Can Microsimulation Be Used to Estimate Intersection Safety?

Saleem, Persaud, Shalaby, Ariza. 2

ABSTRACT

A safety prediction model is designed to estimate the safety of a road entity and, in most cases,these models link traffic volumes to crashes. A major problem with such models is that crashesare rare events and that crash statistics do not take into account many factors that may havecontributed to the crashes. The use of traffic conflicts to measure safety can overcome theseproblems since conflicts occur more frequently than crashes and can either be measured in thefield, or estimated using microsimulation models. In this paper, crash prediction models aredeveloped from simulated peak hour conflicts for a group of urban 4-legged signalizedintersections in Toronto, Canada, and their predictive capabilities are evaluated. Twomicrosimulation packages, VISSIM and Paramics, are used as case studies to demonstrate the useof microsimulation for estimating safety performance. To further demonstrate the versatility of theapproach, VISSIM is used with pre-calibrated parameter values while a substantial effort isdevoted to calibrating Paramics parameters using the crash data. To assess the predictive capabilityof the crash-conflict models, specifically to test whether the models can capture the safety impactsof geometric and operational variables, the effects of a hypothetical left turn treatment on crashesand conflicts are explored and compared to results of an empirical Bayes study that evaluatedactual treatments in the same city. For this task, the predictive ability of the models for intersectionsin various AADT ranges and with various combinations of left and right turn lanes is also assessed.The overall results indicate that the use of simulated conflicts is a viable and promising approachfor intersection safety performance estimation.

Keywords: Intersection Safety, Crash Prediction Models, Conflicts, Microsimulation, VISSIM,Paramics, SSAM, Surrogate Measures, Highway Safety Manual


INTRODUCTIONAnalysis aimed at evaluating/improving traffic safety of roadways is generally based on historicalcrash data, typically utilizing safety prediction models. These models estimate the expectednumber of crashes per year for an entity using variables such as the average annual daily traffic(AADT), and geometric and traffic control features. The main issue with these models is that theydo not take into account all the factors that may have contributed to crash occurrence. Furthermore,the historical crash records modelled may be incomplete and may not be representative of the realcrash history. For example, in Ontario many minor crashes can go unrecorded if the damage doesnot fall over the minimum damage threshold as identified in the Highway Traffic Act.

The use of traffic conflicts to measure the safety of an entity and diagnose its crash riskcan help address these issues. Conflicts have distinct advantage over crashes as they occur muchmore frequently, thus providing a larger sample of outcomes, and they can be quickly measured inthe field or estimated using microsimulation models.

VISSIM (1) and Paramics (2) are among the leading microscopic simulation programscurrently available for traffic flow modelling. With their unique high level of detail, they canaccurately simulate urban and highway traffic including pedestrians, cyclists and motorizedvehicles. They also provide options for exporting the simulation results in formats that can beanalyzed in other software packages to identify conflicts.

In the research for this paper, crash prediction models were developed from simulated peakhour conflicts for a group of 4-legged signalized intersections in Toronto and their predictivecapabilities were evaluated. To demonstrate the versatility of the approach, the paper bringstogether the results of two separate research projects in which peak hour traffic was simulatedusing VISSIM and Paramics; the simulation results were then processed using the Surrogate SafetyAnalysis Model (SSAM) (3, 4) to identify conflicts.

To further demonstrate the versatility of the approach and the capabilities of thesemicrosimulation programs, VISSIM was used with pre-calibrated parameter values, while asubstantial effort was devoted to calibrating Paramics parameters using the crash data. Paramics-simulated conflicts were used to develop a model linking total crashes to total conflicts whileVISSIM-simulated conflicts are used to develop models of specific crash types, including totalcrashes, against their relevant conflict type, e.g., rear end crashes against rear end conflicts.

The promise of the approach has been demonstrated in the very development of SSAM,for which models were developed to relate collisions to conflicts from microsimulation. Morerecently El-Basyouny and Sayed (5) investigated the relationship between crashes and conflictsand came to a conclusion that traffic conflicts provide useful insight into the failure mechanismthat leads to crashes. The current research builds on the earlier studies by looking into how wellthe conflict based crash prediction models behave under different scenarios such as the presenceof turn lanes, and under different ranges of AADT.

This paper also explores the ability of these models to capture the effects of geometric andoperational variables, complementing recent research by Sachi et al. (6) who used conflict-basedanalysis to evaluate a right turn treatment at signalized intersections, concluding that there was aconsiderable reduction in the severity and frequency of related collisions. For this component ofthe research, the effects of a hypothetical left turn treatment on crashes and conflicts is investigatedand the results compared to those of a crash-based before-after evaluation for actual treatments inthe same city by Srinivasan et al. (7).


DATA AND METHODOLOGYThe data for this study were provided by the City of Toronto’s Traffic Control Centre and pertainedto 4-legged signalized intersections. The data consisted of peak hour and average daily trafficvolumes averaged over the years 2006-2010 for the VISSIM analysis and 1998-2002 for theParamics analysis. Crash counts were provided for each intersection over these periods. Signaltiming and phasing data were also provided. Most intersections had semi-actuated operation.

Some guidelines were set to select the sites that were to be used for the microsimulation.The main challenge in setting these guidelines was that the number of sites to be used and thenumber of crashes at these sites should be sufficiently large to yield a model. To explore differentmodel types in demonstrating the versatility of the approach, VISSIM simulation was further usedto estimate and model conflicts of various types, in addition to total conflicts.

Scope and Methodology for the VISSIM based AnalysisThe intersections considered for microsimulation in VISSIM did not have advanced left turnphasing and were right angled 4-legged intersections of roads classified by the City of Toronto aseither major arterial or minor arterial. A total of 113 intersections met these criteria.

Peak-hour conflicts were estimated using microsimulation whereby the peak-hour trafficwere simulated in VISSIM and the results of simulation, i.e., the vehicle trajectories are processedusing the Surrogate Safety Analysis Model (SSAM) (3, 4) to identify conflicts. Model calibrationresults from the Wiedemann 99 car-following model for right-side motorized rule traffic behaviourwere used (8). These calibrated values are pre-set in VISSIM as one of the default models that canbe chosen. A study conducted by Cunto and Saccomanno (9) found out that among the availablevariables in the Wiedemann 99 model, three of them are the most sensitive and are the bestrepresentation of traffic operation at signalized intersections. These parameters are DesiredDeceleration (calibrated value of 2.8m/s2), CCO (Standstill Distance), which is the desireddistance between two stopped cars, with a calibrated value of 1.5m, and CC1 (Headway Time),which is the desired time the following vehicle driver should keep behind the leading vehicle, witha calibrated value of 0.90 sec. Ten simulation runs were done for each intersection and averageresults of these runs were used in modelling. The maximum time to collision (TTC) used was 1.5seconds, while a post encroachment time (PET) of 5 seconds was used.

A key issue is that simulation is typically done at the peak-hour level while conventionalcrash prediction models used in safety management have crashes per year as the dependent variableand average daily traffic as the main independent variable, and not peak (or design) hour values asare used for traffic management in Highway Capacity Manual applications (10). To resolve thisissue and enhance the practical value of the models, peak-hour conflicts were modelled againstcrashes/year (occurring during all hours) by introducing an extra variable to capture the effect ofthe ratio between the peak-hour vehicular traffic and the average daily traffic, a variable that isavailable in the data supplied by the City of Toronto. Models were developed for total crashes vs.total conflicts as well for other crash types against their relevant conflict type, e.g. rear end crashesagainst rear end conflicts. The idea is that the microsimulation models can then be used as a toolto explore the safety effects of various operational and safety measures.

Scope and Methodology for the Paramics based AnalysisThe intersections used for microsimulation in Paramics were randomly chosen but had similarmean volumes and crashes to the dataset used for VISSIM. Of the 132 four legged signalized(4SG) intersections selected, 66 were used for model calibration while the other 66 were simulated


using Paramics. The simulation results were then processed using the Surrogate Safety AnalysisModel (SSAM) (3, 4) to identify conflicts, which were again averaged over 10 simulation runs forthe estimation of the final crash-conflict models. In contrast to the VISSIM application, anextensive model calibration was undertaken for Paramics, specifically for the input parameters ofagent to vehicle ratio (AVR), the mean headway time, and the mean reaction time, as is detailedbelow. Model calibration was done using SSAM’s linearized model as a reference. The form ofthis model is:log( ℎ ) = 1.09 × log( ) + 0.98 (1)

Calibration of Simulated Agent to Vehicle RatioInitial simulation runs were performed with one agent per 100 vehicles (i.e., running the simulationbased on sets of 100 vehicles). Two sets of parameters were tested with agent to vehicle ratios(AVRs) of 1:50, 1:75, and 1:100. A lower ratio implies a higher resolution simulation, so the mainimplication of running simulations at higher ratios would be potentially insufficient data since thesimulation would be run at a lower resolution. The output trajectory (TRJ) files increased fromapproximately 2 GB at a ratio of 1:100, to around 15-20 GB for simulations at a 1:50 ratio.Simulations were attempted at a ratio of 1:25, resulting in over 30 GB of data in the output TRJfiles; however, SSAM would crash due to a lack of available memory for such high-resolutionanalysis.

At the 1:50 agent to driver ratio, SSAM required over half a day to analyze the vehicularmovements and produce a list of conflicts. As a result, simulation runs with a higher AVR werenot undertaken, a decision that would not be critical as long as the objective of demonstrating theviability of the approach could be met. The computational time at this level was 3-4 times thanthat at the 1:75 ratio, as the size of the corresponding TRJ file was also 3-4 times larger. Thesimulation network was set up with a mean headway time (MHT) of 0.75 seconds and a meanreaction time (MRT) of 0.4 seconds for the first set of parameters, and a mean headway time of0.25 seconds and a mean reaction time of 0.3 seconds for the second set of parameters. Themaximum time to collision (TTC) in both analyses was 1.5 seconds.

The results of the different agent to driver ratios show that the performance of the crash-conflict prediction models, which are presented in Table 1, improved as the resolution of the modelincreased, as was expected. One item of note is that the models were fitted against 5-year crashcounts, and not yearly crash frequencies (as is the case with the models calibrated from VISSIMsimulated conflicts).The goodness of fit statistics varies in their assessment of AVR. The 1:75agent to vehicle ratio resulted in the highest residual sum of squares (SSerr) and chi-squared value,and the lowest R2 value. The statistics show that with the first set of parameters (MHT = 0.75s,MRT = 0.4s), the 1:100 ratio performed better than the 1:50 ratio. The second set of parameters(MHT = 0.25s, MRT = 0.3s) produced similar results.

Calibration of Mean Headway Time and Reaction TimeThe mean headway time (MHT) and mean reaction time (MRT) were calibrated simultaneously.Sets of parameter values were defined, used in runs to generate conflicts, and compared on thebasis of the goodness of fit of the resulting crash-conflict models. The initial parameter valueswere MHT = 1.25 seconds and MRT = 0.61 seconds. The results using this parameter set wereworse than sets with lower MHT and MRT values. Lower values for either parameter correspondsto more aggressive driving. Paramics suggests an MHT of 0.85-0.95 for urban areas; however,


lower MHT values of 0.25, 0.5, and 0.75 seconds were tested to see if lower values would resultin an improved crash prediction model. The default Paramics value for MRT is 1.0 second;however, the lower values of 0.2, 0.3 and 0.4 were tested.

Each MHT value was used in a simulation run with each of the MRT values, with theexception of the MHT = 0.75s, MRT = 0.2s pair. By the time that set was to be tested, it hadalready been noted that an MHT value of 0.75 seconds was providing poorer quality predictions.In addition to the 8 remaining possible combinations of MHT and MRT, three more parameter setswere proposed: MHT = 0.15s, MRT = 0.3s, MHT 0.4s and MRT = 0.2s, and MHT = 1.25s, MRT= 0.61s. The model parameters and the goodness-of-fit statistics for the resulting crash predictionmodels are shown in Table 2.

The parameter pair with MHT = 0.25s and MRT = 0.3s appears to have performed best. Ithas the lowest residual sum of squares, highest R2 value, and lowest Χ2. Additionally, it has thelowest intercept value and the highest conflict coefficient, indicating that those two parametersprovide conflicts with the best explanatory properties for crash prediction.

MODEL FITTING AND EVALUATIONConsistent with state-of-the-art methods, generalized linear modelling, with the specification of anegative binomial (NB) error structure, was used to develop the crash prediction models (11) usingthe SAS software (12). The specification of an NB-error structure allows for the direct estimationof the over dispersion parameter (k), which can be used to assess the models since it is related tothe variance of the predictions. Over dispersion occurs when the data have larger variance than isexpected under the assumption of a Poisson distribution.

Model Fitting Using VISSIM Simulated ConflictsThe model form used for developing the models with peak-hour conflicts (obtained from VISSIMsimulation and SSAM analysis) and the peak-hour traffic ratio (ratio of peak hour traffic volumeto the average daily traffic volume) as the explanatory variables was as follows:ℎ / = × × (2)

It was possible to consider the peak hour ratio as a variable because it varied fromintersection to intersection, depending on the intersecting road classification, intersection location,and day, date and time of the peak hour counts. Table 3 shows the coefficient estimates and thedispersion parameters for models distinguished by their specific crash – conflict types.

As can be seen from Table 3, the estimates of both β1 and β2 are statistically significant (atthe 10% level) for almost all of the models. The goodness of prediction measures, which are shownin Table 4, also suggest reasonably good fits in that the MAD/year/site (Mean Absolute Deviation)and the MPE/year/site (Mean Prediction Error) for all the models are small when compared to theaverage observed crashes per year per site.

Table 5 shows the crash predictions from the peak hour conflict based model forintersections grouped by different ranges of entering AADT. As is evident, the model predictscrashes very well for entering AADTs between 15,000 and 30,000, with the ratio of observed topredicted crashes oscillating close to a value of 1. For entering AADTs lower than 15,000, themodel is systematically over-predicting crashes, an observation that will require furtherinvestigation. In principle, using an alternative model form can “force” a better fit, but it may bethat VISSIM parameters need to be adjusted for lower AADTs to generate conflicts that are more


consistent with the model form used here. For entering AADT’s higher than 30,000, the model isunder predicting crashes substantially in some cases. This is possibly due to the small number ofsites in this AADT range.

Table 6 compares the observed and predicted crashes by the VISSIM simulated conflictmodels grouped by various combinations of number of intersection approaches with left and/orright turn lanes, a key geometric/operational variable in the predictive methodology for urban andsuburban arterial intersections in the Highway Safety Manual (13). As is evident from Table 6, theratio of observed to predicted crashes is oscillating around, and is reasonably close to 1, with littleor no bias. This shows that the estimated conflicts and the crash-conflict models appear to becapturing the effect of the number of turn lanes on crashes reasonably well – an important test ofthe overall approach being investigated in this research.

Model Fitting Using Paramics Simulated Total Conflicts and Comparison with OtherModelsFor the Paramics microsimulation, a non-linear form similar to that used for the models withVISSIM generated conflicts was applied for developing the crash prediction model. The model,which was fitted using the R software package (14), is presented in Table 7. The model form wasas follows (4):ℎ / = × (3)

The coefficient estimate for conflicts is statistically significant at the 10% level.Interestingly, this coefficient estimate (0.3892) is close in value to that estimated for VISSIMgenerated conflicts (0.3461), suggesting that the effect of conflicts on crashes is relativelyinsensitive to which of the two software packages is used to generate the conflicts. This similarityis depicted in Figure 1, along with the dissimilarity with the equivalent crash-conflict modelprovided in the SSAM documentation. The latter model, which had a conflict exponent coefficientof 1.419, was rescaled to match the sum of the crash predictions from the sample sites using theParamics and VISSIM generated conflicts.

CAN CRASH-CONFLICT MODELS BE USED FOR ESTIMATING THE EFFECTS OFA POTENTIAL SAFETY TREATMENT?This part of the paper aims at further exploring whether the conflict-crash models (estimated fromVISSIM simulated conflicts) can reasonably capture the effects of changes in geometric andoperational variables by estimating the effects of one safety treatment. Specifically, the provisionof left turn movement protection at signalized intersections is used as a case study treatment. Theconflict type of interest for this exploration is the crossing conflicts. This analysis estimates howthe numbers of crossing conflicts and its pertinent crash types (angle and turning) will change ifthe left turn phasing at some intersections in the sample were to be changed from permissive toprotected-permissive. Effects of this treatment on other conflict and crash types are also examined.The estimated effects are then compared to those estimated in a crash-based before-after studyconducted by Srinivasan et al. (7) for a group of similar Toronto intersections that actuallyunderwent a change from permissive to protected-permissive left turn phasing.

The criteria used for selecting intersections for applying the hypothetical treatment wasthat the intersections should have at least one approach with an exclusive left turn lane and thatthe level of service (LOS) and traffic volumes would warrant the installation of a protected-


permissive signal. A total of 20 of the 113 intersections used for the modelling were selected forthe hypothetical treatment.

The LOS for the left turning traffic at these 20 intersections was C or worse, and the leftturning traffic volume was more than 50 vehicles per hour. Of the 20 intersections, 1 approach wastreated at 1 intersection, 2 approaches were treated at 7 intersections, 3 approaches were treated at3 intersections, and 4 approaches were treated at 9 intersections. Signal timings (including theprotected-permissive left turn phasing) were optimized using the SYNCHRO software package(15) and the traffic was then simulated in VISSIM.

Table 8 shows a summary of the number of peak hour conflicts at the 20 sites before andafter the hypothetical treatment was applied. The table also provides crash predictions from thecrash-conflict models, using Equation 2 with the appropriate exponents, β1 and β2, taken fromTable 3. Also shown is the percentage of each crash type with respect to the total predicted crashes.

As seen in Table 8, crossing conflicts would have the largest reduction (51.6%) if thetreatment were to be applied, while rear end and turning conflicts would be reduced by 38.9% and35.1%, respectively. These reductions in conflicts translate into reductions in numbers of angleand turning crashes (the target crash types), of 17.8 and 21.4%, respectively, as shown in the lastcolumn of Table 8. These values are quite close to the estimated 23.8% reduction (s.e. = 8.8%) inleft turn opposed crashes (which include both turning and angle crashes) reported in an empiricalBayes before-after study by Srinivasan et al. (7). Their results are based on 12 intersections in theCity of Toronto at which the left turn phasing was actually changed from permissive to protected-permissive at more than one approach. (Note that, for the microsimulation study, the hypotheticaltreatment was applied at more than one approach for all but one of the 20 intersections.)

The study by Srinivasan et al. (7) found a statistically insignificant decrease in total crashesof 5.5% (s.e. = 4.0%) and a statistically insignificant increase in rear-end crashes of 2.1% (s.e. =6.2%) at the 12 intersections. These results are somewhat inconsistent with those from the conflict-based results for non-target crashes, although, for the latter, standard errors could not be estimated.This may be because the samples for the two analyses are different, but it is also possible thatoptimization of the VISSIM inputs, in the same way as was done for Paramics, may generateconflicts that would alter the outcome for the effect of changing left turn phasing on non-targetcrashes.

SUMMARY AND CONCLUSIONSThe paper provides insights into estimating intersection safety using simulated conflicts as the keyvariable instead of traffic volumes. Two different case studies were presented in this paper todemonstrate the versatility of the approach. One involves the use of VISSIM microsimulation withpre-calibrated model parameter values to estimate conflicts, while the other case study involvedthe use of a Paramics model, this time with parameter values endogenously estimated.

The resulting crash-conflict models, which were based on data for four legged signalizedintersections in Toronto, had coefficient estimates for the conflict variables that were not onlystatistically significant, but which were also remarkably similar in value. However, the new crash-conflict relationships are quite different from that recommended in the documentation for theSurrogate Safety Assessment Model (SSAM) that was used to identify conflicts from the trafficsimulation. The ability of the new models to provide reasonable estimates for sites grouped bydifferent ranges of volumes and different combinations of turn lanes is further evidence of theirrobustness and their ability to capture the effects of geometric factors.


To further demonstrate the versatility of the approach, the second part of the analysislooked into the possible effects of hypothetically changing left turn phasing from permissive toprotected-permissive. The results indicate that the treatment would be beneficial in reducing thenumber of angle and turning crashes (the target crash types), with estimates that are reasonablysimilar to those from a robust empirical Bayes crash based evaluation for a group of intersectionsin the City of Toronto that were actually treated.

The results are encouraging enough to suggest that this line of research should continuewith a view to considering the evaluation of safety effects of treatments when crash-based beforeevaluations cannot be undertaken due to inadequate sample sizes or other practical issues.

ACKNOWLEDGEMENTSThe authors would like to thank the Traffic Management Centre, Transportation Services, City ofToronto, for providing the data. The research was supported by discovery grants from the NaturalSciences and Engineering Research Council of Canada.

REFERENCES

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https://www.researchgate.net/publication/257356501_Safety_performance_functions_using_traffic_conflicts?el=1_x_8&enrichId=rgreq-75045e11f0ce385b0e76216076413e84-XXX&enrichSource=Y292ZXJQYWdlOzI4MDIxMDkzOTtBUzoyNTU3NzMwODMxNzI4NjRAMTQzNzk5MjQ2MzAzMA==

https://www.researchgate.net/publication/257356501_Safety_performance_functions_using_traffic_conflicts?el=1_x_8&enrichId=rgreq-75045e11f0ce385b0e76216076413e84-XXX&enrichSource=Y292ZXJQYWdlOzI4MDIxMDkzOTtBUzoyNTU3NzMwODMxNzI4NjRAMTQzNzk5MjQ2MzAzMA==

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15. Trafficware. SYNCHRO 8: Overview. www.trafficware.com/synchro.html. Accessed July23, 2013.


LIST OF TABLESTABLE 1 Crash Prediction Models for Different Agent to Vehicle Ratios (AVRs)TABLE 2 Crash Prediction Models for Sets of Driver Behaviour ParametersTABLE 3 Parameter Estimates for Crash Models based on VISSIM Simulated ConflictsTABLE 4 Goodness of Fit for Crash Models based on VISSIM Simulated ConflictsTABLE 5 Comparison of Observed and Predicted Crashes for Various Crash-Conflict Models -Grouped by Total Entering AADT (VISSIM Conflicts)TABLE 6 Ratio of Observed and Predicted Crashes by Number of Approaches with Turn Lanesfor Crash Models based on VISSIM Simulated ConflictsTABLE 7 Coefficient Estimates and Goodness of Prediction Measures for Paramics SimulatedTotal Conflicts ModelsTABLE 8 Crash and Conflict Estimates Before & After Hypothetical Treatment

LIST OF FIGURESFIGURE 1 Plot of VISSIM, Paramics and SSAM Models


TABLE 1. Crash Prediction Models for Different Agent to Vehicle Ratios (AVRs)Model Form: ( ℎ 5 ) = × log( ) −

MHT (s) MRT (s) AVR α β

0.75 0.4 1:50 0.2845 -2.9247 27.19 0.27 12.52

0.75 0.4 1:75 0.3219 -2.7000 29.97 0.2 12.26

0.75 0.4 1:100 0.3653 -2.8472 25.92 0.31 10.39

0.25 0.3 1:50 0.3646 -2.4423 26.64 0.29 10.43

0.25 0.3 1:75 0.3732 -2.3448 29.36 0.21 11.75

0.25 0.3 1:100 0.3936 -2.588 28.89 0.23 11.56


TABLE 2. Crash Prediction Models for Sets of Driver Behaviour ParametersModel Form: ( ℎ 5 ) = × log( ) −

MHT (s) MRT (s) α β0.15 0.3 0.3168 -2.5893 27.71 0.26 11.29

0.25 0.2 0.3340 -2.5316 29.63 0.21 12.28

0.25 0.3 0.4100 -2.1038 24.63 0.34 10.27

0.25 0.4 0.3506 -2.5998 26.74 0.28 10.00

0.4 0.2 0.3649 -2.3162 27.13 0.27 11.44

0.5 0.3 0.3462 -2.5109 27.54 0.26 10.71

0.5 0.3 0.3248 -2.7005 25.82 0.31 10.71

0.5 0.4 0.2823 -2.8049 29.09 0.22 12.29

0.75 0.3 0.3017 -2.6894 29.28 0.22 11.80

0.75 0.4 0.2845 -2.9247 27.19 0.27 12.52

1.25 0.61 0.2827 -2.9698 27.72 0.23 12.05


TABLE 3. Parameter Estimates for Crash Models based on VISSIM Simulated Conflicts

Crash typefordependentvariable

Conflict typeforindependentvariable

α Estimate(Pr>ChiSq)

β1 Estimate(Pr>ChiSq)

β2 Estimate(Pr>ChiSq)

Dispersionparameter (k)

Total Total -0.9722 (0.2771) 0.3461 (<0.0001) -1.0775 (0.0023) 0.235

Total Crossing 1.062 (0.1047) 0.2741 (<0.0001) -0.5788 (0.0730) 0.250

Total Rear-end -0.6492 (0.4536) 0.3065 (<0.0001) -1.0334 (0.0035) 0.239

Total Lane change 1.0071 (0.1437) 0.2450 (0.0003) -0.6489 (0.0520) 0.254

Injury Total -1.7527 (0.0543) 0.3030 (<0.0001) -0.8498 (0.0164) 0.201

Injury Crossing -0.0934 (0.8837) 0.3043 (<0.0001) -0.4059 (0.1939) 0.198

Injury Rear-end -1.4876 (0.0910) 0.2720 (0.0001) -0.8117 (0.0217) 0.203

Injury Lane change -0.263 (0.7012) 0.2402 (0.0003) -0.5746 (0.0823) 0.207

PDO Total -1.4144 (0.1346) 0.3593 (<0.0001) -1.1303 (0.0025) 0.262

PDO Crossing 0.7333 (0.2928) 0.2655 (<0.0001) -0.6148 (0.0742) 0.282

PDO Rear-end -1.0782 (0.2391) 0.317 (<0.0001) -1.0871 (0.0038) 0.266

PDO Lane change 0.7129 (0.3288) 0.2451 (0.0008) -0.6574 (0.0635) 0.285

Angle Crossing -0.8015 (0.2791) 0.2549 (0.0020) -0.7117 (0.0485) 0.274

Rear-end Rear-end -1.2676 (0.2341) 0.3423 (<0.0001) -0.6609 (0.1264) 0.336

Sideswipe Lane change -1.6218 (0.1494) 0.2608 (0.0159) -1.0133 (0.0639) 0.550

Turning Crossing -0.7581 (0.3321) 0.3158 (0.0009) -0.5477 (0.1643) 0.349


TABLE 4. Goodness of Fit for Crash Models based on VISSIM Simulated Conflicts

Crash type fordependentvariable

Conflict type forindependentvariable

Averagecrashes/site/year MAD/site/year MPB/site/year

Total Total 15.119 0.051 0.065

Total Crossing 15.119 0.054 0.069

Total Rear-end 15.119 0.051 0.065

Total Lane change 15.119 0.051 0.068

Injury Total 3.657 0.013 0.016

Injury Crossing 3.657 0.013 0.017

Injury Rear-end 3.657 0.013 0.016

Injury Lane change 3.657 0.013 0.016

PDO Total 11.448 0.04 0.052

PDO Crossing 11.448 0.043 0.055

PDO Rear-end 11.448 0.041 0.053

PDO Lane change 11.448 0.041 0.055

Angle Crossing 2.869 0.011 0.014

Rear-end Rear-end 4.784 0.020 0.025

Sideswipe Lane change 2.244 0.012 0.018

Turning Crossing 2.416 0.011 0.015


TABLE 5. Comparison of Observed and Predicted Crashes for Various Crash-ConflictModels -- Grouped by Total Entering AADT (VISSIM Conflicts)

Crash type fordependent variable

Conflict type forindependent variable

Entering AADT0-15000(n=22)

Entering AADT15000-30000

(n=87)

Entering AADT>30000(n=4)

Total Total 0.784 1.030 1.274

Total Crossing 0.715 1.087 1.215

Total Rear-end 0.777 1.031 1.330

Total Lane change 0.775 1.028 1.350

Injury Total 0.811 1.027 1.243

Injury Crossing 0.759 1.078 1.132

Injury Rear-end 0.805 1.027 1.287

Injury Lane change 0.812 1.025 1.284

PDO Total 0.775 1.031 1.095

PDO Crossing 0.701 1.09 1.494

PDO Rear-end 0.767 1.032 1.719

PDO Lane change 0.762 1.029 0.856

Angle Crossing 0.816 1.057 10.95

Rear-end Rear-end 0.604 1.062 1.494

Sideswipe Lane change 0.806 0.998 1.719

Turning Crossing 0.612 1.111 0.856


TABLE 6. Ratio of Observed and Predicted Crashes by Number of Approaches with TurnLanes for Crash Models based on VISSIM Simulated Conflicts

No. ofapproachesw/ rightturn lanes

No ofapproachesw/ left turnlanes

Intersections Total Injury PDO AngleRear-end

Side-swipe

Turning

0 0 33 1.131 1.093 1.144 1.307 0.974 1.262 0.964

1-2 0 7 1.319 1.074 1.399 1.037 1.512 2.023 0.990

1-4 1 10 0.815 0.719 0.847 0.450 0.965 1.050 0.700

1-4 2 27 0.800 0.848 0.783 0.786 0.750 0.855 0.871

1-4 3 5 0.837 0.874 0.824 1.078 1.062 0.522 0.605

1-4 4 31 1.049 1.126 1.025 1.095 1.142 0.684 1.310


TABLE 7. Coefficient Estimates and Goodness of Prediction Measures for ParamicsSimulated Total Conflicts ModelsParameter Estimate Pr > ChiSq

α 0.3892 0.0742

β 2.6099 0.3014

Dispersion parameter 0.311 n/a

Pearson chi-square 85.628 n/a


TABLE 8. Crash and Conflict Estimates Before & After Hypothetical Treatment

Crashtype

Conflicttype

Before Treatment After Treatment %change

inconflicts

%change

incrashes

Predicted crashes(estimated conflicts)

% oftotal

Predicted crashes(estimated conflicts)

% oftotal

Total Total 1646.6 (163.5) 100 1368.3 (99.9) 100 -38.9 -16.9

Angle Crossing 304.8 (9.8) 18.5 250.7 (4.7) 18.3 -51.6 -17.8

Rear-end

Rear-end

519.4 (143.4) 31.5 433.2 (88.4) 31.7 -38.3 -16.6

TurningLanechange

259.9 (10.3) 15.8 204.2 (6.7) 14.9 -35.1 -21.4


FIGURE 1. Plot of VISSIM, Paramics and SSAM Models

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