Integrating Observational and Traffic Simulation Models for Priority Ranking of Unsafe Intersections Usama Elrawy Shahdah, Frank F. Saccomanno, and Bhagwant Persaud future. However, if crashes occur in a random fashion, consistency of prediction will not provide a good metric for identifying high-risk sites in the future. The problem of consistency in crash occurrence over time becomes critically important in the development of sound priority-ranking models for safety intervention. The application of observational models on the basis of the reported crash history is the most common approach used to prioritize unsafe sites for safety interventions. Recently, microscopic traffic simulation has been used to estimate surrogate measures of safety performance for prediction of high-risk vehicle interactions for different traffic conditions. Proponents of the latter models argue that a better understanding of the safety problem can be gained when these higher-risk interactions are taken into account. In crash prediction models, crashes are viewed as objective and verifiable failures in the transportation system. Such a view thereby provides an objective basis for assessment of the lack of safety. However, not all failures of the transportation system result in crashes. Reliance on reported crashes poses a number of problems for these types of prediction models, such as low rates of reporting of less severe crashes and unreported near misses (2–5). For example, Hauer and Hakkert reported that 50% of cashes with injuries and 60% of property-damage-only crashes were not reported in police data (6). These low-severity crashes and near misses may contain essential information concerning the lack of safety that is important for effective safety intervention. The use of traffic conflicts was initially proposed by Perkins and Harris as an alternative approach that may be used to overcome some of the limitations of conventional observational crash-based traffic safety studies (7). Amundsen and Hyden defined traffic conflicts to be “observable situations in which two or more road users or vehicles approach each other in space and time to such an extent that there is a risk of collision if their movement remains unchanged” (8). The use of traffic conflicts in safety studies is based on the premise that conflicts occur more frequently than crashes, although the mechanisms leading to both types of events are comparable. As a consequence, conflicts can address some of the statistical issues linked to the rare nature of crashes, especially those with low severity. Additionally, they consider the transportation failure mechanism from a perspective somewhat broader than that implied in observational crash data alone (9–11). Figure 1 shows an illustration of Hyden’s safety pyramid, in which the full spectrum of vehicle interactions, from undisturbed passages at the base of the pyramid to less frequent traffic conflicts, near misses, and crashes closer to the peak, is considered (12). As conditions in the traffic stream progress from the base to the peak, the presence of a safety problem presumably becomes more pronounced, as does the probability of crashes.
Observational models based on reported crash history are the most common measures for identifying unsafe sites for priority intervention. Observational models are good for predicting higher-severity crashes but ignore higher-risk vehicle interactions (e.g., near misses) that failed to result in crashes that are reported in historical data. Proponents of microscopic simulation models argue that failure to recognize these higher-risk interactions can significantly understate the safety problem at a given site and lead to misallocation of scarce treatment funds. This paper takes the position that a complete understanding of the safety problem at a given site can emerge only if both crash potential and traffic conflicts are taken into account. A priority-ranking model that integrates estimates from observational crash prediction models into an analysis of traffic conflicts is presented. Traffic conflicts were based on simulated vehicle interactions and deceleration requirements for different traffic scenarios. The suitability of the approach for priority ranking of sites was assessed with six ranking approaches: crash frequency, empirical Bayes, potential for safety improvement, conflict frequency, conflict rate (sum and cross product of traffic volume), and integrated model. Priority ranking was evaluated with five test criteria: site consistency, method consistency, rank difference, total rank score, and sensitivity and specificity. These models were applied to a sample of 58 signalized intersections from Toronto, Ontario, Canada, for the period from 1999 to 2006. The integrated model was found to yield better results for the five evaluation criteria; this result suggests that the proposed approach has promise.
The high cost of intersection crashes provides strong justification for the development of efficient, objective guidelines for safety intervention. These guidelines must be based on reliable priority-ranking m ethods that identify locations for cost-effective safety improvements (1). The majority of crashes tend to occur with some consistency over time and are therefore predictable. However, many crashes are purely random in nature and are therefore difficult to predict from the observed crash history. If crashes occur with consistency, then a measure of consistency in the priority ranking of sites over time would be expected, such that sites with high rates of crashes in the past would likely be reflected as sites that will have high rates of crashes in the U. E. Shahdah and F. F. Saccomanno, Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada. B. Persaud, Department of Civil Engineering, Ryerson U niversity, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada. Corresponding author: U. E. Shahdah,
[email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2280, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 118–126. DOI: 10.3141/2280-13 118
Shahdah, Saccomanno, and Persaud
119
crashes near crashes slight conflicts potential conflicts
fatal severe injury slight injury damage only
undisturbed passages
FIGURE 1 Safety pyramid (12).
Traffic conflicts and interactions with higher-risk vehicles can be estimated either by monitoring of the traffic stream with a view to extraction of vehicle paths over time or in a more practical way by application of calibrated traffic simulation to specific traffic scenarios. In the study described in this paper, the second approach is adopted, whereby traffic conflicts are obtained for a sample of signalized intersections from Toronto, Ontario, Canada, as simulated from the VISSIM microscopic traffic simulation model (version 5.30) (13). The inputs into the simulation exercise are intersection approach volumes and turning movements. Furthermore, selected input parameter values in VISSIM were obtained from an intersection traffic study by the use of VISSIM by Cunto and Saccomanno (14). The selected parameters are desired deceleration, standstill distance (VISSIM parameter CC0), and headway time (VISSIM parameter CC1).
Priority Ranking on the Basis of Crash Data Historically, AF has been used for priority ranking of unsafe sites in many jurisdictions, with associated inefficiencies resulting from the regression-to-the-mean bias (15). The EB approach suggested by Hauer can be used to account for this regression-to-the-mean bias and improve efficiency (16). In this paper, three different observational priority-ranking models were applied to the intersection sample data: AF; the EB estimate of the expected crash frequency; and PSI, which is based on the EB estimate. The expected number of crashes by the use of EB for a specific intersection site is given as EBi = α i i E ( yi ) + (1 − α i ) i yi
(1)
where Objectives and Overall Approach The objective of the study described here was to explore and test a conflict-based method for priority ranking of unsafe intersections. To do so, the priority ranking was compared and evaluated by use of the proposed and conventional methods for a sample of 58 fourleg signalized intersections with no exclusive left-turn or rightturn lanes from Toronto, Ontario, Canada. These intersections had 2,331 crashes (all severities combined) over 8 years (1999 to 2006). This sample was used to assess six different ranking approaches: accident frequency (AF), empirical Bayes (EB) expected crash frequency, potential for safety improvement (PSI), conflict frequency, conflict rate (sum and cross product of traffic volume), and an integrated approach that combines both empirical Bayes expected crash frequency and simulated conflicts. Five different evaluation criteria were used for the assessment. A different set of 38 four-leg signalized intersections for which turning traffic volume movements were available was simulated by the use of VISSIM to estimate the expected number of traffic conflicts. The reason for the use of other intersections is that the turning movements are not available for the 58 sites. The 38 intersections are comparable in that they consisted of two lanes in each approach with no exclusive left-turn or right-turn lanes.
EBi = expected number of crashes in n years at site i, E(yi) = expected number of crashes in n years at similar sites from a safety performance function (SPF), αi = weight given to the estimated expected crashes for similar entities, and yi = observed crash counts in n years at site i. The PSI is the difference between the EB expected crash frequency and the crash frequency predicted from the SPF for similar sites, as follows: PSIi = EBi − E ( yi )
(2 )
To compare the priority-ranking methods, the analysis period was separated into two time periods: the first time period, which was used to apply the methods, was the 3 years from 2002 to 2004, and the second time period, which used to evaluate the ranking methods, was the 2 years 2005 and 2006. The time period between 1999 and 2001 was used to calibrate SPFs to estimate the EB expected number of crashes [E(yi)] for the first analysis period (2002 to 2004), whereas the time period from 1999 to 2004 was used to estimate the EB expected number of crashes in the second analysis period (2005 and 2006).
120
Transportation Research Record 2280
Generalized linear modeling techniques were used to fit the models, and a negative binomial distribution error structure was assumed. The model parameters and the dispersion parameter of the negative binomial distribution were estimated by the maximum likelihood method by the use of the PSCL (Political Science Computational Laboratory, Standard University, Palo Alto, California) library in R-statistical software (17). The SPF model forms c onsidered are as follows:
likelihood is −407.938. The generalized linear model estimate and goodness of fit for data from between 1999 and 2004 are as follows: ln ( E ( yi )) = −4.7668 [ 3.18 ] + 0.9596 [ 0.31] × ln ( AADTmaj + AADTmin ) + 0.9811[ 0.13] AADTmin × ln AADTmaj + AADTmin
(8 )
Model Form 1: i i ln ( E ( yi )) = ln β1 + β 2 × ln ( AADTmaj ) + β 3 × ln ( AADTmin )
( 3)
Model Form 2: i i ln ( E ( yi )) = ln β1 + β 2 × ln ( AADTmaj + AADTmin )
(4)
Model Form 3:
where the dispersion parameter is 2.5781, the residual deviance is 63.05 with 55 degrees of freedom, AIC is 484.89, and 2× log likelihood is −476.890. The dispersion parameter (φ) reported in this paper (by the use of R-software) is the inverse of the one usually obtained by SAS statistical software. In this case, the variance of the negative binomial distribution has the following form: Var ( yi ) = E ( yi ) +
ln ( E ( yi )) = ln β1 + β 2 × ln ( AADT + AADT i maj
i min
)
i AADTmin + β 3 × ln i i AADTmaj + AADTmin
(5 )
Model Form 4: i i ln ( E ( yi )) = ln β1 + β 2 × ln ( AADTmaj × AADTmin )
ϕ
(9)
Development of Simulated Measures of Traffic Conflicts Safety Performance Measure
(6)
where E(yi) = expected number of crashes at site i, i AADTmaj = annual average daily traffic in the major approach at site i, i AADTmin = annual average daily traffic in the minor approach at site i, and β1, β2, and β3 = calibration coefficients. The Akaike information criterion (AIC) was chosen to be the sole measure of goodness of fit, given that the value of residual deviance– degrees of freedom is close to 1 for a model to be considered adequate (18). The model with a minimum AIC value was chosen to be the best model to fit the data. The best models for 1999 to 2001 and 1999 to 2004 have the model form given in Equation 3. With a larger database, another model form may have proved superior or a more accurate model may have been achieved, but to achieve the goals of this investigation, it was not necessary to finesse the SPF. The generalized linear model estimate and goodness of fit for data between 1999 and 2001 are as follows, with the standard error given in parentheses after the parameter estimates: ln ( E ( yi )) = −6.4641[ 3.49 ] + 1.0644 [.35 ] × ln ( AADTmaj + AADTmin ) AADTmin + 1.0094 [ 0.15 ] × ln AADTmaj + AADTmin
( E ( yi ))2
(7)
where the dispersion parameter is 2.2568, the residual deviance is 63.157 with 55 degrees of freedom, AIC is 415.94, and 2× log
The use of microsimulation in safety studies requires the use of surrogate safety measures that are a function of vehicle-pair speeds and spacing. Several expressions of safety performance measures have been developed and described in the literature (14, 19–21). In this paper, the deceleration rate to avoid collision (DRAC) is used as the measure of safety performance. DRAC is defined as the rate at which a vehicle must decelerate to avoid the collision with another conflicting vehicle (19, 20). DRAC for rear-end (RE) conflicts can be expressed as (22) DRACRE n (t ) =
(Vn ( t ) − Vn−1 ( t ))2 2 ( Xn ( t ) − X n −1 ( t ) − Ln −1 )
(10 )
where t = time interval, V = vehicle speed, n = following vehicle, n − 1 = lead vehicle, X = position of the vehicles, and L = vehicle length. For potential angle (AG) collisions, estimates of DRAC are obtained by DRACnAG ( t + 1) =
V n2 ( t ) 2 Dn ( t )
(11)
where Dn(t) is the distance between the projected point of collision and vehicle n on the major approach (main traffic stream).
Shahdah, Saccomanno, and Persaud
The measure of DRAC with higher-risk conflicts has been defined for interactions in which DRAC exceeds a value of 1.50 m/s2 to reflect critical driver perception reaction times for braking. By consideration of conflicts for DRAC values greater than 1.50 m/s2, all conflicts that require necessary reactions to avoid crashes will be accounted for (23).
Estimation of Conflicts The 38 four-leg signalized intersections were simulated by the use of the VISSIM (13) microscopic traffic simulation model to estimate the number of conflicts. In this study, the parameter calibration results from Cunto and Saccomanno for a signalized intersection are used (14). These authors used two safety performance measures in the simulation calibration and validation procedure: crash potential index (CPI) and the number of vehicles in conflict. CPI is based on DRAC, as it relates DRAC to vehicle braking capabilities. Among all available driving parameters, Cunto and Saccomanno revealed three parameters that are the most sensitive and the best representation of traffic operations at a signalized intersection (14). Those factors are 1. Desired deceleration, which is used to achieve a predefined desired speed or under stop-and-go conditions (calibrated value = −2.6 m/s2); 2. CC0 (standstill distance), which is the desired distance between stopped cars (calibrated value = 3 m); and 3. CC1 (headway time), which is the time that the driver of the following vehicle wants to keep behind the lead vehicle (calibrated value = 1.50 s). In this study, only the a.m. peak hour is considered in VISSIM to estimate the number of conflicts. The a.m. peak-hour volumes were from 2002 and 2003. For each intersection, 10 simulation runs with 10 random seeds were used to capture the randomness in traffic. For each run, the number of conflicts for DRAC values greater than 1.50 m/s2 was calculated from the trajectories of simulated vehicles at different times. The surrogate safety assessment model was used to estimate the total number of conflicts for DRAC values of ≥1.5 m/s2 (24). The average number of conflicts at each site was then calculated and used to calibrate a relationship between the number of conflicts and the hourly traffic volume. The results of the simulation of the 38 sites were used to develop a model linking conflicts to selected traffic inputs, such as volumes. This model provides information on the potential for traffic conflicts, which replaces the need for simulation at sites with known volumes and other traffic attributes. Generalized linear modeling techniques were used to fit a number of models, and a negative binomial distribution error structure was assumed. The model parameters are estimated in the same fashion used for observational models. The selected SPF forms are the same as those in Equations 3 to 6, with the exception that (a) the hourly traffic volumes Vmaj and Vmin in the a.m. peak hour are used instead of AADTimaj and AADTimin and the daily traffic volumes on the major and the minor roads, respectively, and (b) conflict frequency (CF) instead of the expected number of crashes [E(yi)] is used as the dependent variable. The calibrated model is shown in Equation 12:
121
ln ( CFi ) = −19.5855 [ 0.84 ] + 3.1169 [ 0.11] × ln (Vmaj + Vmin )
(12 )
where the dispersion parameter is 27.748, the residual deviance is 32.425 with 33 degrees of freedom, AIC is 337.29, and 2× log likelihood is −331.289. Equation 12 was then used to estimate the number of conflicts at each of the 58 intersections. Before doing so, AADT had to be converted to hourly volume. This was because the traffic volumes for the 58 intersections were available in the form of daily traffic volumes (AADT), whereas the traffic variables in Equation 12 pertain to hourly volume during the a.m. peak. For this study, a factor of 0.09 was assumed for the conversion of daily traffic volumes to hourly volumes. The simulation yielded three other criteria for evaluating the priority rankings, CF and conflict rates 1 and 2 (CR1 and CR2, respectively), defined as CR1i =
CFi i i AADTmaj + AADTmin
(13)
CR 2 i =
CFi i i AADTmaj × AADTmin
(14 )
where CFi = simulated number of conflicts at site i, i = annual average daily traffic in the major approach at AADTmaj site i, and i AADTmin = annual average daily traffic in the minor approach at site i.
Proposed Integrated Safety Score Priority-Ranking Method An integrated priority-ranking measure based on the weighted sum of EB expected number of crashes and number of traffic conflicts is proposed. It is referred to as a priority-ranking safety score (SC), which is defined as safety score i = CFi + W × EBi
(15)
where CFi = simulated number of conflicts at site i, W = weight factor to convert crashes to equivalent number of simulated conflicts, and EBi = expected number of crashes at site i estimated by the EB method. The weight factor in Equation 15 needs to be determined because it is not known how much importance should be placed on crashes and how much should be placed on conflicts. A number of weight factor values were iteratively considered to determine an optimal weight. It may be possible to develop a weight on the basis of theoretical considerations, but such an exercise was beyond the exploratory scope of the present study.
122
Transportation Research Record 2280
Evaluation Criteria for Assessment of Priority-Ranking Method
where
To evaluate and compare the performance of the ranking from the proposed combined ranking method with that from observational and simulation ranking methods, five evaluation criteria were used. These criteria relate to performance attributes, such as efficiency in identification of sites that show consistently unsafe performance, reliability in identification of the same hot spots (unsafe sites) during subsequent time periods, and ranking of consistency. The selection of the ranking criteria is important because a different ranking list can be obtained on the basis of different ranking criteria for a method. The data in the first period were used to produce a ranked list of potential unsafe locations, whereas data in the succeeding period were used to rank another list of such sites. Then, the results from these two ranked lists were compared and evaluated by the use of the evaluation criteria. Specifically, the evaluation tests are the 1. Site consistency test, 2. Method consistency test, 3. Total rank differences test, 4. Total score test, and 5. Sensitivity and specificity tests.
C1 j = Y
=
∑Y
n
∑
rank ( kj, i ) − rank ( kj, i +1 )
(18 )
where
The site consistency test rests on the premise that an untreated site identified to be high risk during time period i should also reveal an inferior safety performance in a subsequent time period, i + 1 (25). The method that identifies sites during period i + 1 with the highest total crash frequency is the most consistent one. The test statistic is given as
i +1 j, k
The absolute sum of total differences between the ranks of the highrisk sites identified in the first period (i) and ranks identified in the second period (i + 1) for the same group of sites is used to reflect the performance according to consistent rankings of sites across periods (25). The smaller that the total rank difference is, the more consistent that the ranking method is. The test statistic is given as
k = n − nα
Site Consistency Test
n
Total Rank Differences Test
C 3j =
The following sections elaborate on these tests.
i +1 j
C2j = method consistency test for method j, i {kn−nα , kin−nα+1, . . . , kin}j = top-ranked nα high-risk sites by method j during the first time period i, and i+1 i+1 {k n−nα , k n−nα+1 , . . . , k ni+1}j = top-ranked nα high-risk sites by method j during the second time period i + 1.
(16 )
k = n − nα
where C1j = site consistency test for method j, Yji+1 = sum of observed crash counts in the second time period (i + 1) for ranking method j, n = total number of sites, α = percentage of top-ranked high-risk sites, and i+1 Y j,k = observed crash counts at top-ranked nα sites by method j during the second time period (i + 1). Method Consistency Test
C3j = total rank differences test for method j, n = total number of sites, α = percentage of top-ranked high-risk sites, rank(kj,i) = rank order for site k by method j during time period i, and rank(kj,i+1) = rank order for site k by method j during time period i + 1. Total Score Test The total score test combines the results of the three previous tests to give a synthetic and easily understandable index (26). The test assumes that the three tests have the same weight. If the performance of method j is the best in all of the previous three tests, the value for C4 is equal to 100. The test statistic is given as
C4 j =
C 3 j − min j C 3 100 C1 j C 2 j × + + 1 − max j C 3 3 max j C1 max j C 2 (19 )
where C4j = total score test for method j, maxj C1 = maximum value of C1 among the methods compared, maxj C2 = maximum value of C2 among the methods compared, maxj C3 = maximum value of C3 among the methods compared, and minj C3 = minimum value of C3 among the methods compared.
The method consistency test evaluates a method’s performance by measuring the number of the same hot spots identified during both time periods (25). The greater that the number of hot spots identified in both periods is, the more consistent that the ranking method is. The test statistic is given as
Sensitivity and Specificity Tests
C 2 j = { kni − nα, kni − nα +1, . . . , kni } j ∩ { kni +−1nα, kni +−1nα+1 , . . . , kni+1 } j
The test of sensitivity and specificity uses the number of correct positives and correct negatives to assess the performance of vari-
(17 )
Shahdah, Saccomanno, and Persaud
123
ous ranking criteria (27). The idea behind this criterion is that true positives will persist in having a bad safety record, whereas false positives will regress toward a more normal safety record during the second period and will not be flagged. False negatives (i.e., sites that are not detected during the first time period but that are detected during the second time period) also exist. Sensitivity refers to the sites that have a safety problem identified during the first period and that have been identified during the second period as well. Specificity refers to sites with no safety problem during the first and the second time periods. The larger that the sensitivity and the specificity evaluation measures are, the more consistent that the method is. Sensitivity and specificity can be calculated as follows:
C5−1 =
number of correct positives total number of positives
(20)
C5 − 2 =
number of correct negatives total number of negatives
(21)
where C5−1 = sensitivity, C5−2 = specificity, number of correct = number of sites that continue to belong to the positives top-ranked nα in the second period (i + 1), total number of = number of correct (true) positives plus the positives number of false negatives (number of new sites that enter the list nα in the time period i + 1), number of correct = number of sites that do not belong to the negatives top-ranked list nα during both the time periods (i and i + 1), and total number of = number of correct negatives plus the num negatives ber of false positives (number of sites that dropped out of the top-ranked list nα during the second period, i + 1).
Results The priority ranking for unsafe sites was calculated on the basis of the proposed SC given in Equation 15 with different values of W and observational methods (EB, PSI, and AF) along with conflict methods (CF, CR1, and CR2) for two time periods (2002 to 2004 and 2005 to 2006) and 58 signalized intersections. Five evaluation criteria (C1 to C5) were applied to evaluate and compare the SC method with W (W = 1, 10, 100, and 1,000) for the observational and conflict methods (Equation 15). W equal to 1 means that every expected crash has an SC equivalent to one conflict, whereas W equal to 1,000 means that every expected crash has an SC equivalent to 1,000 conflicts. As W increases, SC regresses toward the estimate from the EB method. The comparison results are shown in Table 1 (best performers are shaded). For the site consistency test (Table 1), the AF method is the best method for ranking the top 5, 10, and 15 hot spots, whereas EB methods for SC with W equal to 100 and 1,000 perform the same as AF for the top 5 and 10 hot spots. The conflict methods (CF and CR1) and the SC method with W equal to 1 are the worst for ranking the top 5, 10, and 15 hot spots.
For the method consistency test (Table 1), all of the conflict methods are the best for identifying the top 5 hot spots. The SC method with W equal to 1 is the second best method for identifying the top 5 and 10 hot spots and, along with conflict methods (CF and CR1), is the best for identifying the top 15 hot spots. All of the observational methods and the SC method with W equal to 1,000 are the worst for identifying the top 5, 10, and 15 hot spots. PSI performed the worst at identifying the top 5, 10, and 15 hot spots. For the total rank difference test (Table 1), the SC method with W equal to 1 is the second best method for identifying the top 5 and 10 hot spots and, along with conflict methods (CF and CR1), is the best for identifying the top 15 hot spots. Conflict methods are the best for identifying the top 5 hot spots, whereas the PSI method is the worst for identifying the top 5, 10, and 15 hot spots. For the total score test (Table 1), the SC method with W equal to 100 is the best method for identifying the top 5 and 10 hot spots, whereas AF is the best for identifying the top 15 hot spots. The SC method with W equal to 100 is as good as AF for identifying the top 5 hot spots, whereas the PSI method is the worst for identifying the top 5, 10, and 15 hot spots. For the sensitivity and specificity tests (Table 1), the SC method with W equal to 1 is the second best after conflict methods for identifying the top 5 and 10 hot spots. With the conflict methods, CF and CR1 are the best for identifying the top 15 hot spots. All of the observational methods and the SC method with W equal to 1,000 are the worst at identifying the top 5, 10, and 15 hot spots. From Table 1, the conflict methods perform the best for the method consistency test, the total rank difference test, and the sensitivity and specificity test, whereas they perform the worst for the site consistency test. The observational methods (AF and EB), however, perform the best only for the site consistency test. Depending on the value of W, the performance of the SC method is good for the site consistency test (for W equal to 100 and 1,000) and the method consistency test, the total rank difference test, and the sensitivity and specificity tests (for W equal to 1). The SC method also stands out as the best for the total score test. As a result, it may be concluded that use of an appropriate value for W can reveal good results compared with those obtained by other ranking methods on the basis of either observational crash data or conflicts alone. In an attempt to determine an appropriate value of W for identifying the top 5 (8.62%) and 10 (17.64%) hot spots, the relationship between the weight factor and the total score test was established as shown in Figure 2. From Figure 2 for W values ≥3, the SC method is better than the observational and conflict methods for identifying the top 10 hot spots. For W values ≥7, the SC method gives better results than the other methods for identifying the top 5 and 10 hot spots. The highest values of the total score test for identifying both the top 5 and the top 10 hot spots occur at 12 ≤ W ≤ 33. Furthermore, the highest values of the total score test for identifying the top 5 hot spots occur at W equal to 12, 13, and 33. On the basis of the results shown in Figure 2, the evaluation criteria for the SC method with W equal to 32 are presented in Table 2 for comparison with the other methods (best performers are shaded). For the site consistency test, the SC method with W equal to 32 is the second best method, after EB and AF, for identifying the top 5 hot spots, with a difference of only nine crashes in the evaluation period; and it is the best method for identifying the top 10 hot spots for the same test. For the method consistency test, the SC method with W equal to 32 and conflict methods are the best for identifying the top 5 unsafe sites, but the SC method with W equal to 32 is the second best after
124
Transportation Research Record 2280
TABLE 1 Evaluation Results for Top 5, 10, and 15 Hot Spots at Different Weights Site Consistency Test Ranking Method EB PSI AF CF CR1 CR2 SC (W = 1) SC (W = 10) SC (W = 100) SC (W = 1,000)
Method Consistency Test
Total Rank Differences Test
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
158 122 158 35 35 20 35 149 158 158
226 178 226 96 96 45 96 200 226 226
283 221 287 123 123 73 123 255 280 283
3 2 3 5 5 5 4 4 4 3
7 5 7 9 9 10 9 7 8 7
12 7 12 15 15 14 15 12 12 12
10 98 11 0 0 2 1 3 7 9
53 157 56 7 7 4 7 20 48 53
79 212 69 12 12 5 10 47 78 79
Note: Best performers are shaded.
SC Method for Top 5 Hotspots
SC Method for Top 10 Hotspots
100 SC = CF + W × EB
Total Score Test Value
95 90 85
EB for top 5 hotspots EB for top 10 hotspots
80
CF for top 10 hotspots CF for top 5 hotspots
75 70 65 0
20
40
60 Weight Factor
80
100
120
FIGURE 2 Relationship between value of W and total score test value.
TABLE 2 Evaluation Results for Top 5, 10, and 15 Hot Spots at Weight of 32 Site Consistency Test Ranking Method EB PSI AF CF CR1 CR2 SC (W = 32)
Method Consistency Test
Total Rank Differences Test
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
158 122 158 35 35 20 149
226 178 226 96 96 45 228
283 221 287 123 123 73 274
3 2 3 5 5 5 5
7 5 7 9 9 10 8
12 7 12 15 15 14 13
10 98 11 0 0 2 6
53 157 56 7 7 4 31
79 212 69 12 12 5 56
Note: Best performers are shaded.
Shahdah, Saccomanno, and Persaud
Total Score Test
125
Sensitivity Test
Specificity Test
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
83.27 39.07 82.93 74.05 74.05 70.21 67.04 90.41 90.95 83.61
79.60 43.77 78.96 76.86 76.86 73.30 76.86 82.77 83.99 79.60
81.23 42.01 83.27 79.85 79.85 72.92 80.17 83.01 81.04 81.23
0.60 0.40 0.60 1 1 1 0.80 0.80 0.80 0.60
0.70 0.50 0.70 0.90 0.90 1 0.90 0.70 0.80 0.70
0.80 0.47 0.80 1 1 0.93 1 0.80 0.80 0.80
0.96 0.96 0.96 1 1 1 0.98 0.98 0.98 0.96
0.94 0.94 0.94 0.98 0.98 1 0.98 0.94 0.96 0.94
0.93 0.93 0.88 1 1 0.98 1 0.93 0.93 0.93
standing of the safety problem at a given site and should be considered in priority ranking. Such consideration should result in the more efficient allocation of scarce intervention funds to those sites most in need of treatment. The proposed SC method is conceptually appealing in that it is essentially a Bayesian framework that incorporates two partly independent clues about an intersection’s safety. Thus, it seems reasonable that future research could develop a theoretical, or at least a logical, basis for the weight used, in much the same way that theory-based weights are used for EB crash predictions. Use of such a theoretical or logical basis will facilitate the transferability of a methodology for application contexts without the need to undertake a cumbersome, iterative, optimization of the weights, as was done for this exploratory research.
conflict methods, with a difference of two sites, at identifying the top 10 unsafe sites. For the total rank difference method, the SC method with W equal to 32 is the second best after conflict methods. The SC method with W equal to 32 is found to be the best method for identifying the top 5, 10, and 15 unsafe sites on the basis of the total score test. Furthermore, for sensitivity and specificity tests, the SC method with W equal to 32 and conflict methods are the best for identifying the top 5 hot spots, but the SC method with W equal to 32 is the second best after conflict methods for identifying the top 10 hot spots. Overall, it may be concluded that the SC method with W equal to 32 is the best method for identifying the hot spots, since it performed very well with all evaluation criteria. Conclusions This paper presents and illustrates a new method for ranking hot spots that combines the results of a simulation of traffic conflicts with EB crash predictions. The integrated model was found to identify hot spots better than conventional observational crash-based models and traffic conflicts alone. This result confirms that higher-risk interactions and near misses are important to obtain a better under-
Total Score Test
Sensitivity Test
Acknowledgments The authors acknowledge the Toronto Traffic Management Center (Traffic Safety Unit) for providing the data required to complete this research. The research was supported by grants from the Natural Sciences and Engineering Research Council of Canada.
Specificity Test
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
Top 5
Top 10
Top 15
83.27 39.07 82.93 74.05 74.05 70.21 96.06
79.30 43.54 78.67 76.73 76.73 73.25 87.60
81.23 42.01 83.27 79.85 79.85 72.92 86.03
0.60 0.40 0.60 1 1 1 1
0.70 0.50 0.70 0.90 0.90 1 0.80
0.80 0.47 0.80 1 1 0.93 0.87
0.96 0.96 0.96 1 1 1 1
0.94 0.94 0.94 0.98 0.98 1 0.96
0.93 0.93 0.88 1 1 0.98 0.95
126
References 1. Traffic Safety Facts 2008. Publication DOT HS 811 170. NHTSA, U.S. Department of Transportation, 2009. http://www-nrd.nhtsa.dot.gov/ Pubs/811170.pdf. Accessed March 15, 2012. 2. Nicholson, A. J. The Variability of Accident Counts. Accident Analysis and Prevention, Vol. 17, No. 1, 1985, pp. 47–56. 3. Farmer, C. M. Reliability of Police-Reported Information for Determining Accident and Injury Severity. Traffic Injury Prevention, Vol. 4, No. 1, 2003, pp. 38–44. 4. Davis, G. Possible Aggregation Biases in Road Safety Research and a Mechanism Approach to Accident Modeling. Accident Analysis and Prevention, Vol. 36, No. 6, 2004, pp. 1119–1127. 5. Saunier, N., and T. A. Sayed. Automated Analysis of Road Safety with Video Data. In Transportation Research Record: Journal of the Transportation Research Board, No. 2019, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 57–64. 6. Hauer, E., and A. S. Hakkert. Extent and Some Implications of Incomplete Accident Reporting. In Transportation Research Record 1185, TRB, National Research Council, Washington, D.C., 1988, pp. 1–10. 7. Perkins, S., and J. L. Harris. Traffic Conflict Characteristics—Accident Potential at Intersections. General Motors Corporation, Warren, Mich., 1967. 8. Amundsen, F., and C. Hyden. Proc., First Workshop on Traffic Conflicts, Institute of Transport Economics, Oslo, Norway, 1977. 9. Brown, G. R. Traffic Conflicts for Road User Safety Studies. Canadian Journal of Civil Engineering, Vol. 21, No. 1, 1994, pp. 1–15. 10. Sayed, T., G. Brown, and F. Navin. Simulation of Traffic Conflicts at Unsignalized Intersections with TSC–sim. Accident Analysis and Prevention, Vol. 26, 1994, pp. 593–607. 11. Van der Horst, A. R. A. A Time-Based Analysis of Road User Behaviour in Normal and Critical Encounters. PhD dissertation. Delft University of Technology, Delft, Netherlands, 1990. 12. Hyden, C. The Development of a Method for Traffic Safety Evaluation: The Swedish Traffic Conflicts Technique. Bulletin 70. Department of Traffic Planning and Engineering, Lund University, Lund, Sweden, 1987. 13. VISSIM 5.30 User Manual. Planung Transport Verkehr AG, Karlsruhe, Germany, 2011. 14. Cunto, F., and F. F. Saccomanno. Calibration and Validation of Simulated Vehicle Safety Performance at Signalized Intersections. Accident Analysis and Prevention. Vol. 40, No. 3, 2008, pp. 1171–1179. 15. Elvik, R. A Survey of Operational Definitions of Hazardous Road Locations in Some European Countries. Accident Analysis and Prevention, Vol. 40, No. 6, 2008, pp. 1830–1835.
Transportation Research Record 2280
16. Hauer, E. Identification of Sites with Promise. In Transportation Research Record 1542, TRB, National Research Council, Washington, D.C., 1996, pp. 54–60. 17. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. http://www.R-project.org. Accessed March 15, 2012. 18. McCullagh, P., and A. J. Nelder. Generalised Linear Models, 2nd ed. Chapman & Hall/CRC, Boca Raton, Fla., 1989. 19. Gettman, D., and L. Head. Surrogate Safety Measures from Traffic Simulation Models. In Transportation Research Record: Journal of the Transportation Research Board, No. 1840, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 104–115. 20. Archer, J. Indicators for Traffic Safety Assessment and Prediction and Their Application in Micro-Simulation Modelling: A Study of Urban and Suburban Intersections. PhD dissertation. Royal Institute of Technology, Stockholm, Sweden, 2005. 21. Cunto, F. Assessing Safety Performance of Transportation Systems Using Microscopic Simulation. PhD dissertation. University of W aterloo, Waterloo, Ontario, Canada, 2008. 22. Cooper, D. F., and N. Ferguson. Traffic Studies at t-Junctions: A Conflict Simulation Model. Traffic Engineering and Control, Vol. 17, No. 7, 1976, pp. 306–309. 23. Hyden, C. Traffic Safety Work with Video-Processing. Technical report. Transportation Department, University Kaiserslautern, Germany, 1996. 24. Pu, L., and R. Joshi. Surrogate Safety Assessment Model (SSAM): Software User Manual. Publication FHWA-HRT-08-050. FHWA, U.S. Department of Transportation, 2008. http://www.fhwa.dot.gov/publications/ research/safety/08050/08050.pdf. Accessed March 15, 2012. 25. Cheng, W., and S. P. Washington. New Criteria for Evaluating Methods of Identifying Hot Spots. In Transportation Research Record: Journal of the Transportation Research Board, No. 2083, Transportation Research Board of the National Academies, Washington, D.C., 2008, pp. 76–85. 26. Montella, A. A Comparative Analysis of Hotspot Identification Methods. Accident Analysis and Prevention, Vol. 42, No. 2, 2010, pp. 571–581. 27. Elvik, R. Comparative Analysis of Techniques for Identifying Locations of Hazardous Roads. In Transportation Research Record: Journal of the Transportation Research Board, No. 2083, Transportation Research Board of the National Academies, Washington, D.C., 2008, pp. 72–75. The Safety Data, Analysis, and Evaluation Committee peer-reviewed this paper.
