16.682 4 53,422 45 23.81 2 355100000 1.415 1.6 146 17,300 40 0 348004000 8.239 8.789 38 35,507 40 41.21 348012000 3.57 3.808 21 36,429 35 9.8 348012000 4.08 4.443 25 36,943 35 32.14 348012000 4.583 4.682 10 40,833 35 80.81 348070000 4.2 4.47 52 31,500 35 0 348070000 4.47 6.029 42 40,500 35 0 348070000 6.597 6.88 32 53,500 35 0 355005000 0.748 1.25 44 31,400 40 6.64 355040000 11.553 11.839 21 36,250 25 4.66 355090000 1.6 2.78 45 33,601 40 33.62 357030000 10.905 11.151 61 33,000 35 8.13 357030000 12.241 12.475 17 43,689 35 29.91 357040000 12.377 12.977 17 44,500 35 0 348020000 10.489 10.98 55 35,759 40 18.33 348020000 10.98 11.194 61 34,891 35 35.83 355060000 7.68 8.543 25 42,319 30 43.65 357040000 0.659 2.22 46 45,301 30 14.52 357040000 2.22 3.421 54 45,467 40 12.49 357040000 3.421 4.661 31 43,500 40 2.15 Lower Speed 6 357040000 12.977 13.933 37 38,800 35 3.49 PAGE 93 82Appendix D (Continued) Table D.4 Critical TWLTL Sections for District 4 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 486100000 8.397 8.5 10 56,125 45 51.78 4 486100000 4.2 5.09 44 41,265 45 19.1 Higher Speed 6 486016000 5.012 5.214 59 44,000 45 8.25 2 486010000 0.825 2.463 63 27,467 35 6.92 486010000 2.719 5.948 65 32,560 35 11.15 486100000 0 0.693 45 43,875 40 11.54 486100000 0.965 2.569 40 41,996 40 28.89 486100000 2.569 4.2 49 41,948 40 25.75 486100000 8.5 10.028 2 46,674 40 20.07 486210000 3.153 3.325 64 28,500 40 3.88 488010000 4.794 5.614 67 28,364 35 8.94 488010000 5.614 5.809 77 28,000 35 1.71 489090000 13.849 14.576 25 41,292 35 5.5 493040000 0 0.391 82 27,909 35 9.38 493120000 20.33 20.401 56 29,500 35 0 493200000 8.228 9.127 73 27,545 35 14.83 494010000 10.25 11.777 51 39,936 40 10.26 494010000 11.777 12.23 42 36,705 40 16.19 494010000 12.23 12.731 68 35,267 40 9.98 494010000 12.731 13.496 47 31,786 30 6.1 494010000 13.496 13.957 61 28,750 35 10.12 4 494120000 7.853 9.286 42 35,967 40 3.49 486040000 14.173 15.384 49 36,155 35 7.98 486100000 10.215 10.317 10 49,944 40 29.41 Lower Speed 6 486200000 3.51 3.635 8 53,582 40 5.33 PAGE 94 83Appendix D (Continued) Table D.5 Critical TWLTL Sections for District 5 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 575010000 2.032 2.3 7 51,500 55 0 575050000 0.232 0.491 12 46,500 55 0 575050000 5.44 5.8 53 39,600 45 4.63 575060000 5.34 5.85 43 48,583 45 19.61 575060000 5.85 6.786 41 48,409 45 23.5 577120000 4.228 4.45 18 54,950 45 15.02 577120000 4.45 4.825 16 53,450 45 8.89 4 577120000 4.825 4.987 37 54,891 45 47.33 511040000 4.83 5.285 37 44,688 45 11.72 570100000 10.144 10.586 38 47,209 45 20.36 575003000 4.995 7.078 56 56,037 45 30.4 575003000 7.078 7.197 67 51,594 45 44.82 575003000 7.638 7.825 48 45,091 50 39.22 575010000 5.967 6.745 45 47,453 45 40.7 575010000 7.252 7.578 43 44,273 45 11.25 575010000 7.578 8.024 72 44,000 45 15.7 575010000 8.271 8.564 78 44,353 45 19.34 575010000 8.792 10.045 71 45,560 45 22.08 575010000 10.045 11.065 62 50,398 45 28.76 577010000 0.963 1.385 45 62,000 45 15.8 592030000 0.29 0.51 64 43,000 45 9.09 592030000 0.51 0.625 43 45,000 45 2.9 592090000 12.759 12.867 28 60,838 45 46.3 592090000 12.867 13.37 64 60,906 45 18.56 Higher Speed 6 592090000 13.37 13.774 52 59,952 45 18.98 PAGE 95 84Appendix D (Continued) Table D.5 Critical TWLTL Sections for District 5 in Florida (Contd.) Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 511040000 2.32 2.715 84 30,333 35 5.06 511040000 4.015 4.095 62 28,500 35 16.67 536010000 14.711 14.823 116 28,000 40 2.98 536010000 14.823 15.226 94 29,222 40 7.44 536080000 0.47 0.81 79 27,400 35 9.8 570140000 1.057 1.457 62 29,750 40 20 575006000 0.138 0.929 71 33,833 35 6.32 575006000 0.929 1.034 114 31,333 35 19.05 575010000 12.347 12.902 41 31,385 35 23.42 575030000 4.881 5.977 63 34,581 35 11.25 575040000 11.855 12.283 35 34,332 35 22.59 575040000 12.283 12.525 58 30,000 35 2.75 575050000 15.44 15.789 63 33,000 40 0 575060000 0 1.88 43 49,227 40 26.95 575060000 1.88 2.18 63 45,444 40 20 575060000 2.18 2.653 59 46,776 40 20.44 575060000 19.653 20.309 82 46,000 35 0 575060000 20.309 20.804 56 48,000 35 0 575260000 3 3.08 88 26,000 40 0 579030000 3.228 4.277 66 30,290 40 9.85 579030000 4.302 5.515 72 27,444 40 2.47 579040000 7.52 8.2 66 30,219 40 7.84 579040000 8.2 8.265 62 31,000 40 10.26 Lower Speed 4 592010000 11.726 12.229 111 25,967 40 9.94 PAGE 96 85Appendix D (Continued) Table D.5 Critical TWLTL Sections for District 5 in Florida (Contd.) Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 511040000 4.622 4.83 106 45,000 35 12.82 536001000 24.07 24.959 79 29,563 35 12 536003000 0 0.673 67 36,050 35 4.95 570010000 16.24 17.168 71 36,938 40 5.75 570020000 0 0.413 68 41,643 40 5.65 570020000 0.413 0.83 62 40,500 40 3.2 570020000 2.721 3.865 69 47,250 40 11.07 570020000 3.96 4.22 85 46,250 35 5.13 570020000 4.22 4.511 103 37,938 40 9.16 575250000 5.898 6.016 34 40,000 40 11.3 592030000 0 0.29 76 42,875 40 9.2 592090000 13.774 14.07 71 60,982 40 12.39 592090000 14.07 14.95 74 49,337 40 29.55 Lower Speed 6 592090000 14.95 15.386 55 48,935 40 23.7 PAGE 97 86Appendix D (Continued) Table D.6 Critical TWLTL Sections for District 6 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 4 Higher Speed 6 2 6870010007.646 7.874 57 37,143 40 10.23 6870080007.896 10.117 66 27,787 40 11.26 68703000011.722 11.857 15 35,214 30 17.28 68703000012.89 13.835 33 36,225 30 17.99 68703000015.574 16.14 34 33,375 35 14.13 68703000016.14 16.5 47 39,688 35 7.41 68703000018.057 19.261 41 31,256 35 24.92 6870440007.978 8.466 59 37,720 35 17.08 6870530001.663 6.029 57 36,269 40 15.04 6870620004.57 5.064 51 35,522 40 15.52 6870720003.864 5.161 57 29,377 40 18.76 68709000010.412 10.512 20 42,125 40 40 68709000010.512 12.263 27 40,305 40 21.51 68709000012.263 13.493 17 39,628 40 20.05 68712000010.245 13.159 59 39,591 35 21.96 68712000013.387 14.385 43 33,525 35 27.05 6871400005.649 5.71 82 29,500 40 60.11 6872810000 2.617 21 35,924 40 4.2 6872810005.837 6.663 25 36,281 35 6.46 4 6872810006.663 8.185 45 35,966 40 9.64 68703000011.419 11.722 20 38,571 30 7.7 Lower Speed 6 6872810005.645 5.822 23 40,000 35 13.18 PAGE 98 87Appendix D (Continued) Table D.7 Critical TWLTL Sections for District 7 in Florida Posted Speed Level Number of Lanes Road ID Begin Milepost End Milepost Access Density ADT Posted Speed Avg Crashes 2 710130000 3.806 3.874 132 29,325 45 98.04 710130000 4.5 4.796 44 41,036 45 15.77 4 715120000 5.65 5.723 27 53,500 50 9.13 710030000 1.554 1.697 112 43,125 45 9.32 710030000 1.798 2.166 76 43,040 45 22.64 710030000 2.36 3.014 73 42,771 45 17.84 710130000 8.827 8.926 61 49,375 45 13.47 710130000 9.596 9.789 78 64,984 45 55.27 710160000 0.265 0.646 63 74,224 45 25.37 710160000 0.899 1.24 62 78,722 45 17.6 710160000 1.24 1.939 44 77,500 45 0 715040000 4.693 4.843 13 50,833 45 6.67 715040000 4.947 5.541 71 52,850 45 16.84 Higher Speed 6 715040000 5.841 5.911 43 52,167 45 14.29 715020000 0 1.073 79 21,692 30 4.04 715020000 3.67 4.952 83 25,167 40 1.56 2 715020000 7.571 9.23 33 28,174 40 4.62 715007000 3.544 3.798 83 28,100 40 6.56 715040000 0.803 1.034 82 25,700 35 14.43 715090000 1.254 2.227 99 24,709 35 3.77 4 715090000 2.227 2.338 117 29,667 40 9.01 702000000 14.203 14.545 99 26,450 40 9.75 710030000 0.052 0.449 86 41,568 40 36.94 710030000 0.545 0.9 79 41,688 40 30.05 Lower Speed 6 710030000 1.064 1.441 61 42,921 40 55.7 PAGE 99 88 xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001469388 003 fts 006 med 007 cr mnuuuuuu 008 040524s2004 flua sbm s0000 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0000289 035 (OCoLC)55730731 9 AJR1142 b SE SFE0000289 040 FHM c FHM 090 TA145 1 100 Peng, Haolei. 0 245 Effects of twoway leftturn lane on roadway safety h [electronic resource] / by Haolei Peng. 260 [Tampa, Fla.] : University of South Florida, 2004. 502 Thesis (M.S.C.E.)University of South Florida, 2004. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 99 pages. 520 ABSTRACT: Twoway leftturn lane (TWLTL) is one of the common median treatments on the roadway. It is found that a number of crashes reported in Florida State are related to TWLTLs. This research focused on evaluating the effect of TWLTLs on these crashes by using the statistical crash prediction model that can estimate the expected number of crashes on TWLTLs. The crash database for analysis was extracted from the Florida Traffic Crash Database based on the TWLTL section list provided by FDOT and combined with some traffic characteristics. It consisted of totally 1688 sample sections within a threeyear period from 1996 to 1998. Based on the crash database, distribution fittings for Poisson, Negative Binomial and Lognormal regression were conducted for average number of crashes. According to the results, statistical crash predictive model was developed to estimate the average number of crashes. Negative Binomial regression was applied with four variables, ADT, access density, posted speed and number of lanes for the TWLTL sections. The regression parameters were estimated by using maximum likelihood method with statistical software. The findings of the analysis indicated that all of the variables adopted in the predictive model significantly affect the occurrence of crashes. And the average number of crashes increases with the increase of ADT, access density and number of lanes, while with the decrease of posted speed. After that, the goodnessoffit of developed model was performed in term of Pearson's Rsquare and likelihood ratio index. The results showed that the Negative Binomial regression model could explain the relationship between the variables and the crash occurrence In the third part, an approach was developed to identify the TWLTL sections with safety concern. For an undivided roadway, the approach can be carried out to judge if the TWLTL is appropriate to be selected as the median treatment. During the process, the whole database was divided into six categories according to the posted speed and number of lanes. By adopting the selected percentile value from the distribution of average number of crashes for each category in the predictive model, the critical ADT values according to specific access density, number of lane and posted speed level for each category were calculated and tabulated. With the comparison of the actual ADT value and the critical ADT value, if the actual ADT is higher than the critical value, the TWLTL section is determined as the critical section, which means the TWLTL is not appropriate to be selected as the median treatment in this roadway section. 590 Adviser: Jian John Lu 653 critical section. number of lanes. average number of crashes. distribution. prediction model. access density. posted speed. ADT. 690 Dissertations, Academic z USF x Civil Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.289 