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TRB Paper #: 09-2515 Are Incident Durations and Secondary Incidents Interdependent? Asad Khattak Civil and Environmental Engineering Department 135 Kaufman Hall, Old Dominion University Norfolk, VA 23529 T: (757) 683-6701 E: [email protected] Xin Wang Civil and Environmental Engineering Department 135 Kaufman Hall, Old Dominion University Norfolk, VA 23529 Hongbing Zhang Civil and Environmental Engineering Department 135 Kaufman Hall, Old Dominion University Norfolk, VA 23529 NOV 15, 2008 Word count 5249 + 2250 (3 figures + 6 tables) = 7499 Submitted to: 2009 Transportation Research Board Annual Meeting Washington, D.C. TRB 2009 Annual Meeting CD-ROM Paper revised from original submittal.

Are Incident Durations and Secondary Incidents … Paper #: 09-2515 Are Incident Durations and Secondary Incidents Interdependent? Asad Khattak Civil and Environmental Engineering

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Page 1: Are Incident Durations and Secondary Incidents … Paper #: 09-2515 Are Incident Durations and Secondary Incidents Interdependent? Asad Khattak Civil and Environmental Engineering

TRB Paper #: 09-2515

Are Incident Durations and Secondary Incidents Interdependent?

Asad Khattak Civil and Environmental Engineering Department

135 Kaufman Hall, Old Dominion University Norfolk, VA 23529 T: (757) 683-6701

E: [email protected]

Xin Wang Civil and Environmental Engineering Department

135 Kaufman Hall, Old Dominion University Norfolk, VA 23529

Hongbing Zhang

Civil and Environmental Engineering Department 135 Kaufman Hall, Old Dominion University

Norfolk, VA 23529

NOV 15, 2008

Word count 5249 + 2250 (3 figures + 6 tables) = 7499

Submitted to:

2009 Transportation Research Board Annual Meeting

Washington, D.C.

TRB 2009 Annual Meeting CD-ROM Paper revised from original submittal.

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Are Incident Durations and Secondary Incidents Interdependent?

Asad Khattak, Xin Wang, and Hongbing Zhang

Abstract: Incidents impose substantial social and personal costs on drivers. Some of the larger incidents that cause delays are also associated with secondary incidents. However, we do not fully know the nature of interdependence between primary and secondary incidents. The objective of this study is to understand how primary incident duration and secondary incident occurrence are related. Specifically, secondary incidents are more likely to occur if the primary incident lasts long; at the same time, the durations of primary incidents are expected to be longer if secondary incidents occur. After obtaining traffic incident and road inventory data in the Hampton Roads area, we proceeded by identifying secondary incidents, defined as incidents occurring on the same roadway segment (which average 1 mile in length) as the primary incident and within the actual duration of the primary incident. If the primary incident blocked lanes, then the actual duration plus 15 minutes was used as the threshold. Models for primary incident durations and whether or not a secondary incident occurs are estimated. The interdependence is modeled by considering incident duration as endogenous in the secondary incident occurrence models. The results show statistical evidence for interdependence, but when it is taken into account, no substantial differences in the magnitudes and statistical significance for the estimated independent variables are found (compared to when the interdependence is not accounted for). Statistically significant correlations are found between secondary incident occurrence and other variables, allowing us to recommend specific operational strategies.

___________________

Keywords: Traffic incidents, Hampton Roads, two-stage least squares, incident management.

INTRODUCTION Traffic incidents are a common occurrence on urban roadways. They are estimated to cause between 30 and 50 percent of the congestion problems on urban roads, which also result in associated safety, fuel, and environmental impacts[1-3]. Incidents can cause a reduction of roadway capacity if they block a lane or the shoulder. The resulting queuing and congestion created by the loss of capacity can increase the potential for other incidents, referred to as secondary incidents. Secondary incidents can also occur due to distractions caused by primary incidents. They further increase the time needed to return traffic to normal flow. Freeway or safety service patrols and other incident management strategies can potentially mitigate the occurrence of secondary incidents by helping to reduce the clearance time of the initial incident, but many questions exist about how best to manage secondary incidents.

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This research defines the “primary,” “secondary,” and “neither” incident categories. If an incident was associated with the occurrence of another incident, the first incident is termed primary incident, the incident, caused (at least in part) by another incident, is called a secondary incident. The remaining incidents are not associated with another incident (or caused by other incidents). The paper first identifies primary and secondary incident pairs by using spatial as well as temporal thresholds. Secondary incidents are defined as incidents occurring on the same roadway segment (which average 1 mile in length) as the primary incident and meanwhile within the actual duration of the primary incident if the primary incident did not block lanes, if the primary incident blocked lanes, then the actual duration plus 15 minutes was used as the temporal threshold. After identifying the secondary incident pairs, their spatial distribution is explored from an incident management perspective. Importantly, the interdependence between primary incident duration and the occurrence of secondary incidents is explored by applying appropriate statistical methods. The study provides decision makers valuable information about how to effectively deal with incidents that involve high risks of secondary incidents. LITERATURE REVIEW Table 1 provides a summary of the key studies on secondary incidents. The key issue is to define a secondary incident—and our literature review shows that Raub [4, 5] first defined the secondary incident using the temporal and spatial parameters in his study. He assumed that the secondary incidents are those occurring less than 15 minutes plus clearance time after an initial accident and within a distance 1 mile upstream. He found that more than 15% of the crashes reported by police may be secondary in nature. Average secondary crash occurrences were within 36.4 min and about ½ mile upstream of primary accident. Karlaftis et al. [6] also adopted this threshold to examine the primary crash characteristics that influence the likelihood of secondary crash occurrence. They found that more than 15% of all crashes might have resulted from an earlier incident.

Moore et al. [7] and Hirunyanitiwattana and Mattingly [8] magnified the time and space thresholds to 120 minutes and 2 miles. Also, they did not include the secondary incidents if the primary incidents were non-accidents or the secondary crashes that occurred in the opposite direction. Moore et al. [7] examined secondary accident rates on Los Angeles freeways using accident records from the California Highway Patrol’s First Incident Response Service as well as data from loop detectors. A key conclusion was that secondary accidents are considerably rarer events than previous studies suggest, and the study found a lower frequency of secondary crashes, i.e., secondary crashes per primary crash range between 1.5% and 3.0%. The study accounted for the possibility of secondary accidents in opposing traffic streams. Zhan [9] defined a secondary incident as a crash that occurs at most two miles upstream of the primary incident location in the same direction of travel and within the period from the start of the primary incident to 15 minutes after the clearance of the primary incident. Meanwhile Zhan [9] assumed that only incidents with lane blockages can potentially cause secondary crashes. 7.9% of all lane blockage incidents were identified as primary incidents.

All of above studies classified secondary incidents using static space-time thresholds. Sun [10] proposed an improved dynamic threshold methodology to extract the

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secondary accidents from an incident database. The dynamic threshold is derived from a master incident progression curve. The analysis shows that the static and dynamic methods can differ by over 30% in terms of identifying secondary incidents.

A major gap in the reviewed literatures is the lack of knowledge regarding the complex interrelationship between incident durations and the occurrence of secondary incidents. An investigation of how incident durations are associated with secondary incident occurrence can deepen the understanding of the traffic uncertainties caused by unexpected events, e.g., how much reductions in secondary incidents are possible if incident durations can be shortened. This can help formulate effective strategies for incident and emergency management.

METHODOLOGY Interdependence between Incident Duration and Secondary Incident Occurrence Secondary incidents are more likely to occur if incident clearance times/durations are longer [5-7], there are more lanes at the incident site, large trucks are involved, on weekdays, and during peak period [6, 8], and if crash involves speeding or rollovers [9]. Further, secondary incidents are less likely if primary incident occurs during winter months and it occurs on a ramp or median shoulder [6].

Studies of incident durations have been plentiful (e.g., [11], [12], [13], [14], [15] and [16]), and identify the factors that influence incident durations by taking different modeling approaches, e.g., linear regression and hazard-based models. Incident durations are typically longer if response times are longer, more vehicles are involved, heavy vehicles are involved, hazardous materials or other loadings are spilled from heavy vehicles, injuries occur, freeway facility is damaged, and extreme weather conditions exist [17]. However, incident duration models have not quantified the impacts of secondary incidents on durations.

Generally, increases in incident durations associated with secondary incident occurrence, has received relatively little attention in existing literature, with a few exceptions (e.g., [9]). Clearly, there may be several factors associated with the incident durations and the occurrence of secondary incidents, such as incident type, detection source, weather, and the freeway facility damage caused by incidents, etc. Importantly, incident duration, and the occurrence of secondary incidents may be interdependent. A (primary) incident can result in queuing upstream. This causes speed reductions, and sometimes sudden slowing, surprising some drivers and increasing the possibility of secondary incidents. If a secondary incident occurs shortly after the primary, it will lead to longer primary incident duration due to additional impedance and interference, e.g., with clearance operations of the primary incident and potentially increase the primary incident duration. The factors which may be related to primary incident duration and secondary incident occurrence are shown in Figure 1. To reiterate, there is a possibility of interdependence between primary incident duration and the occurrence of secondary incidents. That is, secondary incidents are more likely to occur if the primary incident lasts long; at the same time, durations of primary incidents are expected to be longer if secondary incidents occur. To account for such interdependence, with respect to the secondary crash variable, appropriate statistical methods are available and are applied.

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Table 1: Secondary Incidents Literature Review Summary Raub [4] Karlaftis et al. [6] Moore et al.[7] Hirunyanitiwattana &

Mattingly [8] Sun [10] Zhan [9]

Temporal parameter

clearance time+15 minutes

clearance time+15 minutes

clearance time < 120 minutes

clearance time < 60 minutes

Incident duration clearance time+15 minutes

Spatial parameter

<1 mile

<1 mile

Queue length< 2 miles Queue length< 2 miles

Not available

two miles upstream of the primary incident

Definition of secondary incident

Other cond-itions

Excluded non-accidents & secondary crashes in the opposite direction

Excluded secondary crashes in the opposite direction

Uses dynamic thresholds

Factors associated with secondary incident occurrence

Peak hour Weekdays Clearance time

Weekdays Clearance time Vehicle type Primary incident location Season

Clearance time Speed High density traffic

Peak hour Clearance time Speed Urban area Route number

number of vehicles involved; number of lanes; incident duration; time-of-day; Whether or not vehicle rollover occurs during the primary incident.

Data collection method

Police reports

Indiana DOT

California Highway Patrol

Federal Highway Administration

Highway patrol in St. Louis, Missouri

FDOT D4

Data collection period

1995

1992-1995

March, May, July 1999 and December 1998

1999 and 2000

2002

January 2005 to January 2007

Study location

Northern Chicago Borman Expressway Los Angeles Freeway California highway system

I-70 in Missouri I-95, I-75, I-595

Sample size 1796 84,684 170,866 in 1999 and 183,988 in 2000

5,514 4,435 lane blockage incidents

Main findings

1. More than 15% of the crashes may be secondary. 2. Average secondary crash occurs within 36.4 min and 600 meters after primary accident. 3. Average Primary accident duration is 45 min, Added delay 69 min.

1. Clearance time, Car-passage car, semi-truck, and WKD increase the secondary incident likelihood, WNT and RMPMS decrease the chance. 2. More than 15% of all crashes might have resulted from an earlier incident.

Secondary accidents are considerably rarer events than previous studies suggest, lower frequency of secondary crashes (secondary crashes per primary crash range between 0.015 and 0.030)

1. Secondary crashes occur more often during rush hour traffic in the morning and evening. 2. Rear-end collision is the predominant secondary collision type, accounting for about two-thirds of all secondary crashes. 3. Secondary incidents on urban freeways and four lanes are higher.

Not available (does not use regression method)

1. Secondary crashes are usually much less severe than other crashes. 2. Traveler sight conditions (visibility) and the lane blockage durations of primary incidents are significant contributing factors for determining the severity of secondary crashes.

TRB

2009 Annual M

eeting CD

-RO

MPaper revised from

original submittal.

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Figure 1: Relationships between variables

Modeling Interdependence Secondary incidents are identified in the data and a dummy variable created to capture whether an incident has associated secondary incidents. We estimate separate statistical models to capture interdependence—the first one is an Ordinary Least Squares (OLS) regression model (Model 1) of incident duration, using detection sources, vehicles count, etc. as predictors. Note that this model is adopted due to its simplicity and intuitive interpretation of the coefficients, while recognizing that data are non-negative and OLS can potentially give negative predictions (if some of the explanatory variables are negative). DUR = β0 + β1 (Detection) + β2 (Type) + β3 (Closuretime) + β 4 (Vehicles) + β 5 (Responsevehicles) + β6 (AADT) + β7 (Leftshoulder) + β8 (Ramp) + β9 (TOD) + ε

(Model 1) Where:

DUR = Incident duration (minutes) Detection = Incident detection source (categorical variable) Type = Incident type (1 = Crash, 0 = Otherwise) Closuretime = Duration of Lane closed (minutes) Vehicles = Number of vehicles involved Responsevehicles = Number of responding vehicles AADT = Average annual daily traffic (per 1000 vehicles) Leftshoulder = Left shoulder affected (1= Yes, 0 = No) Ramp = Ramp affected (1= Yes, 0 = No) Restime = Response time (minutes) TOD = Time of day (1= Peak, 0 = Off-peak) ε = Error term.

A variable representing secondary incident occurrence can be added to the above specification. We can test whether there is a relationship between duration and secondary incident occurrence. This gives rise to a secondary incident occurrence model (Model 2) with duration as an independent variable. However, Model 1 hypothesizes that primary incident duration may be correlated with variables such as detection source, incident type, peak periods, and so on, which are also associated with secondary incident occurrence possibility. This gives rise to the possibility that endogeneity may exist between duration

- Incident factors - Operational factors - Roadway factors - Environmental factors

Incident Duration

Secondary Incident Occurs

Interdependence

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and secondary incident occurrence, which means incident duration may be associated with the residual η in Model 2. We can test this endogeneity by estimating a duration model (Model 1) and calculating residual, ε, and then using duration and ε as independent variables in the secondary incident occurrence model (Model 3). If the coefficient of ε is significantly different from zero, then duration is considered endogeneous. SEC = γ0 + γ1 (Detection) + γ2 (Type) + γ3 (Vehicles) + γ4 (Response vehicles) + γ5

(AADT) + γ6 (Leftshoulder) + γ7 (Ramp) + γ8 (TOD) + γ9 (Laneclose) +γ10 (Duration) + η

(Model 2)

Duration = Observed incident duration SEC = Secondary incident occurred (1=Yes, 0=No) η = Error term in Model 2.

SEC = γ0 + γ1 (Detection) + γ2 (Type) + γ3 (Vehicles) + γ4 (Response vehicles) + γ5

(AADT) + γ6 (Leftshoulder) + γ7 (Ramp) + γ8 (TOD) + γ9 (Laneclose) +γ10 (Duration) +

γ11 (ε) + ξ (Model 3) Where:

ε = Error term in Model 1 ξ = Error term in Model 3

The exogeneity of the independent variables is one crucial assumption in the

development of the classical linear regression models. So if the duration is tested to be endogenous, the binary models estimated making the assumption of exogeneity will be problematic. One solution to this problem is using a binary (logit or probit) model with endogenous regressors. This means that a two-stage approach is needed to obtain unbiased coefficients. The principle for 2SLS (Two-Stage Least Squares) is that in the first stage, a duration model is estimated (Model 1), then the predicted duration is used in the second stage model as independent variable (Model 2). The advantage of 2SLS is that the fitted duration would be uncorrelated with the η (error term of the secondary incident occurrence model), which is a key benefit of 2SLS. Statistical software STATA is used to estimate a secondary incident occurrence model with duration as endogenous variable. This implies using predicted duration in Stage 2, i.e., tionaDur ˆ (duration instrumented) in Model 2, based on Stage 1 (Model 1). Furthermore, the model is estimated using conditional maximum likelihood estimator, fully accounting for the information in the data. The result using conditional maximum likelihood estimator may be different from using directly the predicted duration generated by first stage OLS and then using it in the second stage probit model. Wooldridge[18] recommends avoiding estimation of the second stage manually, as the standard errors and test statistics obtained in this way are not correct. Note that we estimated the binary probit model for secondary incident occurrence. Additionally, we estimated an equivalent binary logistic model without correcting for the endogeneity of incident duration in order to compare our results with earlier literature. Furthermore, the Wald test for endogeneity is also reported, in order to determine whether the model with instrumental variable is more suitable.

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DATA SOURCES AND STUDY AREA

The incident data were provided by Hampton Roads Smart Traffic Center (STC) located in Virginia Beach, VA. In this study, 2006 incident data was used, which covers the freeways patrolled by Safety Service Patrol (SSPs) of Hampton Roads area. Vehicular based incident records are collected by STC. All incident records were organized as yearly based Microsoft Excel tables, with critical characteristics such as start and end time of incidents, incident type, duration, weather condition, detection sources, lane blockage information, location code and direction, responding agencies, and so on, which provides a good foundation for further statistical analysis. The road inventory data were obtained from the Hampton Roads Planning District Commission and the traffic flow data were provided by Virginia Transportation Research Council (VTRC).

In this study, a secondary incident is defined as an incident that occurs in the same direction as primary incident and within the actual duration of the primary incident. If the primary incident blocks one or more lanes, then the actual incident duration plus 15 minutes is used to identify secondary incidents. Note that the duration recorded by SSP only considers the clearance period starting from the detection of the incident and ending when the patrol leaves the scene. This may be shorter than the “true” incident duration due to detection lag. Furthermore, recovery time is not included in the incident duration. The program for identifying secondary incidents has been developed using a Microsoft application package in Excel. A total of 38,086 incidents that occurred in 2006, and have clear spatial location information and incident duration, comprise the final dataset.

Using the thresholds mentioned above, 736 incidents were identified as primary incidents in 2006 which is 1.93% of all incidents; 764 incidents were identified as secondary which accounts for 2.01% of all incidents. The remaining 36,633 incidents are identified as neither primary incident nor secondary incident. Note that a few secondary incidents which are caused by a primary incident can possibly cause a tertiary incident; although few, these incidents are identified as both primary and secondary in the database.

The findings about frequency of secondary incidents are consistent with literature [7], which found that secondary accidents are considerably rarer events. Note that the incident durations used in this study have measurement error towards the shorter side, as we used relatively restrictive criteria to identify secondary incidents, i.e., that the secondary incident must occur with the duration of the primary incident and on the same segment, and we have not included secondary incidents due to rubbernecking in the opposite direction (the percentage of secondary incidents will be higher if rubbernecking incidents were to be included).

Using the available data, incidents were geo-coded. Figure 2(a) shows the geographic distribution of incidents in 2006. It indicates where incident management is needed most. Figure 2(b) shows the frequency of secondary incident pairs by different route segments. The size of circles indicates incident frequency, with the ratio of the red and yellow representing the relative proportion of primary and secondary incidents. Generally, the proportion of primary and secondary incidents is 1:1, which means that one primary incident is associated with one secondary incident. On some segments, one primary incident was associated with multiple secondary incidents, e.g., the segment north of HRBT (Hampton Roads Bridge Tunnel). The figure identifies locations where

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secondary incidents are more likely to occur and consequently higher service patrol, police and tow coverage may be needed (in order to respond secondary incidents).

Figure 2(a): Spatial Distribution of Incidents in 2006

Figure 2(b): Spatial Distribution of Primary Incidents vs. Secondary Incidents in 2006

Incident Duration Descriptive Statistics

Table 2 shows the mean of incident durations, which is quite different across primary and

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secondary incidents. The mean of duration for all incidents in the data is 14.3 minutes. However, the average duration for incidents that are neither primary nor secondary, is less than 14 minutes, while the average duration for primary incidents is nearly 37 minutes, indicating that larger incidents are likely to result in secondary incidents, as expected. Interestingly, the average duration for secondary incident is slightly more than 18 minutes, which is still longer than the mean for non-primary/secondary incidents. This indicates that secondary incidents are, on average, relatively severe in terms of their durations (they are not just minor rear-end fender benders).

Table 2: Descriptive Statistics of Incident durations in 2006

Mean (min) N min Max Std. Dev. (min)

All incidents 14.27 38,086 1 728 20.215

Primary 36.75 736 1 728 48.635

Secondary 18.37 764 1 320 25.773

Neither primary nor secondary

13.78 36,633 1 651 18.882

Descriptive statistics (Table 3) are presented after we exclude incidents identified as

secondary. Specifically, the duration model does not use all incident data listed in Table 2. Since the primary and secondary incidents have an associative relationship and OLS assumes independence among observations, the data used in the duration model does not include secondary incidents; only primary incidents and “neither” (primary nor secondary) incidents are included. This results in a sample size of 37,369 (=736+36,633).

The descriptive statistics seem reasonable in terms of their means and ranges. The mean duration for all samples is 14.23 minutes. The variable ‘laneclose’ means whether or not lane closure is caused by the incident. A total of 9.5% incidents in the sample resulted in lane closures, with average lane closure lasting 30 minutes. A dummy variable nonlaneclose was created to indicate whether lane closure was involved in the incident. The mean for nonlaneclose is 0.905. The variable ‘vehicles’ means the number of vehicles involved in an incident. On average, 1.08 vehicles were involved in each incident. The variable ‘Left_shoulder’ means whether or not the left shoulder is affected by the incident. About 8% of the incidents that occurred in 2006 affected the left shoulder. Similarly 85.8% of the incidents affected the right shoulder. The variable ‘ramp’ means whether or not the ramp is affected by the incidents and 4.8% of the incidents affected a ramp. About 2% of the incidents had Emergency Medical Services respond. Regarding Time of Day (TOD), 34.8% of the incidents occurred in peak hours. The responding vehicles which include EMS, SSP, VDOT, Local Police, Fire, etc., were 1.14, with the smallest number being 1 and the largest number 7. Response time represents how long it will take for SSP or other responding agencies to arrive at the incident scene. However, due to the fact that the start-time is mostly recorded when the SSP patroller is on the scene, many response times when SSP is the detection source are coded as zero. The average response time is only 1.06 minutes for valid incident data. Moreover, for

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modeling, a dummy variable is created to represent 5.6% of the incidents with no valid response time information recorded. Finally, disabled incidents form a majority of the incidents (nearly 85%), followed by accidents, and abandonments.

Table 3: Descriptive Statistics for Incidents in 2006

Variables N Min Max Mean Std. Dev.

Freq. %

Duration 37,369 1 728 14.228 20.155

Laneclose 37,369 0 1 0.095 0.293 3,532 9.5

Closure Time 3,532 1 728 30.130 35.128

Nonlaneclose 37,369 0 1 0.905 0.293

Vehicles 37,369 1 10 1.076 0.366

Left_shoulder 37,369 0 1 0.080 0.272

Right_shoulder 37,369 0 1 0.858 0.349

Ramp 37,369 0 1 0.048 0.214

SEC 37,369 0 1 0.020 0.139

TOD 37,369 0 1 0.348 0.476

Response vehicles 37,369 1 7 1.144 0.547

Response time 35,258 (94%) 0 261.7 1.056 4.213

Dummy_rt 37,369 0 1 0.056 0.231

CCTV 37,369 2,088 5.59

Other 37,369 132 0.36

Phone Call 37,369 1,034 2.77

SSP 37,369 33,086 88.54

Detection source

VSP Radio 37,369 1,029 2.75

Abandoned 37,369 2,502 6.70

Accident 37,369 2,817 7.54

Disabled 37,369 31,725 84.90 Incident

Type

Other 37,369 325 0.87

MODELING RESULTS

Incident Duration Models

A simple duration model (Model 1) is reported in Table 4, along with a model that contains a variable for secondary incident occurrence. This confirms that secondary incident occurrence is associated with longer durations of primary incidents.

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Table 4: Modeling Results for Duration with and without secondary incident predictor

Model 1: OLS Duration Model 1-2: OLS

Duration Coef P-value. Coef P-value.

CCTV 7.684 0.000*** 7.402 0.000***

VSP_radio 8.354 0.000*** 8.323 0.000***

Phone_call 9.377 0.000*** 9.428 0.000*** Detection source

(Base: SSP)

Other 4.603 0.001*** 4.474 0.001***

Accident 6.249 0.000*** 5.982 0.000***

Disabled -1.260 0.133 -1.384 0.098 Incident type (Base: Other)

Abandoned -8.059 0.000*** -8.160 0.000*** Response vehicles

Re_veh 2.914 0.000*** 2.913 0.000***

AADT 0.005 0.002*** 0.004 0.013** AADT (per 1000) AADT_dummy 0.400 0.741 0.399 0.740 Affects left shoulder? Left_shoul 3.832 0.000*** 3.813 0.000***

Affects ramp? Ramp 2.953 0.000*** 2.987 0.000***

In peak hours? TOD 0.071 0.666 0.003 0.986

Vehicle involved Vehicles 1.944 0.000*** 1.727 0.000***

Closure time Durationclos 0.835 0.000*** 0.829 0.000***

Nonlaneclose Dummy 10.183 0.000*** 10.313 0.000*** Secondary

incident occurs SEC 9.237 0.000***

Constant -3.732 0.000*** -3.479 0.000***

Number of Observations 37369 37,369

R2 0.4481 0.452

Prob>F 0.00 0.00 Note: * p<0.10; ** p<0.05; *** p<0.01.

Results show that variables have the expected signs and reasonable magnitudes. Model 1 in Table 4 shows the following associations:

Detection source is associated with incident duration. Compared with incidents detected by SSP, the duration of incidents detected by CCTV are about 7.7 minutes longer, on average, compared with SSP detection; the duration of incidents detected by VSP-Radio are 8.4 minutes longer; and the duration of incidents detected by phone call are 9.4 minutes longer, on average.

Compared with the other incidents, accidents are 6 minutes longer on average; abandoned incidents are about 9 minutes shorter than the “other” category. Disabled incidents are not statistically significantly different than the other category.

Only 9.5% of incident involved lane closure and the average lane closure duration is 30.1 minutes. If none of the lanes are closed, 10 minutes can be added into the incident duration, on average, but if incident did involve lane closure, one additional minute of lane closure adds 0.84 minutes to the duration.

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One additional vehicle involved in the incident is associated with increase in the duration by nearly 1.95 minutes. Incidents responded to by an additional vehicles are associated with longer incident durations—an additional response vehicle is associated with 2.9 minutes longer durations. Note that additional response vehicles do not make the incidents last longer, but typically they are needed when larger incidents occur.

The incidents with left shoulder affected and ramp affected are associated with 3.8 and 2.9 minutes longer durations, respectively, which indicate that incident with a left shoulder affected may has a higher severity. Incident duration is associated with the AADT of the segment where the incident occurs. Additional 1000 vehicles of AADT are associated with 0.005 minutes longer durations.

Model 1-2 considers secondary incident occurrence, showing that secondary incident occurrence is associated with nearly 9 additional minutes of primary incident duration, on average.

Overall, the results are consistent with the literature, showing that the factors associated with longer incident durations are detection by non-SSP sources, accidents, freeway facility damage, longer the lanes closures, more vehicles involved, severe injuries, if incident affects the left shoulder or ramp, and longer lane closure times. Testing for Simultaneity To test for simultaneity, with respect to the secondary crash variable, appropriate statistical methods are applied to calculate the residual variable as follows:

ε = Duration - tionaDur ˆ tionaDur ˆ = Predicted Duration in Model 1

Note that ε is added to the original regression to account for the simultaneity. The

probit regression results are listed in Table 5. The model is statistically significant, and shows that the residual is statistically significant indicating that a simultaneous relationship exists and that primary incident duration is endogenous with secondary incident occurrence. This implies that duration should not be used directly in the binary model; instead it should be used as an endogenous variable.

2SLS Secondary Incident Regression

Three secondary incident occurrence models are reported in Table 6. Model 2-0 is a binary probit model estimated with observed duration. Model 2-1 is a binary probit model using observed duration without the closure time variables and a related dummy. Model 2-2 is a probit model estimated with endogenous regressors, instrumenting incident duration (and it is directly comparable to Model 2-1). Note that lane closure times and a dummy variable for no lane closure are used as instruments in the first stage only.

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Table 5: Modeling secondary incidents-residual of incident duration as explanatory var.

Model 3 Secondary incident occurrence as dependent Coef. P>z

CCTV 0.362 0.000 VSP_radio 0.106 0.191 Phone_call -0.073 0.475

Detection source (Base: SSP)

Other_dete 0.204 0.323 Accident 0.650 0.006 Disabled 0.344 0.142

Incident type (Base: Other)

Abandoned 0.248 0.317 Response vehicles Res_vh 0.035 0.192

AADT1 0.002 0.000 AADT (per 1000)

AADT_dummy -0.169 0.664 Affects left shoulder? Left_shoul 0.072 0.144

Affects ramp? Ramp -0.052 0.481 In peak hours? TOD 0.160 0.000 Vehicle involved vehicles 0.135 0.000

Observed Duration Duration 0.005 0.000 Residual for Duration ε 0.003 0.005

constant -3.199 0.000 Number of obs 37369

Pseudo R2 0.1057

Prob > chi2 0

Log likelihood -3236.731

Note: * p<0.10; ** p<0.05; *** p<0.01.

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Table 6: Modeling Results for Secondary Incident Occurrence

Number of observations: 37,369 Model 2-0: Probit model

Model 2-1: Probit model

Model 2-2: Probit model: Endogenous

Observed Duration as independent

Observed Duration as independent

Duration as Instrumented

Independent variables Coef. Marg. eff. Coef. Marg. eff. Coef. Marg. eff. CCTV 0.291*** 0.014 0.342*** 0.017 0.362*** 0.019

VSP_radio 0.049 0.002 0.086 0.003 0.106 0.004 Phone_call -0.141 -0.004 -0.101 -0.003 -0.073 -0.002

Detection source (Base: SSP)

Other_dete 0.182 0.008 0.132 0.005 0.204 0.009 Accident 0.589** 0.037 0.667*** 0.045 0.649*** 0.044 Disabled 0.404* 0.011 0.384 0.011 0.343 0.010

Incident type (Base: Other)

Abandoned 0.340 0.017 0.304 0.014 0.247 0.011 Closure time Durationclos -0.004*** -0.0002

Nonlaneclosure Dummy_close -0.404*** -0.021 Vehicle involved Vehicles 0.114*** 0.004 0.127*** 0.005 0.135*** 0.005 Resp. vehicles Re_veh -0.011 -0.0004 0.008 0.0003 0.035 0.001

AADT 0.002*** 0.0001 0.003*** 0.0001 0.002*** 0.0001 AADT (per 1000) AADT_dummy -0.179 -0.005 -0.166 -0.005 -0.169 -0.005

Affects left shoulder? Left_shoul 0.038 0.001 0.062 0.002 0.072 0.003 Affects ramp? Ramp -0.078 -0.003 -0.058 -0.002 -0.051 -0.002

Duration Duration 0.009*** 0.0002 0.007*** 0.0002 0.005*** 0.0002 in peak hours? TOD 0.159*** 0.006 0.162*** 0.006 0.160*** 0.006

Constant -2.839*** -3.226*** -3.195*** Independent variables Duration instrument

CCTV 7.688 0.000*** VSP_radio 8.357 0.000*** Phone_call 9.381 0.000***

Detection source (Base: SSP)

Other 4.605 0.001*** Accident 6.254 0.000*** Disabled -1.265 0.131

Incident type (Base: Other)

Abandoned -8.065 0.000*** Response vehicles Re_veh 2.919 0.000***

AADT 0.005 0.002*** AADT(per 1000) AADT_dummy 0.400 0.740

Affects left shoulder? Left_shoul 3.835 0.000*** Affects ramp? Ramp 2.955 0.000*** In peak hours? TOD 0.071 0.665 Vehicle involved Vehicles 1.946 0.000***

Closure time Durationclos 0.836 0.000*** nonlaneclose Dummy 10.231 0.000***

Constant

-3.780 0.000*** Prob > chi2 0 0 0

Log likelihood -3214.43 -3240.66 -157,389 Pseudo R2 0.11 0.10 NA

Wald Test NA NA Rho=0.049; Prob > chi2 = 0.0048

Note: * p<0.10; ** p<0.05; *** p<0.01; The marginal effect are at the means of the independent variables.

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The dependent variable is unbalanced, with only a small fraction of incidents having associated secondary incidents (about 2%), making it difficult to estimate good models. Nonetheless, the models are statistically significant overall and have reasonable goodness-of-fit. The marginal effects provide information about the magnitudes of the independent variable associations. The Wald test of exogeneity is significant, indicating that the probit model with instrumental variables is appropriate.

The magnitude of the duration parameter in Model 2-2 (probit model with endogenous regressors) is smaller than Model 2-1, while the marginal effects is identical. Ten more minutes in primary incident duration is associated with 0.2% higher secondary incident possibility. Also, note that most of the other variables do not change substantially from the model with observed duration.

In terms of detection source, only CCTV detection is associated significantly with a higher possibility of occurrence of secondary incidents. Compared with incidents detected by SSP, the possibility for occurrence of secondary incidents is 1.9% higher when the incidents are detected by CCTV. Accidents are associated with 4.4% higher of possibility of secondary incident occurrence compared with other incidents. One more vehicle involved in the primary incident will add 0.5 % to the possibility of secondary incident occurrence. The possibility of secondary incident occurrence is associated with the AADT of the segment where the incident occurred. Additional 1000 vehicles will increase the possibility of secondary incident occurrence by 0.01%. The possibility of secondary incident occurrence is higher by 0.6% for incidents occurring during the peak hour. Whether the incidents affected left shoulder or ramp have no significant association with the possibility of secondary incident occurrence.

Figure 3 shows the relationship between the instruments, endogenous variable and secondary incident occurrence. To summarize, the factors associated with longer duration are detection resources (CCTV, Radio and Phone), accident, lane closure time, more vehicles involved, more response vehicles, higher AADT, left shoulder/ramp affected, and peak hours. Moreover, longer duration is associated with higher secondary incident occurrence. In addition, factors associated with higher secondary incident occurrence are accidents, peak hours, more vehicles involved in incident, and higher AADT.

The results are largely consistent with the findings in the literature. The equivalent models reported in the literature are binary logit. Although we can obtain comparable estimates by multiplying the probit coefficients by π/√3 ≈ 1.8 or 1.6 (Greene [19]), we estimated equivalent binary logistic models (without correcting for the endogeneity of incident duration). Relevant parameters are compared informally, without presenting the complete models and computing their marginal effects, due to space limitations. Specifically, Karlaftis et al. (1999) report the parameter of incident clearance time to be 0.027 for a logit model (2.7% higher odds), as opposed to 0.015 in this study (1.5% higher odds). Zhan et al. (2008) reported Ln (Primary incident duration) coefficient of 0.526 compared with 0.644 (if log transformed logit estimator is used) in this study, which are fairly close. Similarly, the coefficients for number of vehicles involved are 0.115 in Zhan et al. (2008) and 0.187 (using a logit model) in this study. Again, they are fairly close. Compared with earlier literature, this study contributes by testing for interdependence between incident duration and secondary incident occurrence and further investigating the associations of secondary incidents with detection source and incident type.

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Figure 3: Relationship between Dependent, Endogenous Variable and

CONCLUSIONS AND IMPLICATIONS

Using freeway incident and roadway inventory data from the HampVirginia, modeling techniques were applied to develop incident duincident occurrence prediction models. The research provides a dethe occurrence of secondary incidents and points to the increasedin the secondary incident occurrence. We proposed and tested a hinterdependence between the primary incident duration and seconoccurrence. The interdependence was found to be statistically signntusing simple binary probit (or logit) model directly may be problemduration as an independent variable is correlated with the error tersecondary incident occurrence model, using instrumented durationsubstantially the coefficients of the other variables for this particular datvaluable to identify the interdependence and implement the methopaper when using other incident databases. Practically speaking,

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durations may be different if the interdependence of duration and secondary incident occurrence is not taken into account.

The results can aid in identifying incident management strategies to mitigate the impacts of both primary and secondary incidents. Incidents are complex and while they have common features, each one has its own multifaceted context. Over simplified generic solutions will hinder those responsible for managing incidents rather than help them [20]. Clearly, incident duration is a key factor in terms of reducing the possibility of secondary incidents. The incident management role when larger incidents occur is often distributed between different agencies, and it can become rather cumbersome and somewhat fluid, hampering clearance. The model shows that more response vehicles are indeed associated with longer incident durations, as expected. While realizing that proper procedures must be followed, sometime agencies (e.g., law enforcement) are reluctant to aggressively remove incident-involved vehicles/cargo for a number of reasons, e.g., liability. This study indicates that aggressive clearance on certain roadways can reduce secondary incidents ultimately improving public safety.

Furthermore, the information generated in this study can help with incident management strategies, especially, locating patrol vehicles on high frequency segments, and special equipment in areas that experience secondary incidents. Another issue that can benefit from the attention of incident managers is incident type, where crashes and involvement of more vehicles are clearly problematic in terms of their association with secondary incident occurrence. Peak periods would also place a heavier demand on incident management resources, owing to the higher chances of secondary incident occurrence. Further, it will be prudent to monitor the end of the traffic queue and provide motorists with information and warnings about the length of the queue and its tail.

In future research, the secondary incident occurrence models presented in this paper are being developed to allow the State Department of Transportation to estimate the durations of incidents in real time, and the chances of a secondary incidents based on the characteristics of the primary incident. This will facilitate incident managers to identify relevant incident management strategies that can deal with both primary and secondary incidents.

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TRB 2009 Annual Meeting CD-ROM Paper revised from original submittal.