UNIVERSITY OF TORONTO CONFLICT ANALYSIS USING MICROSIMULATION MODELING CHRISTIAN BACHMANN

Transcription

1 UNIVERSITY OF TORONTO CONFLICT ANALYSIS USING MICROSIMULATION MODELING BY CHRISTIAN BACHMANN A THESIS SUBMITTED TO THE FACULTY OF APPLIED SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF APPLIED SCIENCE CHRISTIAN BACHMANN DEPARTMENT OF CIVIL ENGINEERING TORONTO, ON APRIL 2009

2 Department of Civil Engineering Faculty of Applied Science and Engineering University of Toronto Unsupervised Term Work Statement CIV 499H1 S Thesis I hereby certify that I am thoroughly familiar with the contents of this thesis. It is substantially my own work, I have referenced all my sources of information, and I am the sole author. Name (Please print): Christian Bachmann Student No.: Supervisor s Name: Matthew J. Roorda and Baher Abdulhai Student s Signature Date Submitted: April 10 th, 2009 ii

3 ABSTRACT Transportation agencies have traditionally relied on historical crash records as the primary indicator to measure the safety of roadways. Due to the infrequent and sporadic occurrence of accidents, and the long period of time required to collect such accident data, surrogate safety measures have been developed. One of the more prevalent surrogate measures of safety is the conflict, an observable situation in which two or more road users approach each other in time and space to such an extent that there is risk of collision if their movements remain unchanged. In 2003, the Federal Highway Administration (FHWA) provided a framework for conflict analyses using microsimulation modeling. The algorithm developed by the FHWA involved a simplified calculation of the time to collision (TTC), which was adopted in subsequent studies. This study presents a different approach to calculating the TTC based on the theoretical collision point of the two vehicles. The simplified approach is then contrasted with this new theoretical approach to investigate the impact these have on creating meaningful conflict rates by number and by type. To examine the differences further, the speed and acceleration rate of the following vehicle in each conflict were analyzed. Lastly, the conflict algorithms were applied to a microsimulation of the 400 series highways in the Greater Toronto Area (GTA), where no conflict analysis has been done previously. The results of the simulation runs showed that significant differences between the simplified approach and the theoretical approach to calculating the TTC exist. The simplified approach underestimates the TTC and thus produces inflated conflict rates. Notably, two cases were identified where the simplified approach is calculating a TTC where one does not even exist. Further, the theoretical approach practically eliminates the unexpected acceleration behaviour of the following vehicle in rear-end conflicts. iii

4 ACKNOWLEDGEMENTS I am grateful to the many people who helped me, both directly and indirectly, in preparing this thesis. During the progression of this work I have accumulated many debts, only a part of which I have space to acknowledge here. I want to express my gratitude to my friends, family and colleagues, whose support and encouragement kept me motivated to do my best. The research I carried out builds on work done by Samah El-Tantawy and Shadi Djavadian to whom I thank for providing me with a suitable starting point. I would like to acknowledge the help of Asmus Georgi who oriented me in the ITS lab and helped me get started. Similarly, I would like to thank Hossam Abd El-Gawad for his continuous help with the Paramics software when the manuals did not suffice. I wish to express my gratitude to Professor Baher Abdulhai for inspiring me to do an undergraduate thesis in transportation engineering. Likewise, I would like to thank Professor Matthew Roorda for quickly becoming involved and providing continual guidance and encouragement. Working with two exceptional professors has been a privilege that most undergraduate students do not receive. Conducting this thesis has been a tremendous learning experience for me; I hope the end result is educative to its readers as well. iv

5 TABLE OF CONTENTS ABSTRACT... iii ACKNOWLEDGEMENTS... iv LIST OF TABLES... vii LIST OF FIGURES... viii NOMENCLATURE... x 1. INTRODUCTION Background Conflicts as a Measure of Safety Application of Conflicts in Highway Studies Conflicts as a Measure of Safety Using Microsimulation Modeling Study Objectives Structure of the Thesis THEORETICAL CONSIDERATIONS Conflict Types Rear-End Conflict Lane-changing and merging conflict Sideswipe conflict Time To Collision PROCEDURES Paramics Suite Paramics Modeller v

6 3.1.2 Paramics Processor Paramics Programmer Implementing Conflict Algorithms in a Microscopic Traffic Simulation Project Process Warming Up Programming Analysis RESULTS AND DISCUSSION Comparing Calculations of TTC TTC Distributions Investigating different thresholds Series Highways Analysis CONCLUSIONS RECOMMENDATIONS REFERENCES APPENDICES vi

7 LIST OF TABLES Table 1: A comparison of conflict rates based on two approaches Table 2: Conflict rates for different TTC thresholds using the theoretical approach Table 3: Conflict rates on the 400 series highway network Table 4: Vehicle Operating Characteristics Table 5: Paramics Core Configuration Options Table 6: Lane-change Conflicts, Simplified Approach, 0.5 sec TTC Table 7: Merging Conflicts, Simplified Approach, 0.5 sec TTC Table 8: Rear-end Conflicts, Simplified Approach, 0.5 sec TTC Table 9: Lane-change Conflicts, Theoretical Approach, 0.5 sec TTC Table 10: Merging Conflicts, Theoretical Approach, 0.5 sec TTC Table 11: Rear-end Conflicts, Theoretical Approach, 0.5 sec TTC Table 12: Conflict Summary, Theoretical Approach, 0.5 sec TTC threshold Table 13: Conflict Summary, Theoretical Approach, 1.5 sec TTC threshold Table 14: Conflict Summary, Theoretical Approach, 2.5 sec TTC threshold Table 15: Conflict Summary, Theoretical Approach, 3.5 sec TTC threshold Table 16: Conflict Summary, Theoretical Approach, 4.5 sec TTC threshold Table 17: Conflict Summary, Theoretical Approach, 5.5 sec TTC threshold Table 18: Lane-change conflicts on 400 series highway network Table 19: Merging conflicts on 400 series highway network Table 20: Rear-end conflicts on 400 series highway network vii

8 LIST OF FIGURES Figure 1: A traffic conflict with a cross-street vehicle (Parker et al. 1989)... 2 Figure 2: Gardiner Expressway Network (Djavadian et al. 2008)... 7 Figure 3: SSAM Operational Concept (Gettman et al. 2008)... 9 Figure 4: The 400 series highway network Figure 5: Rear-end conflict time-space diagram (Gettman and Head 2003) Figure 6: Lane-changing/merging conflict time-space diagram (Liu and Garber 2007) Figure 7: TTC as defined in previous literature (a simplified approach) Figure 8: TTC as calculated in this study (theoretical approach) Figure 9: TTC when the leading vehicle is travelling faster than the following vehicle Figure 10: TTC when the leading and following vehicles have the same speed Figure 11: Procedure Summary Diagram Figure 12: Lane Change Algorithm. (Adapted from Djavadian et al. 2008) Figure 13: Comparison of conflict type proportions based on two approaches Figure 14: Rear-end conflicts using the simplified approach Figure 15: Merging conflicts using the simplified approach Figure 16: Lane-change conflicts using the simplified approach Figure 17: Rear-end conflicts using the theoretical approach Figure 18: Merging conflicts using the theoretical approach Figure 19: Lane-change conflicts using the theoretical approach Figure 20: Distribution of lane-change conflicts Figure 21: Distribution of merging conflicts Figure 22: Distribution of rear-end conflicts viii

9 Figure 23: Pie chart of conflict types on 400 series highway network Figure 24: Rear-end conflicts using the theoretical approach Figure 25: Merging conflicts using the theoretical approach Figure 26: Lane-change conflicts using the theoretical approach ix

10 NOMENCLATURE ADT API DLL DR FHWA GTA FVA LGV LVA MOE OGV PET PFI PMTT SSAM TCT TRJ TTC = Average Daily Traffic = Application Program Interface = Dynamically Linked Libraries = Deceleration Rate = Federal Highway Administration = Greater Toronto Area = Following Vehicle Attributes = Light Goods Vehicle = Leading Vehicle Attributes = Measure of Effectiveness = Other Goods Vehicle = Post-encroachment Time = Potential For Improvement = Predefined Maximum Tracing Time = Surrogate Safety Assessment Model = Traffic Conflict Technique = The filename extension for vehicle trajectory files. = Time to Collision x

11 1. INTRODUCTION 1.1 Background Crashes are complex in nature because a large number of variables are contributing to their occurrence. Factors such as human behaviour, road conditions, and vehicle failures play a role in 94 percent, 34 percent and 12 percent of crashes respectively (Gettman et al. 2008). Transportation agencies studying the safety of their roadways generally use historical crash records as the primary measure of safety. Once a specific location is identified as having a high number of crashes, the location is further studied to determine possible fixes to reduce the risk of crashes; but there are problems with relying on accident data. For example, all accidents are not reported. Sometimes data errors and incomplete information are found in accident records. Also, accidents are fairy infrequent and happen sporadically, so a long period of time is needed to collect enough accident data to be useful (Parker et al. 1989). In order to assess the safety of traffic facilities more effectively, surrogate safety measures were developed. Surrogate safety measures are measures of safety that are not based on a series of actual crashes. These techniques are of interest for two particular needs: to assess the safety of traffic facilities without waiting for statistically significant abnormal or relatively greater number of crashes to actually occur, and to assess the safety of experimental roadway design or operational strategies before they are actually built or employed in the field. Several different surrogate safety measures have been examined in various studies including: vehicle delay or travel time, approach speed, percentage of stopped vehicles, queue lengths, stopbar encroachments, red-light violations, percentage of left turns, speed distribution and deceleration distribution. The most prevalent literature focuses on observing traffic conflicts. A conflict is defined as an observable situation in which two or more road users approach each other in time and space to such an extent that there is risk of collision if their movements remain 1

12 unchanged (Amundsen and Hyden 1977) (see figure 1). Conflicts can be categorized by the type of driving manoeuvre and by several measures of severity. In the past, identifying traffic conflicts was conducted by field observers who watched for strong braking and evasive manoeuvres at intersections (Parker et al. 1989). The main criticism of this technique is the uncertainty associated with the collection of accurate data due to the subjectivity of individual observers. Nonetheless, the method described above has been shown to have some correlation to crash prediction and there is a general consensus that higher rates of conflicts indicate lower levels of safety (Gettman et al. 2008). Figure 1: A traffic conflict with a cross-street vehicle (Parker et al. 1989) 1.2 Conflicts as a Measure of Safety The traffic conflict technique (TCT) was originally developed to investigate whether General Motors vehicles were driven differently than others. The method was soon adapted to evaluate accident potential and operational deficiencies at intersections. It was believed that a direct 2

13 relationship between accidents and conflicts existed but many efforts to verify such a relationship had been unsuccessful. Glauz et al (1985) set out to suggest normal and abnormal levels of conflict rates and illustrate that a reasonable agreement does exist between conflicts and accidents. Their study collected conflict and accident data at 46 urban intersections (signalized and unsignalized) located in the greater Kansas City metropolitan area in the Unites States. Their work produced tables of daily conflict rates for intersections based on volume and signal control. The procedure for validating the use of traffic conflicts as accident surrogates was as follows. Within each class of intersections, two locations were randomly selected. With the conflict rates and variances obtained from the study, the expected accident rates and their variances were computed and compared with those based on the average of actual accident counts. Overall, for the set of intersections and conflict types considered, the total number of accidents based on conflicts was estimated to be 18.20, extremely close to the expected number based on accidents of The actual total number of accidents for the year predicted was 20. This suggests conflicts are nearly as good at predicting accidents as previous accidents. Their study also showed that estimates of expected accidents based on both history and conflict data can be combined to produce an estimate that is more precise than would be obtained by using either one individually. Overall, Glutz et al (1985) concluded that traffic conflicts of certain types are good surrogates of accidents in that they produce nearly as accurate and precise estimates as those produced from historical accident data. A TCT study should be very helpful in predicting safety when sufficient accident data is unavailable. Their study is frequently referenced as the basis for future conflict studies. More recently, projects have been undertaken to evaluate the ability of simulation models to output meaningful measures of safety based on the occurrence of conflicts during the simulation. 3

14 Traditionally, microscopic traffic simulation models have been used to predict the performance of transportation facilities before they are constructed, but provided no safety guidance to analysts. In 2003, the Federal Highway Administration (FHWA) released a report titled: Surrogate Safety Measures From Traffic Simulation Models that introduced the idea of using traffic simulation models for obtaining surrogate safety measures. The approach suggests collecting detailed data on all conflict events that occur between any two vehicles during the simulation. Two requirements are suggested for recording a conflict event: one of the vehicles makes an evasive action to avoid a collision, and the resulting surrogate measure must be a significant value (i.e. less than a predefined threshold). They propose a number of surrogate measures to collect: minimum time to collision (TTC), minimum post-encroachment time (PET), maximum speed of the two vehicles, maximum difference in speed between the two vehicles during the conflict event, initial deceleration rate (DR) of the reacting vehicle, and the location of the start and end points of the conflict event. Computational algorithms for calculating surrogate measures for different conflict types were described and example diagrams were shown to illustrate the calculations graphically. Lastly, an event file that could be produced by simulation models was presented. The data recorded to this file is essentially a time history of the speed, acceleration, and location of vehicles that are candidates for conflict events. The event file could be supported by the simulation model developers and read by a separate module and post processed. The entire process of computing, extracting, and analyzing the surrogate safety measures from traffic simulation models has been denoted as SSAM (Surrogate Safety Assessment Model). 4

15 1.2 Application of Conflicts in Highway Studies Motivated by continuous growth of freight transportation over recent years, Liu and Garber published a study in 2007, titled: Identifying the Impact of Truck Lane Restriction Strategies on Traffic Flow and Safety Using Simulation. Truck lane restriction strategies are expected to reduce the interaction between trucks and passenger cars and therefore reduce highway crashes, as well as increase traffic mobility. In previous research of truck lane restriction strategies, only conventional measures of effectiveness (MOEs) such as lane changes and speed differentials were considered. Their study uses the conflict as a measure of safety for at least two explicit reasons: the conflict measure has been proven to be highly related to traffic crashes on freeways according to them, and the high frequency of conflicts makes it possible to collect adequate data for statistical analysis. Their study focused on evaluating safety by varying lane restriction strategies, traffic conditions, and geometric characteristics. Liu and Garber used the framework for conflict analysis presented by the FHWA in They modified the definitions of different conflicts to fit the case of a highway, as the types described by the FHWA were specific to intersections. The conflict data they collected from simulation runs consisted of lane-changing, merging, and rear-end conflicts. The lane-changing classification is defined as a conflict between a vehicle that makes a lane-changing manoeuvre and the vehicle following immediately after it in the same lane. The rear-end classification is defined by conflicts between a vehicle that suddenly reduces its speed and the vehicle following behind it in the same lane. The merging classification is similar to the lane-changing type, only the leading vehicle is merging to the highway from a ramp. While the SAMM approach suggested to analyze exported vehicle trajectory data once the simulation run is over, Liu and Garber s methodology analyses conflicts at each simulation time step while the simulation runs. In the simulation, the process of tracing a potential conflict is 5

16 triggered by a lane changing manoeuvre, a merging manoeuvre, or a sudden braking manoeuvre. Once one of these conditions is satisfied, the position, speed and acceleration of the vehicles involved in the potential conflict will be traced at each simulation time step for a certain period. At each time step, the TTC is calculated. The minimum of all TTCs calculated in the tracing period is then regarded as the final TTC. If this value is less than a certain threshold a conflict is recorded. Liu and Garber developed this methodology through the use of the Paramics software suite. The Paramics Modeller was used to build up the simulation network, set up the truck lane restriction strategies and to input the traffic data. The Paramics Programmer was used to develop a plugin embedded in Paramics Modeller to compute the safety measures and extract the data as described above. The advanced Application Program Interface (API) functions in Paramics Programmer can pass additional configuration parameters into the simulation, read or write information from the network and increase the data analysis by tracing vehicles throughout the simulation. Therefore, the combination of Paramics Modeller and Paramics Programmer made it possible to create a microsimulation model of truck lane restriction strategies and a plugin to analyze conflicts in the model. Djavadian et al. (2008) analyzed truck restricted lanes and dedicated truck lanes on the Gardiner Expressway in Downtown Toronto. In their study, simulation scenarios were developed by varying lane strategies and truck percentages. Similar to the study done by Liu and Garber, each of the scenarios are evaluated and tested based on conflict-based measures of effectiveness also using the Paramics microsimulation software suite. Their study essentially builds upon the work of Liu and Garber by extending the scope of work to include the analysis of dedicated truck lanes as well as truck restricted lanes. In addition, their work provides a real network application as opposed to a hypothetical experiment. This study based its definitions for conflicts, including 6

17 lane-changing, merging, and rear-end conflicts, on the definitions provided by Liu and Garber. The primary occurrence measure of conflicts used in this research is the TTC which is defined as the expected time for two vehicles to collide if they remain at their present speed and on the same path. The algorithm used in this study is based on the definition developed by FHWA, which computes TTC as the time it takes the encroaching vehicle to reach the current position of the other vehicle if the encroaching vehicle remains at its present speed on the same path. Note the discrepancy between the theoretical definition of TTC and how it was calculated in the simulation. Their algorithm finds a different value than the theoretical TTC because it calculates the magnitude of TTC based on the original position of the leading vehicle. Nevertheless, this is how Liu and Garber calculated TTC in their study as well. The micro simulation conducted by Djavadian et al. (2008) includes the Gardiner Expressway from Bathurst Street in the West to the Don Valley Parkway in the East. The network also includes a buffer area extending from the Toronto Waterfront in the South to Front/Wellington Street in the North (see figure 2). The network consists of 564 nodes, 1333 links, and 51 zones. 47 traffic signals were coordinated to reflect signal timing plans provided by the City of Toronto. In addition, the aerial photographs were used to establish geometric accuracy and traffic counts were used to calibrate driver behaviour patterns. Unfortunately, truck percentages were assessed on a scenario basis because adequate data on truck origin destination flows is not collected in the Toronto Area. Figure 2: Gardiner Expressway Network (Djavadian et al. 2008) 7

18 Four lane strategies were tested: no restriction, restricting trucks from using the leftmost lane, restricting trucks from the two leftmost lanes, and dedicating the leftmost lane to trucks (trucks are permitted to use other lanes as well). A total of 360 traffic simulation runs were conducted: Number of simulation runs = 4 (strategies) * 3 (truck %s) * 3 (MOEs) * 10 (random seeds) = 360. As a result of these simulation runs, a number of pertinent observations were made regarding truck traffic and its effect on traffic conflicts. An increase of truck percentages results in an increase in the frequency of lane changes. However, there is a substantial decrease in total lanechanging conflicts with an increase in truck percentage. Increases in truck percentage also decrease the frequency of car-car lane-changing conflicts and increase truck related conflicts. This result is intuitive as there is an increase in truck exposure and decrease in car exposure. Dedicating the leftmost lane to trucks also tends to reduce truck related lane-changing conflicts by 17-21%. Truck related merging conflicts increase with an increase in truck percentage, likely caused by the increase in the number of trucks on the unrestricted rightmost lane which is used for merging. Dedicating the leftmost lane only to trucks results in an increase in the frequency of truck related merging conflicts, possibly due to increased levels of congestion in the rightmost lane due to the reduced capacity available for cars. Rear-end conflicts occurred less, one third as often as merging conflicts and between 0.5 to 2 percent as often as lane changing conflicts. According to the analysis of variance, different truck lane restriction strategies have significant impact on lane-changing and merging conflicts; they were not shown to have a statistically significant affect on rear-end conflicts. With an increasing proportion of trucks on the Gardiner Expressway, their model predicts a decrease in the number of total lane changing conflicts, an increase in the number of merging conflicts, and an increase in the number of rear end collisions. 8

19 1.3 Conflicts as a Measure of Safety Using Microsimulation Modeling By the summer of 2008, the FHWA combined traffic simulation and automated traffic conflict analysis to develop a software utility referred to as Surrogate Safety Assessment Model (SSAM), which is compatible with four traffic simulation software suites: AISUN, PARAMICS, TEXAS, and VISSIM. SSAM classifies conflicts and computes a series of surrogate safety measures from a trajectory file (TRJ) that is generated from one of the above software suites after a simulation is complete. Furthermore, the utility provides basic visualization and statistical features to facilitate analysis and generate reports. See figure 3 below: Figure 3: SSAM Operational Concept (Gettman et al. 2008) The FHWA made three distinct efforts to validate SSAM: a sensitivity analysis, a theoretical validation and a field validation. The purpose of the sensitivity analysis was merely to capture the differences between simulation software suites. The main purpose of the theoretical validation was to determine if the surrogate measures computed with the SSAM approach could discriminate between intersection layouts in a simulation model. In addition, the theoretical validation could identify any correlations between the surrogate safety measures produced by the SSAM approach and existing models from literature. The main purpose of the field validation effort was to correlate the conflicts produced by microsimulation models with actual crash data in North America. Traditional volume-based crash prediction models are used as a basis for 9

20 comparison as well. The field validation consisted of five tests to assess the predicative safety performance abilities of microsimulation modeling. In the first test, the ranking of intersections from SSAM according to the average conflict frequency is compared to the ranking of the same intersections based on actual statistical crash records. Each intersection was simulated five times for one hour. The sum of the total conflicts occurring over all five simulations was computed and then divided by five to determine the average hourly conflict frequency. For comparison, the average yearly crash frequency for each intersection was determined by at least three years of statistical crash data. Finally, the intersection rankings based on average hourly conflict frequency is compared to the intersection rankings based on average yearly crash frequency. The Spearman rank correlation coefficient value of this ranking comparison was 0.463, which is significant at a 95-percent level of confidence. This suggests that a significant correlation between intersection rankings based on simulated average hourly conflict frequency and yearly crash frequency was found. It should be noted that the results of this comparison are based on simulation of the AM peak-hour volumes and not the ADT values, suggesting an even superior correlation could be derived from a more comprehensive simulation. The second test is similar to the first, but the intersections are ranked by incident types. The following incident types were considered: rear end, crossing, and lane-changing. The results of this test were aimed to determine the capability of SSAM to accurately identify and rank intersections that have a high risk for a specific crash type. The results showed significant differences between conflict distributions by type and actual crash distributions by type. The conflicts per hour to crashes per year ratios were found to be 0.01, 2.06, and 0.65 for crossing, rear-end, and lane-changing respectively. The FHWA suggest it is plausible that the conflicts-to- 10

21 crashes ratios may be lower for more severe incidents and higher for less dangerous incidents. The Spearman rank correlation coefficient value for the rear-end incident and lane-changing incident ranking were and respectively, both of which are significant at the 95- percent level of confidence. Unfortunately, there were too few crossing conflicts recorded to perform its ranking comparison. Therefore, this test demonstrated a significant correlation between rear-end conflicts and rear-end crashes, and between lane-change conflicts and lane change crashes. The third test was used to correlate conflicts and crashes by developing a regression equation to estimate average yearly crash frequencies at an intersection as a function of hourly conflict frequencies found by SSAM. The result intends to develop a conflict based model for crash prediction. Three statistical measures were considered to determine the goodness of fit of the models to the real world data: Pearson chi-squared, scaled deviance, and the R-squared. Two models were developed: A normal linear regression model for crashes as a function of conflicts, Ln(Crashes) = 1.09 Ln(Conflicts) 0.98, and a nonlinear regression model for crashes as function of conflicts, Crashes = Conflicts The R-squared values of 0.27 and 0.41 for the linear and nonlinear regression models are low but in the range of correlations found with traditional crash prediction models studied by the FHWA. The fourth test was conducted to indentify incident prone locations. A conflict prediction model was developed to predict intersection conflict frequency as a function of intersection traffic volume. Similarly, a crash prediction model was developed to predict intersection crash frequency as a function of intersection traffic volume. Then, the two models were compared to determine whether or not the conflict prediction model can predict risk in the same way a crash prediction model can for intersections with the same characteristics. This comparison is made by 11

22 the identification and ranking of incident prone locations. The crash prediction model indentified 20 crash-prone locations, while the conflict prediction model identified 12; only one incidentprone intersection was identified by both models. The Spearman rank correlation coefficient values of the ratio and potential for improvement (PFI) intersection ranking comparisons were and 0.033, implying very insignificant correlation between intersections with excessive crashes and intersections with excessive conflicts. The fifth test is similar to the fourth, but the identification of type specific incident prone locations is considered. No significant correlations were found with respect to indentifying or ranking incident prone locations by specific type. The results of the validation effort demonstrated that the surrogate measures derived by microsimulation models were significantly correlated with actual crash data in the field, with some exception. For comparison, traditional safety assessments based on average daily traffic volumes were compared to the conflicts based safety assessment. The traditional assessments provided by this study did show better correlations to crash history than did the surrogate measures from simulation. Nonetheless, the effort found that correlation between simulated conflicts and actual crashes is significant. Summarizing, the validation effort of safety assessment by conflict analysis of micro simulations shows potential but the results are not definitive, especially to highway studies since intersections were the focus of their analysis. 1.4 Study Objectives Ideally, this project would provide a first real world application for the SSAM software just developed a few months ago. While the software is available freely to the public from Siemens Energy and Automation, there is no site for direct download yet. Upon contacting Siemens Energy and Automation, Steve Shelby provided a fully functional prelease edition of the 12

23 software utility for research purposes. After a few small scale tests on individual intersections, SSAM appeared to be functioning correctly. Unfortunately, because the software was developed to analyze conflicts predominantly at intersections, there is an inherent limit on the size of the area of analysis that can be handled by SSAM. Upon trying to analyze a trajectory file generated from a Gardiner Expressway simulation, SSAM noted that the area of analysis was too large and the operations were aborted. Considering the Gardiner Expressway simulation model was too large, the 400 series highway network (figure 4) could not be analyzed with SSAM either. The microsimulation model of the 400 series highways includes Highways 403, 407, 410, 401, 427, 409, 400, 404, the Queen Elizabeth Way (QEW), the Don Valley Parkway (DVP) and the Gardiner Expressway. The 401 segment begins just before Winston Churchill Blvd in the west, and terminates just past Brock Rd in the East. The 407 segment starts in Burlington and ends at Brock Rd in the East. The 403 also terminates in Burlington. The network consists of 4307 nodes, 8472 links, and 673 zones. Therefore, in light of taking this opportunity to assess the capabilities of SSAM, the methodology used in this project is similar to that of Liu and Garber and Djavadian et al., and is described in the procedures section. The objectives of this study were as follows: Review literature regarding the relationship between conflicts and accidents. Improve the conflict algorithm by revising the calculation of TTC. Investigate the differences between the simplified and theoretical approaches to calculating TTC in generating conflict rates. Implement the improved algorithm into a new and more realistic environment, the 400 series highways, where future truck lane restrictions or dedicated truck lanes might be considered. 13

24 Collect more detailed information of each conflict that occurs. Deceleration rate (DR) and absolute speed were highly recommended in previous studies PICKERING BRAMPTON TORONTO DVP QEW 407 OAKVILLE 403 BURLINGTON Figure 4: The 400 series highway network 14

25 1.5 Structure of the Thesis Chapter 1 examined the state of current knowledge in the field of conflict analysis to establish the context of this study. The remainder of the report is organized as follows: Chapter 2 discusses the different conflict types considered in this study, and gives detailed algorithms of the different approaches to calculating TTC. Chapter 3 presents the Paramics microsimulation software and describes how the conflict algorithms were implemented in this software suite. In addition, the project process is reviewed. Chapter 4 shows the results of the analysis and a discussion of these results. Chapter 5 presents the conclusions based on the literature reviewed and the results of the microsimulation modeling. Chapter 6 provides recommendations following from the conclusions drawn in the previous chapter. 15

26 2. THEORETICAL CONSIDERATIONS 2.1 Conflict Types The three types of conflicts considered are: rear-end, lane-changing, and merging. Sideswipe conflicts are not investigated Rear-End Conflict The braking done by the leading vehicle is the indicator of the need to check for a rear-end conflict event. A timeline of a rear-end conflict event is illustrated in figure 5 below. The topmost curve represents the time-space trajectory of the following vehicle which is continuing straight. The bottommost curve represents the time-space trajectory of the leading vehicle which in this example is slowing down to turn off the road. Figure 5: Rear-end conflict time-space diagram (Gettman and Head 2003) 16

27 At time t 1, the leading vehicle begins to decelerate to turn off the current road At time t 2, the following vehicle beings to brake to avoid a collision At time t 3, the next simulation time-step begins and the vehicle tags are updated. At time t 4, the following vehicle would have reached the first encroachment point if it had not braked to avoid the leading vehicle. The other times can be interpreted similarly. The predefined maximum tracing time (PMTT) is not shown Lane-changing and merging conflict A lane-changing conflict is defined as the conflict between the vehicle that changes to a new lane and the following vehicle in that lane. A merging conflict is similar to that of the lane-changing conflict except that the vehicle is merging from a ramp onto the highway. Figure 6 displays a graphical representation of a lane-changing or merging conflict: Figure 6: Lane-changing/merging conflict time-space diagram (Liu and Garber 2007) 17

28 At time t s, the leading vehicle initiates a lane change manoeuvre into the lane of the following vehicle At time t s +TTC1, the following vehicle would reach the first conflict point if it did not decelerate to avoid a collision. At time t s +Δt, the next simulation time step begins and the vehicle tags are updated. At time PMTT, the predefined maximum tracing time is reached Sideswipe conflict A sideswipe collision occurs when a vehicle in the process of changing lanes strikes an adjacent vehicle in the side, possibly because it: accepts the gap too early, does not see the vehicle because of obstructions, or the vehicle struck has made its own manoeuvre simultaneously. These conflicts are not considered in the safety analysis done here. 2.2 Time To Collision As can be seen in the above diagrams taken from previous studies, the algorithm developed by FHWA (2003) computes TTC as the time it takes the following vehicle to reach the former position of the leading vehicle if the following vehicle remains at its present speed on the same path (see figure 7). 18

29 Distance p l TTC v l v f p l -p f p f t i = current time-step Time TTC* v f = p l -p f TTC = (pl-pf)/vf Figure 7: TTC as defined in previous literature (a simplified approach) This method of calculating TTC is actually a simplification of the actual computation. In reality, the leading vehicle is not always stationary and can continue along its trajectory as well. For this reason, the calculation of TTC in this research has been modified. Below, figure 8 shows how TTC is computed. Note the derivation includes the speed of the leading vehicle while the former calculation did not. 19

30 Distance p l(new) TTC p l p f v l v f p l(new) -p f TTC* v f = p l(new) p f TTC*v f = (p l +v l *TTC) p f TTC(v f v l ) = (p l p f ) TTC = (p l -p f )/(v f -v l ) t i = current time-step Time Figure 8: TTC as calculated in this study (theoretical approach) Note that there is a new constraint placed on the calculation of TTC, being that the leading vehicle must be travelling slower than the following vehicle. Otherwise, no collision could potentially occur between the two vehicles. Therefore, two cases arise where a TTC cannot be computed with the theoretical approach: Figure 9 shows the case of the leading vehicle travelling faster than the following vehicle, which yields a negative time to collision if the equation developed above is applied. Figure 10 shows the scenario if both vehicles have the same speed, for which no time to collision can be calculated. Neither of the two cases described above are conflicts, although a TTC would be computed using the simplified approach. This is an early sign that the simplified approach might yield problematic results since it is calculating a TTC where one does not actually exist in two cases. 20

31 Distance p l v l v f p f TTC = (p l -p f )/(v f -v l ) = negative TTC Time t i Distance Figure 9: TTC when the leading vehicle is travelling faster than the following vehicle. p l v l v f p l -p f p f TTC = (p l -p f )/(v f -v l ) = undefined Time t i Figure 10: TTC when the leading and following vehicles have the same speed. 21

32 3. PROCEDURES 3.1 Paramics Suite Quadstone Paramics is a modular suite of microscopic simulation tools providing an integrated platform for modeling a complete range of real world traffic and transportation systems. The Paramics software is capable of handling an entire city s traffic system or even all of the 400 series highways in the GTA. This suite is used extensively in the ITS lab at the University of Toronto. The Paramics suite includes multiple components: Modeller, Analyser, Processor, Estimator, Designer, Converter, Programmer, and Monitor. The components used for this work are described below Paramics Modeller Paramics Modeller provides the fundamental tools for traffic microsimulation including building a model, running a traffic simulation, and outputting statistical data. Every aspect of the transportation network can be investigated using Modeller in a graphical user interface (GUI). Notably, it allows the user to set a time-step, at which the state of each vehicle can be updated. This makes it possible to investigate the interactions between vehicles and output position, speed, and time data as frequently as desired. In this research, Modeller is used to build up the simulation network and input traffic data. This was done by other colleagues Paramics Processor Paramics Processor is similar to Modeller except that it dramatically increases the speed of each simulation run by eliminating the on screen visualization. In other words, more computer processing power is dedicated to running the simulation as opposed to drawing it on the screen. This component is used to run simulations in batch mode, with different seeds, to obtain quicker results. 22

33 3.1.3 Paramics Programmer Paramics Programmer is a component for advanced users to customize features of the simulation through an API. The Programmer interface includes four function types: those that override standard code, those that extend standard code, those that get a value from the standard code, and those that set a value in standard code. Programmer is implemented via DLL files (dynamic linked libraries). A base plugin is provided by Paramics that includes Microsoft Visual C++ project and workspace files that are used for compiling on the PC Platform. Once the plugin is loaded into Microsoft Visual C++, custom code can be written using the multiple functions offered by Programmer in conjunction with the C programming language. The Programmer is used to develop a plugin embedded in the Modeller to compute the safety surrogate measures at each time-step during the simulation and extract the results to an output file. For the purpose of this study, three plugins were created corresponding to the three types of conflicts being analysed (lane-change, merging, and rear-end). Therefore, it is the Programmer component that allows the SSAM process to be created here using only the Paramics software suite. The interaction of the various programs is summarized below: Paramics Programmer Microsoft Visual Studio Paramics Modeller Plugin.dll OR Paramics Processor Output.txt Figure 11: Procedure Summary Diagram 23

34 3.2 Implementing Conflict Algorithms in a Microscopic Traffic Simulation The conflicts algorithms built for Paramics for each type of conflict are essentially the same with the exception of the triggering condition which was discussed earlier. Figure 12 illustrates how the lane-change conflict algorithm functions within the microsimulation. Notably, each vehicle can be considered in any one of the four cases. In the first case, the vehicle is not being traced and does not make a lane change manoeuvre. Since both tests are negative, the vehicle is disregarded for the current time step. The second case is where the vehicle is not being traced but makes a lane change manoeuvre in the current time step. In this case, the vehicle is tagged and a TTC is calculated. The third case is when the vehicle is being traced and does not make another lane-change in this time-step. If the following vehicle did not change lanes, and the PMTT has not been exceeded, the tag is updated with new LVA (leading vehicle attributes), FVA (following vehicle attributes), and TTC. If the new TTC is smaller than the one calculated at the previous time step, it is retained; otherwise the previous TTC is kept since it is the smaller value. If the following vehicle did change lanes or the PMTT is exceeded, than the TTC associated with the tag is compared to a predefined threshold. If the TTC is lower than the threshold, a conflict event is recorded and the tag is deleted. The fourth case is that when the vehicle being traced (the leading vehicle) makes another lane change manoeuvre. In this case, the TTC associated with the previous lane change is compared to a predefined threshold. If the TTC is lower than the threshold, a conflict event is recorded. Then, the steps considered for case two are performed to track possibility of another conflict as a result of the new lane change manoeuvre. 24

35 Start of Simulation (t=0) No Vehi cl e V is traced Yes Vehicle V changes its lane Vehicle V changes its lane No (Case 3) No (Case 1) Yes (Case 2) Extract Tag Information Yes (Case 4) Extract Tag Information Create vehicle tag, record: Current time step (ts) LVA (id l, type l, v l, p l) FVA: (id f, type f, v f, p f) t ts < PMTT & ID of the following vehicle = idf TTC < τ Yes No Calculate TTC (if possible): TTC = p f p l / v f v l No Yes Conflict Occurred, Save Event Attach ts, LVA, FVA, TTC to Vehicle V as a tag Update vehicle tag, record: Current time step (ts) LVA (id l, type l, v l, p l) FVA: (id f, type f, v f, p f) Delete Vehicle s Tag Calculate n ew TTC (if p ossible): TTC= p f p l / v f v l Keep minimum of previous TTC and new TTC Create new vehicle tag, record: Current time step (ts) LVA (id l, type l, v l, p l) FVA: (id f, type f, v f, p f) Attach ts, LVA, FVA, TTC to Vehicl e V as a tag Calculate TTC (if possible): TTC = p f p l / v f v l TTC < τ Yes No Attach ts, LVA, FVA, TTC to Vehicle V as a tag Conflict Occurred, Save Event Delete Vehicle s Tag t = t + simulation time step Yes t < T (Simulation Time) No Extract Disaggregate Conflict Data Figure 12: Lane Change Algorithm. (Adapted from Djavadian et al. 2008) 25

36 3.3 Project Process Warming Up The first step in this project was re-creating the results produced by Djavadian et al. in the newest version of Paramics (Version 6), which was installed in the ITS Lab at the University of Toronto after their work was complete. This required rebuilding the plugins with the correct libraries and files so that they can be initialized by Paramics Modeller correctly. Microsoft Visual Studio 2008 was used to build the plugins. After this had been done, simulations were rerun on the Gardiner Expressway model to ensure that the plugins were functioning correctly as before. Once this has been verified, changes to the plugins for the purposes of this study could begin Programming While the algorithm used at each time step was modified as described earlier, the data extraction process also needed to be modified so that conflicts could be disaggregated by crash severity at the end of the simulation run. In addition to collecting the lowest TTC in the PMTT and checking if this was below the conflict threshold, the new plugin also collected the speed and deceleration rate of the following vehicle corresponding to the minimum TTC. The end result is that conflicts can be disaggregated by speed and deceleration rate. Further to this, truck and car conflicts were separated as well so that they could be analyzed individually. For the merging conflict algorithm, there is no API function in Paramics to indentify the onset of a merging manoeuvre. Instead, all of the ramp nodes in the network need to be hard-coded into the plugin so that ramps can be distinguished from other link types. For the Gardiner Expressway model, coding in a mere 3 ramps was a trivial task. The 400 series highway network however, has 299 ramps. The task of sorting through the ramp node file and creating a sufficient checking 26

37 algorithm was done by creating a short two-part program (.exe) in C. The first part takes the node file from the Paramics network and creates a new node file that only includes those that are ramp nodes. The second part opens the node file created by the first part and writes an if statement that can later be copied into the plugin code to be used as the checking condition. Essentially, a program was developed to write code for the purpose of inserting it into the plugin. Note that the if statement created by the program was over two pages long for the Highway 400 series network, hence it was not written manually. The ramps identified by the program were checked with the master node file to ensure that all of them were found successfully Analysis This research was being conducted simultaneously while the 400 series highway network was being calibrated by other researchers. Thus, the Gardiner Expressway network was used for some of the early research, while the 400 series highway network was used later on. To obtain more precise results, five simulations with five different seeds were run for each scenario modelled. Then, the average of these five simulations was used as the final conflict data for that particular scenario. This is the same number of simulation runs per scenario used by the FHWA in their SSAM project. Driver familiarity on the Gardiner Expressway network was 60% (i.e. 60 percent of vehicles had familiar routing capabilities); on the 400 series highway network it was set at 85%. The vehicle types in both networks included: Car, LGV (Light Goods Vehicle), OGV 1 and OGV 2 (Other Goods Vehicle). The vehicle operating characteristics of these types is provided in the appendix in table 4. To be consistent with Djavadian et al., only OGV 1 and OGV 2 were considered trucks. The core configuration properties of each network are also included in the appendix in table 5. 27

38 4.1 Comparing Calculations of TTC 4. RESULTS AND DISCUSSION As noted earlier, previous studies used a simplified approach to calculating the TTC, with the assumption that this was representative of the actual time to collision. The objective of this analysis was to compare conflict rates generated by each method. Table 1 shows a comparison of conflicts generated for a TTC of 0.5 seconds on the Gardiner Expressway Model with 15% trucks (7.5% OGV1, 7.5% OGV2) using both approaches. Figure 13 shows how drastically the proportions of conflict types changes between approaches. Table 1: A comparison of conflict rates based on two approaches Lane-change Merging Rear-end Trucks Cars Total Trucks Cars Total Trucks Cars Total Simplified Theoretical % Change In addition to comparing the number of conflicts counted by each approach, the conflicts can be disaggregated by speed and deceleration rate to give a more detailed analysis of the difference in each approach. Figures 14 to 16 show conflicts disaggregated by speed and acceleration rate for the simplified approach. Simplified Approach Theoretical Approach Lane change Merging Rear end Lane change Merging Rear end Figure 13: Comparison of conflict type proportions based on two approaches 28

39 Rear end Conflict Speeds Number of Conflicts Trucks Cars Speed Rear end Conflict Acceleration Rates Number of Conflicts Trucks Cars 0 < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 14: Rear-end conflicts using the simplified approach 29

40 Merging Conflict Speeds Number of Conflicts Trucks Cars Speed Merging Conflict Acceleration Rates Number of Conflicts Trucks Cars 0 < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 15: Merging conflicts using the simplified approach 30

41 Lane change Conflict Speeds Number of Conflicts Trucks Cars Speed Lane change Conflict Acceleration Rates Number of Conflicts < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Trucks Cars Acceleration Rate Figure 16: Lane-change conflicts using the simplified approach Similarly, Figures 17 to 19 show conflicts disaggregated by speed and acceleration rate for the theoretical approach. 31

42 Rear end Conflict Speeds Number of Conflicts Trucks Cars Speed Rear end Conflict Acceleration Rates Number of Conflicts Trucks Cars 0 < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 17: Rear-end conflicts using the theoretical approach 32

43 Merging Conflict Speeds Number of Conflicts Trucks Cars Speed Merging Conflict Acceleration Rates 3.5 Number of Conflicts Trucks Cars 0 < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 18: Merging conflicts using the theoretical approach 33

44 Lane change Conflict Speeds Number of Conflicts Trucks Cars Speed Lane change Conflict Acceleration Rates 4 Number of Conflicts < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Trucks Cars Acceleration Rate Figure 19: Lane-change conflicts using the theoretical approach 34

45 The simplified approach for calculating TTC counts over 2000 lane-change conflicts on the Gardiner Expressway network in the AM peak hour. The theoretical approach counts fewer than 10, a decrease of over 99%. This might be reasonable considering that the simplified approach could easily miscount conflicts by failing to recognize a high speed lane change, where the following vehicle reaches the leading vehicles previous position relatively quickly. Even though the following vehicle never had a collision course with the leading vehicle, because it reached the leading vehicles position in a short time, a conflict was counted. Given this explanation, it is reasonable to consider the high number of conflicts counted by the simplified approach as inaccurate and otherwise unexplainable. These phony lane-change conflicts are further supported by the hundreds of conflicts generated by the simplified approach that had the following vehicle accelerating into the leading vehicle. With the theoretical approach, this phenomenon is almost entirely eliminated, with less than 1 conflict occurring with a positive acceleration rate. Merging conflicts decreased by approximately 60%. Note that this decline is not as severe as the lane-change conflict rate decrease because there would not be as many high speed merging manoeuvres accidently counted as conflicts. Generally, cars are still accelerating while merging onto the highway, and thus their speed is not as high as when making lane change manoeuvres. Notably, merging conflicts are no longer occurring at speeds less than 40km/h as they were previously. Aside from this, the distribution of speeds looks similar. Deceleration rates are also less severe with the theoretical approach. Rear-end conflicts dropped the least, just over 20% overall. Considering one of the triggering conditions for the rear-end conflict is for the leading vehicle to be braking, it does make sense that this conflict type would be affected the least by the different approaches to calculating TTC, because as the leading vehicle s speed decreases and gets closer to zero, the theoretical approach 35

46 becomes the simplified approach. Once again, conflicts where the following vehicle is accelerating are reduced to almost none, where as the simplified approach had a spike of conflicts where the following vehicle has accelerations greater than 2 m/s. In fact, if you compare the distributions of acceleration rates from both approaches, they are identical up until the point where acceleration rates become equal to or greater than zero. Afterwards, the simplified approach counts approximately nine more conflicts that have positive acceleration rates, while the theoretical approach counts practically none. Similar to the case of phony lanechange conflicts, a phony rear-end conflict may have been providing these extra nine conflicts. For example, imagine that vehicles are in a queue. As the queue begins to break up, the following vehicles are reaching the previous locations of the leading vehicles in a fairly short time (as they were previously stopped close together), but in fact were not at risk of a collision. With both approaches, the majority of rear end conflicts are occurring at low speeds (i.e. less than 40km/h). 36

47 4.2 TTC Distributions Investigating different thresholds It is obvious that the time to collision in the theoretical approach is larger in every case; the degree to which it is larger depends on the speeds of both vehicles. Nonetheless, it became evident that a new TTC threshold would be appropriate to establish suitable conflict rates. Table 2 shows the results of various TTC thresholds and their corresponding conflict rates. Table 2: Conflict rates for different TTC thresholds using the theoretical approach Lane-change Merging Rear-end TTC Theoretical Trucks Cars Total Trucks Cars Total Trucks Cars Total 0.5sec sec sec sec sec sec From Table 2, it is possible to generate conflict distributions by TTC, which is presented below in figures 20 to 22: Number of Conflicts Distribution of Lane change Conflicts Time To Collision Figure 20: Distribution of lane-change conflicts 37

48 Number of Conflicts Distribution of Merging Conflicts Time To Collision Figure 21: Distribution of merging conflicts Number of Conflicts Distribution of Rear end Conflicts Time To Collision Figure 22: Distribution of rear-end conflicts From the earlier discussion, it is clear that the simplified approach underestimates the time to conflict and produces inflated conflict rates. As a basis for comparison, the theoretical approach was tested with various conflict thresholds. For the lane-change conflict type, when the simplified approach is used with a TTC of 0.5 seconds, it creates conflict rates the same as those 38

49 produced by the theoretical approach with a threshold of 3.5 seconds within 1 percent. For the merging conflict type, when the simplified approach is used with a TTC of 0.5 seconds, it creates conflict rates the same as those produced by the theoretical approach with a threshold of 1.5 seconds within 3 percent. Rear-end conflicts only occurred with a TTC of less than 1.5 seconds using the theoretical approach, and therefore even once this threshold was bumped up, a higher rate for comparison with the simplified approach could not be obtained. But rear-end conflicts rates were inflated the least as stated earlier anyway. Choosing a suitable threshold for producing conflict rates is not objective. Even in the latest software developed by the FHWA, SAMM allows the user to define this criterion. However, a TTC of 1.5 seconds is suggested by the FHWA based on the literature they have reviewed. This critical threshold manifests itself in this study as well, as rear-end conflicts do not occur with a TTC greater than 1.5 seconds. Considering the triggering condition for the rear-end conflict is an unsafe braking distance between the following vehicle and the leading vehicle, this implies that even though other conflict types can obviously have TTCs greater than 1.5 seconds, there would be a safe braking distance between the vehicles and therefore these conflicts are less probable of creating accidents or requiring evasive driving manoeuvres to avoid a collision. Since the triggering conditions of the lane-change and merging conditions do not require an unsafe braking distance as the basis for recording a conflict, conflict rates increase as the threshold grows; this result is intuitive. As can be seen from the distribution of conflicts, there are more conflicts with a greater TTC and fewer and fewer conflicts with a small TTC. In sum, if a threshold of 1.5 seconds is used, all conflicts with an unsafe braking distance are included; any threshold higher than this begins to include conflicts where a safe braking distance is available to the following vehicle and thus it is not a significant conflict. 39

50 Series Highways Analysis Using a threshold of 1.5 seconds, the conflict algorithms were applied to the 400 series highways model for the AM peak hour. The results are summarized below in table 3. Figure 23 helps visualise the proportions of each conflict type. Conflicts disaggregated by speeds and acceleration rates are shown in figures 24 to 26. Table 3: Conflict rates on the 400 series highway network Lane-change Merging Rear-end Trucks Cars Total Trucks Cars Total Trucks Cars Total Lane change Merging Rear end Figure 23: Pie chart of conflict types on 400 series highway network 40

51 Rear end Conflict Speeds Number of Conflicts Trucks Cars Speed Rear end Conflict Acceleration Rates Number of Conflicts < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Trucks Cars Acceleration Rate Figure 24: Rear-end conflicts using the theoretical approach 41

52 Merging Conflict Speeds Number of Conflicts Trucks Cars Speed Merging Conflict Acceleration Rates Number of Conflicts Trucks Cars < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 25: Merging conflicts using the theoretical approach 42

53 Lane change Conflict Speeds Number of Conflicts Trucks Cars Speed Lane change Conflict Acceleration Rates Number of Conflicts Trucks Cars 0 < 5 m/s 4 to 5m/s 3 to 4m/s 2 to 3m/s 1 to 2m/s 0 to 1m/s =0m/s 0 to 1m/s 1 to 2m/s >2m/s Acceleration Rate Figure 26: Lane-change conflicts using the theoretical approach Rear-end and lane-change conflicts share the same speed and acceleration distributions, in that they both occur at high speeds and have extremely high deceleration rates. The greatest proportion of merging conflicts on the other hand occurred at less than 40km/h. Notice that the merging conflicts do have the following vehicle accelerating at the shortest time to conflict (the 43