Traffic Injury Prevention
ISSN: 1538-9588 (Print) 1538-957X (Online) Journal homepage: http://www.tandfonline.com/loi/gcpi20
Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges Fatemeh Baratian-Ghorghi, Huaguo Zhou, Mohammad Jalayer & Mahdi Pour-Rouholamin To cite this article: Fatemeh Baratian-Ghorghi, Huaguo Zhou, Mohammad Jalayer & Mahdi Pour-Rouholamin (2015) Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges, Traffic Injury Prevention, 16:6, 599-604, DOI: 10.1080/15389588.2014.981651 To link to this article: http://dx.doi.org/10.1080/15389588.2014.981651
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Traffic Injury Prevention (2015) 16, 599–604 C Taylor & Francis Group, LLC Copyright ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2014.981651
Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges FATEMEH BARATIAN-GHORGHI, HUAGUO ZHOU, MOHAMMAD JALAYER, and MAHDI POUR-ROUHOLAMIN
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Department of Civil Engineering, Auburn University, Auburn, Alabama Received 17 June 2014, Accepted 24 October 2014
Background: Several previous studies, based upon wrong-way driving (WWD) crash history, have demonstrated that partial cloverleaf (parclo) interchanges are more susceptible to WWD movements than others. Currently, there is not a method available to predict WWD incidents and to prioritize parclo interchanges for implementing safety countermeasures for reducing WWD crashes. Objectives: The focus of this manuscript is to develop a mathematical method to estimate the probability of WWD incidents at exit ramp terminals of this type of interchange. Methods: VISSIM traffic simulation models, calibrated by field data, are utilized to estimate the number of potential WWD maneuvers under various traffic volumes on exit ramps and crossroads. The Poisson distribution model was implemented without field observation and crash data. Results: A comparison between the field data and simulation outputs revealed that the developed model enjoys an acceptable level of accuracy. The proposed model is largely sensitive to left-turn volume toward an entrance ramp (LVE) than stopped vehicles at an exit ramp (SVE). The results indicated that potential WWD events increase when LVEs increase and SVEs decrease. Also, the probability of WWD event decreases as road users are more familiar with the facility. Conclusion: The proposed method can diminish one of the challenges in front of transportation engineers, which is to identify high WWD crash locations due to insufficient information in crash reports. The results are helpful for transportation professionals to take proactive steps to identify locations for implementing safety countermeasures at high risk signalized parclo interchanges. Keywords: wrong-way driving, computer simulation, VISSIM, partial cloverleaf interchange, Poisson distribution
Introduction Wrong-way driving (WWD), by definition, happens when a driver, inadvertently or deliberately, drives in the opposite direction of traffic flow along a physically divided highway or its access ramps (American Traffic Safety Services Association 2014). Each year, hundreds of fatal WWD crashes occur across the United States and thousands of injuries are reported in crashes caused by wrong-way drivers (Baratian-Ghorghi et al. 2014). The nature of WWD, which often tends to be a head-on collision, has drawn the attention of transportation planners for the past few decades. As compiled and reported by the NHTSA’s Fatality Analysis Reporting System in 2011, WWD crashes caused 349 fatalities in the United States. The average fatalities per WWD fatal crash was 1.24 against the rate of 1.09 fatalities for all other roadway fatal crashes (National Transportation Safety Board 2012; NHTSA 2014). Associate Editor Clay Gabler oversaw the review of this article. Address correspondence to Fatemeh Baratian-Ghorghi, Department of Civil Engineering, Auburn University, 238 Harbert Engineering Center, Auburn, AL 36849-5337. E-mail: baratian@ auburn.edu Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gcpi.
Though the main contributing factors in WWD crashes are human-related factors, past studies (Morena and Leix 2012) warned that some interchange types are highly susceptible to WWD movements. In the instance of WWD entry points, special attention should be given to the characteristics of exit ramp and crossroad intersections, including geometric design elements (e.g., raised median, channelizing island, turning radius, etc.), signage, pavement markings, traffic signals, and lighting conditions. Given that many wrong-way drivers are either killed at crash scenes or are unable to remember when they started driving in the wrong direction, many WWD crash reports do not contain information on entry points to identify suspected problem locations. Therefore, it would be beneficial to develop a method to predict the total number of potential wrong-way entries for existing or new interchanges. For those high-risk interchanges, advanced signage, pavement markings, or intelligent transportation systems technologies can be considered. In this study, problematic exit ramp terminals at signalized parclo interchanges were analyzed in terms of potential WWD occurrence based on field observation and computer simulation. Two mathematical models were developed to predict the probability that a turning vehicle may possibly make a wrongway entry. Finally, an evaluation method was recommended to rank signalized parclo interchanges for safety improvements
600 based on existing or predicted traffic patterns at exit ramp intersections.
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Literature Reviews In an attempt to identify contributing factors regarding WWD crashes on Illinois freeways, Zhou et al. collected and analyzed a 6-year period of crash data from 2004 to 2009 (Zhou, Zhao, et al. 2014; Zhou and Pour Rouholamin 2014). In this study, a total of 217 WWD crashes were identified but only 47 crash reports contained the information about wrong-way entry points. In order to rank the high-crash locations, a new methodology was developed to predict the first and second possible entry points based on the crash locations and distance from upstream interchanges. This study recognized parclo interchanges as one of the top interchange types in terms of wrong-way entry frequency. Morena and Leix (2012), in a joint research project between the Michigan Department of Transportation and the Federal Highway Administration, studied 5 years of crash data from 2005 to 2009 and identified 110 WWD crashes. Parclo interchanges were also the originating points of 60% of WWD crashes with known entry points while representing only 21% of total interchanges in Michigan. Surprisingly, one specific parclo interchange was the entry point for 10 out of those 21 crashes. The researchers then targeted the suspect feature of the design, which is the adjacency of 2 parallel exit and entrance ramps in the same quadrant that intersect the crossroad at nearly right angles. After a total of 7 fatalities in 5 reported WWD crashes in Charlotte, North Carolina, between October 2005 and March 2006, North Carolina Department of Transportation officials initiated a thorough analysis of the existing crash data from 2000 to 2005 to further investigate key contributing factors at a statewide scale. Following this effort, a total of 162 (out of 195,313) crashes were found to result from traveling against the stream of traffic (Braam 2006). Another study conducted by the Washington State Department of Transportation reported that there were 30 WWD crashes from 1986 to 1996, resulting in 15 fatalities. Further analyses demonstrated that a large proportion of WWD crashes originated from one specific exit ramp of a parclo interchange. Traffic monitoring cameras from May to December 2001 also captured 18 WWD incidents at the same location (Kaminski Leduc 2008; Moler 2002). Past studies have proven parclo interchanges are the interchange types most likely to have a higher wrong-way entry frequency. The data provided from these studies have prioritized a need for further improvements on these specific interchanges; however, at this time, research has not been conducted on developing a proactive method to rank parclo interchanges based on traffic patterns. On the subject of predictive models, the Poisson distribution is found to be applicable to a variety of traffic problems, such as prediction of crash counts by severity (Ma et al. 2008), the effect of changing the number of lanes on crash rate (Li and Carriquiry 2005), and occurrence of traffic accidents (Tamayo 2009). Zhou, Chen, and Baratian-Ghorghi (2014) developed a probability model to predict the potential traffic conflict rate
Baratian-Ghorghi et al. at intersections with an offset right-turn lane. The authors employed traffic simulation software to verify the model and determine the frequency of the conflicts under various traffic volumes on the major and minor roads at unsignalized intersections.
Methodology Wrong-Way Movements Identification Based on the results of literature reviews, the WWD problem with parclo interchanges is attributed to their feature of having two closely spaced ramps that intersect crossroads at roughly right angles. Figure A1 (see online supplement) depicts a scheme of exit/entrance ramps of parclo interchanges and potential wrong-way movements, as shown in red. Along with intersection geometry and traffic control devices, traffic volume is found to affect probability of WWD incidents at parclo interchanges. In this article, the probability of a WWD incident is a scenario defined as follows: “A left-turn vehicle that intends to move toward the entrance ramp from the crossroad, can possibly enter the exit ramp mistakenly when there are no other vehicles stopped at the exit ramp terminal,” as shown in Figure A1. Past studies have shown that most WWD crashes occurred at midnight or early morning when traffic volumes were very low. On the contrary, during the peak hours of daytime, the traffic on the exit ramps prevented left-turning vehicles from entering exit ramps. Therefore, low traffic volume is found to be a precondition for possible WWD. Figure A2 (see online supplement) illustrates the procedure employed in this article to identify the potential WWD events at certain time intervals under different traffic volume conditions. Field Observation and Computer Simulation In the field study, intersection volumes, signal timing, and possible WWD movements were recorded for each 1-h time interval. Simulation models, verified by potential WWD events, were developed to resemble the existing traffic conditions. In the VISSIM simulation software’s output file, the vehicles’ information at a specific moment and a particular location in the modeled network are recorded (Traffic Mobility Logistics 2008). Taking advantage of this capability, it is possible to determine the operational status of the intersection at any given time and extract the number of possible WWD events. Mathematical Models In dealing with crash frequency and severity, which are always discrete and nonnegative integer values, employing a count data model, such as a Poisson distribution model, is recommended (Caliendo et al. 2007; Chiou and Fu 2013; Miaou 1994; Polus and Cohen 2012). The general equation of the Poisson distribution model can be expressed as (Gerlough and Barnes 1971) P(N = n) =
λn −! e , n!
(1)
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Second Approach/Model Development The precondition for a potential WWD event is defined as the traffic condition when there is no stopped vehicle on exit ramps (SVE) and a presence of at least one LVE during the green time intervals for LVE. A WWD event could occur only if there were vehicles on cross-road left-turn lanes making left turns onto the entrance ramp. The probability of one or more LVEs (PLVE,i (NLVE = 0)) at a given time interval can be expressed as PLVE,i (NLVE = 0) = 1 − PLVE,i (NLVE = 0) = 1 −
λ0LVE −λLVE e 0!
T , 4
(4)
= 1 − e−λLVE , i = 1, 2, . . . ,
Fig. 1. Scheme of a wrong-way movement.
where P (N = n): is the probability of the occurrence of n events at a given time interval, e is the base of natural logarithm (e = 2.71828 . . .), N is the number of potential events, and λ is the arrival rate. In this study, 2 Poisson distribution–based approaches were developed to calculate the probability of WWD events. In the first approach, the number of possible wrong-way entries and cycle length were used as inputs to Eq. (1). It requires field data collection of number of potential wrong-way movements. The second approach was based on traffic flow rates of left-turn volumes from crossroads and traffic volumes on exit ramps. It does not need the number of potential WWD events in the field. Both approaches are elaborated in the following sections. First Approach Figure 1 shows a potential WWD movement as a red dashed line at a signalized intersection of a parclo interchange. The left-turn vehicles onto entrance (LVE) ramp are shown as a green dashed line, having a protected green interval for each cycle. The probability of having one or more WWD at one cycle depends on the number of potential WWD events in the field and cycle length, as expressed in Eq. (2): P1 (C) = 1 − e−λ ,
(2)
where λ is the average number of potential WWD movements recorded in the field in one cycle. Equation (3) is the probability of having one or more potential WWD events in a 1-h time frame (P1 (H, WWD ≥ 1)). P1 (H, WWD ≥ 1) = 1 − (1 − P1 (C)) N = 1 − e−N×λ , where N denotes the number of cycles in 1 h.
(3)
where NLVE is the number of LVEs at a given time interval, λLVE : is the LVE arrival rate, i is the time interval number, and T is the length of red time in one cycle assigned to SVEs. The time interval was assumed to be equal to 4 s, which is the minimum time required for a vehicle to clear an intersection. This time interval length allows LVEs to cross the major road and to enter the entrance ramp, accounting for car-following phenomenon. The probability of no SVEs in the first time interval (PSV E,1 (NSVE = 0)) is calculated as follows: PSV E,1 (NSVE = 0) =
λ0SVE −λSVE e = e−λSVE , 0!
(5)
where NSVE is the number of SVEs at a given time interval (here the first time interval) and λSVE is the SVE arrival rate. It is clear that the probability of making a wrong-way entry to the exit ramp is equal to zero if there is a vehicle stopped at the exit ramp. In other words, LVEs in the ith moment might make a wrong-way entry if no SVEs were observed during those moments. Equation (6) represents the probability of no SVEs in the ith time interval: i (NSVE = 0) = e−i ×λSVE , PSVE,i (NSVE = 0) = PSVE T i = 1, 2, . . . , . 4
(6)
Equation (6) indicates that as the time elapsed after the red signal is on the exit ramps, the probability of having no vehicle queue on exit ramps will decrease. Traffic counts in each approach are assumed to be independent; therefore, the probability of WWD occurrence in the ith time interval, P(Ii ), would be P(Ii ) = PSVE,i (NSVE = 0) × PLVE,i (NLVE = 0) = e−i ×λSVE × [1 − e−λLVE ], i = 1, 2, . . . ,
T . 4
(7)
The probability of a WWD event in each cycle is as follows: P2 (C) = P(I1 ∪ I2 ∪ I3 . . . ∪ IT/4 ) c = 1 − P I1c ∩ I2c ∩ I3c . . . ∩ IT/4
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Table 1. Observed and estimated potential WWD events Field data (observed)
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Time interval
LVEs
SVEs
10:00 p.m.–11:00 p.m. 11:00 p.m.–12:00 a.m. 12:00 a.m.–1:00 a.m 1:00 a.m.–2:00 a.m. 2:00 a.m.–3:00 a.m 3:00 a.m.–4:00 a.m.
18 16 17 11 6 2
130 104 81 31 17 12
10:00 pm.–11:00 p.m. 11:00 p.m–12:00 a.m. 12:00 a.m.–1:00 a.m. 1:00 a.m.–2:00 a.m. 2:00 a.m.–3:00 a.m. 3:00 a.m–4:00 a.m.
32 36 7 10 6 4
78 66 48 32 20 15
Simulation output data (estimated)
Potential WWD events
= 1 − [1 − e−λSVE × [1 − e−λLVE ] ] ×[1 − e−2λSVE × [1 − e−λLVE ] ] . . . × [1 − e−T/4×λSVE × [1 − e−λLVE ] ].
LVEs
SVEs
Potential WWD events
Friday 3 3 4 4 3 1
17 15 18 13 5 2
127 105 81 30 16 14
3 4 4 5 2 1
Saturday 8 10 3 4 3 2
30 34 8 10 7 3
76 65 46 32 19 16
8 9 3 4 2 2
Field Data Collection (8)
Finally, the probability of WWD events for 1 h can be calculated using Eq. (9), similar to Eq. (3): P2 (H, WWD ≥ 1) = 1 − P2 (H, WWD = 0),
(9)
in which the probability of having no WWD incident in 1 h would be P2 (H, WWD = 0) = (1 − P2 (C)) N .
(10)
Based on WWD crash history and field observations of the study intersection, it was found that a high-crash location typically has more than 2 potential WWD events per hour of observation. Considering that in order to identify intersections for improvements, the probabilities of having 2, 3, or more WWD incidents were calculated. Equations (11)–(14) were used to compute the probability of 1, 2, 3, or more WWD incidents in 1 h: P2 (H, WWD = 1, 2) = P2 (H, WWD = 1) + P2 (H, WWD = 2),
(11)
where P2 (H, WWD = 1) = N × P2 (C) × (1 − P2 (C)) N−1
(12)
and
N × P22 (C) × (1 − P2 (C)) N−2 (13) 2 P2 (H, WWD ≥ 3) = 1 − P2 (H, WWD = 1, 2) − P2 (H, WWD = 0). (14)
P2 (H, WWD = 2) =
In order to predict WWD probabilities, field data were collected for 6 consecutive hours (from 10:00 p.m. to 4:00 a.m.) during 2 weekend nights in June 2013 at an intersection with a history of high wrong-way crashes (3 WWD crashes in 3 years; Zhou, Wang, et al. 2012; Zhou, Zhao, et al. 2012), located at South Bluff Road and I-64 in the city of Caseyville, Illinois. This intersection has two abutting exit and entrance ramps separated by a raised median (Figure A1). Researchers collected field data at this intersection. Past studies showed that the possibility of making a wrongway entry is disproportionally high during these time periods (Morena and Leix 2012; National Transportation Safety Board 2012; Sallee 2007). As for signal control, 2 main parameters, cycle length and the red intervals for SVEs (or green intervals for LVEs), were recorded to be 120 and 55 s, respectively, at the study intersection.
Data Analysis and Results Simulation Models To estimate the number of potential WWD events, VISSIM models were built based upon field data at the study intersection. Taking advantage of detectors in VISSIM, the number of LVEs, SVEs, and corresponding traffic signal indications at any given moment were archived, and the time intervals relating to when the WWD maneuvers may occur were identified (Table 1). The results indicated that potential WWD events increase when LVEs increase and SVEs decrease. A comparison between the field data and simulation outputs revealed that the developed model has an acceptable level of accuracy (correlation coefficient between 2 observed and estimated values for LVEs, SVEs, and potential WWD volumes are equal to 0.99). Mathematical Models Comparison Between First and Second Approaches In order to verify that mathematical models can provide reasonable estimate for higher traffic volumes, a total of 23
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simulation models were generated for a combination of gradually increasing LVEs and SVEs, which provided the number of potential WWD events for use in a first approach. In this study, data from simulation models and Eqs. (1)–(10) were used to compare the calculation results by the two approaches (Table A1; see online supplement). As expected, Table A1 shows that the estimated probabilities from both approaches have the same trend against the traffic volumes. A t-test with 99% confidence interval produced a P-value of .5046. This value is greater than initial assumption of .01, meaning that there is no statistically significant difference between the results of the first and second mathematical approaches. Because the number of WWD events are nonnegative integers, the probability resulting from the first approach would be (1 − e(−1) = 0.63). Though there is one potential WWD event observed, this number remains unchanged even with an increase in traffic volumes. The results from the second approach show that the probability will continually decrease as the traffic volumes increase. Effect of Levels of Unfamiliarity Past studies have found that unfamiliar drivers are heavily involved in roadway crashes (Sivak and Schoettle 2010). Therefore, 4 different levels of unfamiliarity (100, 50, 30, and 15%) were considered. The volume of LVEs in Eqs. (1)–(14) is equal to the actual LVEs multiplied by the percentage for unfamiliar drivers. Figure A3 (see online supplement) illustrates the variation in the probabilities versus changes in LVE volume and the percentage of local users. Concurrent Effect of LVE and SVE Volumes The developed model in the second approach is largely sensitive to the change in LVE volume. To prove this relationship, elasticity analysis was accomplished by changing one unit in the volume of LVE and SVE and monitoring the amount of change in WWD event probability (Eqs. (15) and (16)). P2 (H) = +0.00188 VLVE P2 (H) = = −0.00060. VSVE
eLVE =
(15)
eSVE
(16)
Fig. 2. Probability of WWD occurrence per hour.
Fig. 3. Probability of WWD occurrence per hour (cycle length = 120 s and red time = 32 s).
Analyses indicated that the model is 3 times more sensitive to the LVE volume than SVE, which offsets the effects of SVEs on the probability values to some extent. Therefore, the effect of these volumes on the probability needs to be investigated independently (Figure 2). According to Figure 2, the more incidences of SVE, the lower the probability of WWD. On the contrary, the higher the LVE volumes, the higher the probability is calculated. In order to demonstrate the impact of signal timing, the value of WWD probability against LVE and SVE volumes under 2 different cycle lengths and red times for SVE on existing ramps are shown in Figures 3 and 4. To prioritize the intersections for treatment, weights of 0, 5, and 10 were assigned to the situations with no, 1 or 2, and 3 or more WWD in 1 h, respectively. Therefore, the weighted score (the so-called risk score), which varies between 0 and 10 for each intersection, was calculated (e.g., the risk score for the first model is 0.12 × 0 + 0.55 × 5 + 0.33 × 10 = 6). Based on the scores, it can be determined which intersections should be given the highest improvement priority (Table A2; see online supplement). As shown in the table, the highest priority should be given to intersections 2 to 5, which carry relatively low traffic volumes.
Fig. 4. Probability of WWD occurrence per hour (cycle length = 60 s and red time = 32 s).
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This study aimed at developing a method for diminishing one of the challenges of transportation engineers, which is to identify high WWD crash locations due to insufficient information in crash reports. This article demonstrated that the probability of WWD can be calculated at an acceptable level of accuracy by implementing a Poisson distribution model without field observation and crash data. The findings reveal that the proposed model is largely sensitive to left-turn volume toward an entrance ramp compared to stopped vehicles at an exit ramp. The results indicated that the probability of a WWD event decreases as road users are more familiar with the facility.
Acknowledgment The authors would like to extent their sincerest thanks to the technical review panel members for their guidance and support.
Funding This article is based on a research project funded by the Illinois Department of Transportation (IDOT) and the Illinois Center for Transportation (ICT).
Supplemental Materials Supplemental data for this article can be accessed on publisher’s website.
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Baratian-Ghorghi et al. Kaminski Leduc JL. Wrong-Way Driving Countermeasures. 2008. Old Research Report 2008-R-0491. Available at: http://www.cga.ct.gov/2008/rpt/2008-r-0491.htm. Accessed July 29, 2014. Li W, Carriquiry A. The Effect of Four-lane to Three-lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads. Ames, IA: Department of Statistics, Iowa State University; 2005. Ma J, Kockelman KM, Damien PA. Multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods. Accid Anal Prev. 2008;40:964–975. Miaou SP. The relationship between truck accidents and geometric design of road sections: Poisson versus negative binomial regressions. Accid Anal Prev. 1994;26:471–482. Moler S. Stop. You are going the wrong way! Public Roads. 2002;66(2):110. Morena DA, Leix TJ. Where these drivers went wrong. Public Roads. 2012;75(6):33–41. National Transportation Safety Board. Wrong-Way Driving. Washington, DC: NTSB; 2012. Highway Special Investigation Report. NTSB/SIR-12/01, PB2012-917003, Notation 8453. NHTSA. Fatality Analysis Reporting System. Available at: http:// www.fars.nhtsa.dot.gov/main/index.aspx. Accessed July 29, 2013. Polus A, Cohen M. A new, non-canonical Poisson regression model for the prediction of crashes on low-volume rural roads. IATSS Research. 2012;35:98–103. Sallee R. Right solutions for wrong-way driving? Houston Chronicle. March 5, 2007:1A. Sivak M, Schoettle B. Drivers on Unfamiliar Roads and Traffic Crashes. Ann Arbor, MI: Transportation Research Center, University of Michigan; 2010. Report No. UMTRI-2010-31. Tamayo AM. Occurrence of Traffic Accidents in the Philippines: An Application of Poisson Regression Analysis. Philippines: Research and Publication Center, University of Mindanao; 2009. Traffic Mobility Logistics. VISSIM—state-of-the-art multi-modal simulation. PTV vision. 2008. Available at: http://www.ptvap.com/docs/ https://services.crmservice.eu/raiminisite/Image/Download?docid= 2052. Accessed July 29, 2014.. Zhou H, Chen H, Baratian-Ghorghi F. A new probabilistic model for reducing potential vision blockage traffic conflicts at unsignalized intersections. Paper presented at: 93rd Annual Meeting of the Transportation Research Board; January 12−16, 2014; Washington, DC. Zhou H, Pour Rouholamin M. Guidelines for Reducing Wrong-Way Crashes on Freeways. Rantoul, IL: Illinois Center for Transportation; 2014. Zhou H, Wang L, Gahrooei MR, Jalayer M. Contributing factors to wrong-way driving crashes in Illinois. Paper presented at: ITE Midwestern District Conference and TRB 4th Urban Street Symposium; June 24−27, 2012; Chicago, IL. Zhou H, Zhao J, Fries R, Pour Rouholamin M. Statistical characteristics of wrong-way driving crashes on Illinois freeways. Paper presented at: 93rd Annual Meeting of Transportation Research Board; January 12−16, 2014; Washington, DC. Zhou H, Zhao J, Fries R, Wang L, Gahrooei MR. Investigation of Contributing Factors Regarding Wrong-Way Driving on Freeways. Rantoul, IL: Illinois Center for Transportation; 2012.
ISSN: 1538-9588 (Print) 1538-957X (Online) Journal homepage: http://www.tandfonline.com/loi/gcpi20
Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges Fatemeh Baratian-Ghorghi, Huaguo Zhou, Mohammad Jalayer & Mahdi Pour-Rouholamin To cite this article: Fatemeh Baratian-Ghorghi, Huaguo Zhou, Mohammad Jalayer & Mahdi Pour-Rouholamin (2015) Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges, Traffic Injury Prevention, 16:6, 599-604, DOI: 10.1080/15389588.2014.981651 To link to this article: http://dx.doi.org/10.1080/15389588.2014.981651
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Date: 08 November 2015, At: 14:54
Traffic Injury Prevention (2015) 16, 599–604 C Taylor & Francis Group, LLC Copyright ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2014.981651
Prediction of Potential Wrong-Way Entries at Exit Ramps of Signalized Partial Cloverleaf Interchanges FATEMEH BARATIAN-GHORGHI, HUAGUO ZHOU, MOHAMMAD JALAYER, and MAHDI POUR-ROUHOLAMIN
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Department of Civil Engineering, Auburn University, Auburn, Alabama Received 17 June 2014, Accepted 24 October 2014
Background: Several previous studies, based upon wrong-way driving (WWD) crash history, have demonstrated that partial cloverleaf (parclo) interchanges are more susceptible to WWD movements than others. Currently, there is not a method available to predict WWD incidents and to prioritize parclo interchanges for implementing safety countermeasures for reducing WWD crashes. Objectives: The focus of this manuscript is to develop a mathematical method to estimate the probability of WWD incidents at exit ramp terminals of this type of interchange. Methods: VISSIM traffic simulation models, calibrated by field data, are utilized to estimate the number of potential WWD maneuvers under various traffic volumes on exit ramps and crossroads. The Poisson distribution model was implemented without field observation and crash data. Results: A comparison between the field data and simulation outputs revealed that the developed model enjoys an acceptable level of accuracy. The proposed model is largely sensitive to left-turn volume toward an entrance ramp (LVE) than stopped vehicles at an exit ramp (SVE). The results indicated that potential WWD events increase when LVEs increase and SVEs decrease. Also, the probability of WWD event decreases as road users are more familiar with the facility. Conclusion: The proposed method can diminish one of the challenges in front of transportation engineers, which is to identify high WWD crash locations due to insufficient information in crash reports. The results are helpful for transportation professionals to take proactive steps to identify locations for implementing safety countermeasures at high risk signalized parclo interchanges. Keywords: wrong-way driving, computer simulation, VISSIM, partial cloverleaf interchange, Poisson distribution
Introduction Wrong-way driving (WWD), by definition, happens when a driver, inadvertently or deliberately, drives in the opposite direction of traffic flow along a physically divided highway or its access ramps (American Traffic Safety Services Association 2014). Each year, hundreds of fatal WWD crashes occur across the United States and thousands of injuries are reported in crashes caused by wrong-way drivers (Baratian-Ghorghi et al. 2014). The nature of WWD, which often tends to be a head-on collision, has drawn the attention of transportation planners for the past few decades. As compiled and reported by the NHTSA’s Fatality Analysis Reporting System in 2011, WWD crashes caused 349 fatalities in the United States. The average fatalities per WWD fatal crash was 1.24 against the rate of 1.09 fatalities for all other roadway fatal crashes (National Transportation Safety Board 2012; NHTSA 2014). Associate Editor Clay Gabler oversaw the review of this article. Address correspondence to Fatemeh Baratian-Ghorghi, Department of Civil Engineering, Auburn University, 238 Harbert Engineering Center, Auburn, AL 36849-5337. E-mail: baratian@ auburn.edu Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gcpi.
Though the main contributing factors in WWD crashes are human-related factors, past studies (Morena and Leix 2012) warned that some interchange types are highly susceptible to WWD movements. In the instance of WWD entry points, special attention should be given to the characteristics of exit ramp and crossroad intersections, including geometric design elements (e.g., raised median, channelizing island, turning radius, etc.), signage, pavement markings, traffic signals, and lighting conditions. Given that many wrong-way drivers are either killed at crash scenes or are unable to remember when they started driving in the wrong direction, many WWD crash reports do not contain information on entry points to identify suspected problem locations. Therefore, it would be beneficial to develop a method to predict the total number of potential wrong-way entries for existing or new interchanges. For those high-risk interchanges, advanced signage, pavement markings, or intelligent transportation systems technologies can be considered. In this study, problematic exit ramp terminals at signalized parclo interchanges were analyzed in terms of potential WWD occurrence based on field observation and computer simulation. Two mathematical models were developed to predict the probability that a turning vehicle may possibly make a wrongway entry. Finally, an evaluation method was recommended to rank signalized parclo interchanges for safety improvements
600 based on existing or predicted traffic patterns at exit ramp intersections.
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Literature Reviews In an attempt to identify contributing factors regarding WWD crashes on Illinois freeways, Zhou et al. collected and analyzed a 6-year period of crash data from 2004 to 2009 (Zhou, Zhao, et al. 2014; Zhou and Pour Rouholamin 2014). In this study, a total of 217 WWD crashes were identified but only 47 crash reports contained the information about wrong-way entry points. In order to rank the high-crash locations, a new methodology was developed to predict the first and second possible entry points based on the crash locations and distance from upstream interchanges. This study recognized parclo interchanges as one of the top interchange types in terms of wrong-way entry frequency. Morena and Leix (2012), in a joint research project between the Michigan Department of Transportation and the Federal Highway Administration, studied 5 years of crash data from 2005 to 2009 and identified 110 WWD crashes. Parclo interchanges were also the originating points of 60% of WWD crashes with known entry points while representing only 21% of total interchanges in Michigan. Surprisingly, one specific parclo interchange was the entry point for 10 out of those 21 crashes. The researchers then targeted the suspect feature of the design, which is the adjacency of 2 parallel exit and entrance ramps in the same quadrant that intersect the crossroad at nearly right angles. After a total of 7 fatalities in 5 reported WWD crashes in Charlotte, North Carolina, between October 2005 and March 2006, North Carolina Department of Transportation officials initiated a thorough analysis of the existing crash data from 2000 to 2005 to further investigate key contributing factors at a statewide scale. Following this effort, a total of 162 (out of 195,313) crashes were found to result from traveling against the stream of traffic (Braam 2006). Another study conducted by the Washington State Department of Transportation reported that there were 30 WWD crashes from 1986 to 1996, resulting in 15 fatalities. Further analyses demonstrated that a large proportion of WWD crashes originated from one specific exit ramp of a parclo interchange. Traffic monitoring cameras from May to December 2001 also captured 18 WWD incidents at the same location (Kaminski Leduc 2008; Moler 2002). Past studies have proven parclo interchanges are the interchange types most likely to have a higher wrong-way entry frequency. The data provided from these studies have prioritized a need for further improvements on these specific interchanges; however, at this time, research has not been conducted on developing a proactive method to rank parclo interchanges based on traffic patterns. On the subject of predictive models, the Poisson distribution is found to be applicable to a variety of traffic problems, such as prediction of crash counts by severity (Ma et al. 2008), the effect of changing the number of lanes on crash rate (Li and Carriquiry 2005), and occurrence of traffic accidents (Tamayo 2009). Zhou, Chen, and Baratian-Ghorghi (2014) developed a probability model to predict the potential traffic conflict rate
Baratian-Ghorghi et al. at intersections with an offset right-turn lane. The authors employed traffic simulation software to verify the model and determine the frequency of the conflicts under various traffic volumes on the major and minor roads at unsignalized intersections.
Methodology Wrong-Way Movements Identification Based on the results of literature reviews, the WWD problem with parclo interchanges is attributed to their feature of having two closely spaced ramps that intersect crossroads at roughly right angles. Figure A1 (see online supplement) depicts a scheme of exit/entrance ramps of parclo interchanges and potential wrong-way movements, as shown in red. Along with intersection geometry and traffic control devices, traffic volume is found to affect probability of WWD incidents at parclo interchanges. In this article, the probability of a WWD incident is a scenario defined as follows: “A left-turn vehicle that intends to move toward the entrance ramp from the crossroad, can possibly enter the exit ramp mistakenly when there are no other vehicles stopped at the exit ramp terminal,” as shown in Figure A1. Past studies have shown that most WWD crashes occurred at midnight or early morning when traffic volumes were very low. On the contrary, during the peak hours of daytime, the traffic on the exit ramps prevented left-turning vehicles from entering exit ramps. Therefore, low traffic volume is found to be a precondition for possible WWD. Figure A2 (see online supplement) illustrates the procedure employed in this article to identify the potential WWD events at certain time intervals under different traffic volume conditions. Field Observation and Computer Simulation In the field study, intersection volumes, signal timing, and possible WWD movements were recorded for each 1-h time interval. Simulation models, verified by potential WWD events, were developed to resemble the existing traffic conditions. In the VISSIM simulation software’s output file, the vehicles’ information at a specific moment and a particular location in the modeled network are recorded (Traffic Mobility Logistics 2008). Taking advantage of this capability, it is possible to determine the operational status of the intersection at any given time and extract the number of possible WWD events. Mathematical Models In dealing with crash frequency and severity, which are always discrete and nonnegative integer values, employing a count data model, such as a Poisson distribution model, is recommended (Caliendo et al. 2007; Chiou and Fu 2013; Miaou 1994; Polus and Cohen 2012). The general equation of the Poisson distribution model can be expressed as (Gerlough and Barnes 1971) P(N = n) =
λn −! e , n!
(1)
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Second Approach/Model Development The precondition for a potential WWD event is defined as the traffic condition when there is no stopped vehicle on exit ramps (SVE) and a presence of at least one LVE during the green time intervals for LVE. A WWD event could occur only if there were vehicles on cross-road left-turn lanes making left turns onto the entrance ramp. The probability of one or more LVEs (PLVE,i (NLVE = 0)) at a given time interval can be expressed as PLVE,i (NLVE = 0) = 1 − PLVE,i (NLVE = 0) = 1 −
λ0LVE −λLVE e 0!
T , 4
(4)
= 1 − e−λLVE , i = 1, 2, . . . ,
Fig. 1. Scheme of a wrong-way movement.
where P (N = n): is the probability of the occurrence of n events at a given time interval, e is the base of natural logarithm (e = 2.71828 . . .), N is the number of potential events, and λ is the arrival rate. In this study, 2 Poisson distribution–based approaches were developed to calculate the probability of WWD events. In the first approach, the number of possible wrong-way entries and cycle length were used as inputs to Eq. (1). It requires field data collection of number of potential wrong-way movements. The second approach was based on traffic flow rates of left-turn volumes from crossroads and traffic volumes on exit ramps. It does not need the number of potential WWD events in the field. Both approaches are elaborated in the following sections. First Approach Figure 1 shows a potential WWD movement as a red dashed line at a signalized intersection of a parclo interchange. The left-turn vehicles onto entrance (LVE) ramp are shown as a green dashed line, having a protected green interval for each cycle. The probability of having one or more WWD at one cycle depends on the number of potential WWD events in the field and cycle length, as expressed in Eq. (2): P1 (C) = 1 − e−λ ,
(2)
where λ is the average number of potential WWD movements recorded in the field in one cycle. Equation (3) is the probability of having one or more potential WWD events in a 1-h time frame (P1 (H, WWD ≥ 1)). P1 (H, WWD ≥ 1) = 1 − (1 − P1 (C)) N = 1 − e−N×λ , where N denotes the number of cycles in 1 h.
(3)
where NLVE is the number of LVEs at a given time interval, λLVE : is the LVE arrival rate, i is the time interval number, and T is the length of red time in one cycle assigned to SVEs. The time interval was assumed to be equal to 4 s, which is the minimum time required for a vehicle to clear an intersection. This time interval length allows LVEs to cross the major road and to enter the entrance ramp, accounting for car-following phenomenon. The probability of no SVEs in the first time interval (PSV E,1 (NSVE = 0)) is calculated as follows: PSV E,1 (NSVE = 0) =
λ0SVE −λSVE e = e−λSVE , 0!
(5)
where NSVE is the number of SVEs at a given time interval (here the first time interval) and λSVE is the SVE arrival rate. It is clear that the probability of making a wrong-way entry to the exit ramp is equal to zero if there is a vehicle stopped at the exit ramp. In other words, LVEs in the ith moment might make a wrong-way entry if no SVEs were observed during those moments. Equation (6) represents the probability of no SVEs in the ith time interval: i (NSVE = 0) = e−i ×λSVE , PSVE,i (NSVE = 0) = PSVE T i = 1, 2, . . . , . 4
(6)
Equation (6) indicates that as the time elapsed after the red signal is on the exit ramps, the probability of having no vehicle queue on exit ramps will decrease. Traffic counts in each approach are assumed to be independent; therefore, the probability of WWD occurrence in the ith time interval, P(Ii ), would be P(Ii ) = PSVE,i (NSVE = 0) × PLVE,i (NLVE = 0) = e−i ×λSVE × [1 − e−λLVE ], i = 1, 2, . . . ,
T . 4
(7)
The probability of a WWD event in each cycle is as follows: P2 (C) = P(I1 ∪ I2 ∪ I3 . . . ∪ IT/4 ) c = 1 − P I1c ∩ I2c ∩ I3c . . . ∩ IT/4
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Table 1. Observed and estimated potential WWD events Field data (observed)
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Time interval
LVEs
SVEs
10:00 p.m.–11:00 p.m. 11:00 p.m.–12:00 a.m. 12:00 a.m.–1:00 a.m 1:00 a.m.–2:00 a.m. 2:00 a.m.–3:00 a.m 3:00 a.m.–4:00 a.m.
18 16 17 11 6 2
130 104 81 31 17 12
10:00 pm.–11:00 p.m. 11:00 p.m–12:00 a.m. 12:00 a.m.–1:00 a.m. 1:00 a.m.–2:00 a.m. 2:00 a.m.–3:00 a.m. 3:00 a.m–4:00 a.m.
32 36 7 10 6 4
78 66 48 32 20 15
Simulation output data (estimated)
Potential WWD events
= 1 − [1 − e−λSVE × [1 − e−λLVE ] ] ×[1 − e−2λSVE × [1 − e−λLVE ] ] . . . × [1 − e−T/4×λSVE × [1 − e−λLVE ] ].
LVEs
SVEs
Potential WWD events
Friday 3 3 4 4 3 1
17 15 18 13 5 2
127 105 81 30 16 14
3 4 4 5 2 1
Saturday 8 10 3 4 3 2
30 34 8 10 7 3
76 65 46 32 19 16
8 9 3 4 2 2
Field Data Collection (8)
Finally, the probability of WWD events for 1 h can be calculated using Eq. (9), similar to Eq. (3): P2 (H, WWD ≥ 1) = 1 − P2 (H, WWD = 0),
(9)
in which the probability of having no WWD incident in 1 h would be P2 (H, WWD = 0) = (1 − P2 (C)) N .
(10)
Based on WWD crash history and field observations of the study intersection, it was found that a high-crash location typically has more than 2 potential WWD events per hour of observation. Considering that in order to identify intersections for improvements, the probabilities of having 2, 3, or more WWD incidents were calculated. Equations (11)–(14) were used to compute the probability of 1, 2, 3, or more WWD incidents in 1 h: P2 (H, WWD = 1, 2) = P2 (H, WWD = 1) + P2 (H, WWD = 2),
(11)
where P2 (H, WWD = 1) = N × P2 (C) × (1 − P2 (C)) N−1
(12)
and
N × P22 (C) × (1 − P2 (C)) N−2 (13) 2 P2 (H, WWD ≥ 3) = 1 − P2 (H, WWD = 1, 2) − P2 (H, WWD = 0). (14)
P2 (H, WWD = 2) =
In order to predict WWD probabilities, field data were collected for 6 consecutive hours (from 10:00 p.m. to 4:00 a.m.) during 2 weekend nights in June 2013 at an intersection with a history of high wrong-way crashes (3 WWD crashes in 3 years; Zhou, Wang, et al. 2012; Zhou, Zhao, et al. 2012), located at South Bluff Road and I-64 in the city of Caseyville, Illinois. This intersection has two abutting exit and entrance ramps separated by a raised median (Figure A1). Researchers collected field data at this intersection. Past studies showed that the possibility of making a wrongway entry is disproportionally high during these time periods (Morena and Leix 2012; National Transportation Safety Board 2012; Sallee 2007). As for signal control, 2 main parameters, cycle length and the red intervals for SVEs (or green intervals for LVEs), were recorded to be 120 and 55 s, respectively, at the study intersection.
Data Analysis and Results Simulation Models To estimate the number of potential WWD events, VISSIM models were built based upon field data at the study intersection. Taking advantage of detectors in VISSIM, the number of LVEs, SVEs, and corresponding traffic signal indications at any given moment were archived, and the time intervals relating to when the WWD maneuvers may occur were identified (Table 1). The results indicated that potential WWD events increase when LVEs increase and SVEs decrease. A comparison between the field data and simulation outputs revealed that the developed model has an acceptable level of accuracy (correlation coefficient between 2 observed and estimated values for LVEs, SVEs, and potential WWD volumes are equal to 0.99). Mathematical Models Comparison Between First and Second Approaches In order to verify that mathematical models can provide reasonable estimate for higher traffic volumes, a total of 23
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simulation models were generated for a combination of gradually increasing LVEs and SVEs, which provided the number of potential WWD events for use in a first approach. In this study, data from simulation models and Eqs. (1)–(10) were used to compare the calculation results by the two approaches (Table A1; see online supplement). As expected, Table A1 shows that the estimated probabilities from both approaches have the same trend against the traffic volumes. A t-test with 99% confidence interval produced a P-value of .5046. This value is greater than initial assumption of .01, meaning that there is no statistically significant difference between the results of the first and second mathematical approaches. Because the number of WWD events are nonnegative integers, the probability resulting from the first approach would be (1 − e(−1) = 0.63). Though there is one potential WWD event observed, this number remains unchanged even with an increase in traffic volumes. The results from the second approach show that the probability will continually decrease as the traffic volumes increase. Effect of Levels of Unfamiliarity Past studies have found that unfamiliar drivers are heavily involved in roadway crashes (Sivak and Schoettle 2010). Therefore, 4 different levels of unfamiliarity (100, 50, 30, and 15%) were considered. The volume of LVEs in Eqs. (1)–(14) is equal to the actual LVEs multiplied by the percentage for unfamiliar drivers. Figure A3 (see online supplement) illustrates the variation in the probabilities versus changes in LVE volume and the percentage of local users. Concurrent Effect of LVE and SVE Volumes The developed model in the second approach is largely sensitive to the change in LVE volume. To prove this relationship, elasticity analysis was accomplished by changing one unit in the volume of LVE and SVE and monitoring the amount of change in WWD event probability (Eqs. (15) and (16)). P2 (H) = +0.00188 VLVE P2 (H) = = −0.00060. VSVE
eLVE =
(15)
eSVE
(16)
Fig. 2. Probability of WWD occurrence per hour.
Fig. 3. Probability of WWD occurrence per hour (cycle length = 120 s and red time = 32 s).
Analyses indicated that the model is 3 times more sensitive to the LVE volume than SVE, which offsets the effects of SVEs on the probability values to some extent. Therefore, the effect of these volumes on the probability needs to be investigated independently (Figure 2). According to Figure 2, the more incidences of SVE, the lower the probability of WWD. On the contrary, the higher the LVE volumes, the higher the probability is calculated. In order to demonstrate the impact of signal timing, the value of WWD probability against LVE and SVE volumes under 2 different cycle lengths and red times for SVE on existing ramps are shown in Figures 3 and 4. To prioritize the intersections for treatment, weights of 0, 5, and 10 were assigned to the situations with no, 1 or 2, and 3 or more WWD in 1 h, respectively. Therefore, the weighted score (the so-called risk score), which varies between 0 and 10 for each intersection, was calculated (e.g., the risk score for the first model is 0.12 × 0 + 0.55 × 5 + 0.33 × 10 = 6). Based on the scores, it can be determined which intersections should be given the highest improvement priority (Table A2; see online supplement). As shown in the table, the highest priority should be given to intersections 2 to 5, which carry relatively low traffic volumes.
Fig. 4. Probability of WWD occurrence per hour (cycle length = 60 s and red time = 32 s).
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This study aimed at developing a method for diminishing one of the challenges of transportation engineers, which is to identify high WWD crash locations due to insufficient information in crash reports. This article demonstrated that the probability of WWD can be calculated at an acceptable level of accuracy by implementing a Poisson distribution model without field observation and crash data. The findings reveal that the proposed model is largely sensitive to left-turn volume toward an entrance ramp compared to stopped vehicles at an exit ramp. The results indicated that the probability of a WWD event decreases as road users are more familiar with the facility.
Acknowledgment The authors would like to extent their sincerest thanks to the technical review panel members for their guidance and support.
Funding This article is based on a research project funded by the Illinois Department of Transportation (IDOT) and the Illinois Center for Transportation (ICT).
Supplemental Materials Supplemental data for this article can be accessed on publisher’s website.
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