trb2004-000051

Ratrout et al. 1

Validation and Improvement of a Rear-end Conflict Prediction Model Date of Submission: June 16, 2003 Word Count: 3,280 Nedal T. Ratrout (Corresponding author) Department of Civil Engineering King Fahd University of Petroleum & Minerals KFUPM Box 1503 Dhahran 31261, Saudi Arabia Phone: +966-3-860-3185 Fax: +966-3-860-3862 E-mail: [email protected] Khalaf A. Al-Ofi Department of Civil Engineering and Research Institute King Fahd University of Petroleum & Minerals Dhahran 31261, Saudi Arabia Phone: +966-3-860-3419 Fax: +966-3-860-3996 E-mail: [email protected] Shoukat Iyaz Department of Civil Engineering King Fahd University of Petroleum & Minerals Dhahran 31261, Saudi Arabia

Abstract. Traffic conflict is an important parameter for the safety evaluation of signalized intersections. a major drawback of traffic conflict is the fact that it is complex and requires highly trained personnel to collect the relevant data. In a previous work, a one variable regression model was reported for predicting rear-end conflict, namely conflict/hour = 0.0115 (no. stops/hour). This model was limited to four-legged signalized intersections with left turn bays in Al-Khobar, Saudi Arabia. The model was successfully validated via this study. It was also shown that the predictive power of the model can be dramatically improved by adding the mean speed to the no. of stops. Specifically, the best model to predict conflict was found to be: conflict = –6.64 + 0.0066 (no. stops) + 0.1737 (mean speed). It was also shown that TRANSYT-7F is a promising tool in facilitating the prediction of conflict. In a small scale experiment, the simulated stops obtained through the TRANSYT-7F software were successfully used in lieu of the observed stops in predicting rear-end conflict.

INTRODUCTION

Traffic conflict technique has been widely used, alone or with other parameters, in evaluating traffic safety and accident potential at signalized intersections (1–4). In addition, traffic conflict has been used as a measure of traffic safety in lieu of accident data when such data are not available (5). A major drawback of this technique is the data involved, which is cumbersome and requires highly trained manpower to collect. A number of studies have investigated the possibility of utilizing other parameters for evaluating intersection safety, such as real traffic accident images (6), theoretical conflict opportunities (7), and other traffic variables, including average annual daily traffic, volume to capacity ratio, etc. (8). The objective of this paper is to investigate the possibility of predicting rear-end conflict by using easily obtained traffic parameters. This was accomplished by validating and enhancing a regression model for predicting rear-end conflict, which was calibrated previously for the study area in the city of Al-Khobar, Saudi Arabia.

BACKGROUND

In a similar work done previously in the study area, the following regression model was reported (9) for predicting rear-end conflict:

TRB 2004 Annual Meeting CD-ROM Paper revised from original submittal.

Ratrout et al. 2

conflict = 0.01154 (no. stops) model (1) where:

conflict : total number of rear-end conflicts per hour, and no. stops : number of stops per hour.

The model was calibrated for typical four-legged intersections with raised medians, left turning bays and possessing ideal roadway geometry as shown in Figure 1. This model, which will be referred to here as model 1, was calibrated as part of an effort to predict rear-end accidents at signalized intersections, since there is a proven relationship between rear-end conflicts and rear-end accidents in the study area (9). This relationship, which was developed to overcome the problem of poor accident database in the study area, states that rear-end accidents in two years are equal to 2.309 multiplied by the number of rear-end conflicts in the peak hour. Thus, rear-end accidents in the study area may be estimated by direct observation of conflicts (which is a cumbersome task), or by predicting the conflicts using number of stops via model 1. This is theoretically appealing since rear-end accidents usually tend to increase with signalization due to the increase of exposure, which may be reduced by lowering the number of stops. Right-angle accidents, on the other hand, are typically reduced by signalization, and other types of accident can be controlled by proper design of inter-green periods (9). If model 1 is validated, it could be used to evaluate safety in terms of rear-end accidents using any traffic optimization package capable of predicting number of stops. Consequently, by starting with a validation of model 1, the paper investigates the possibility of improving its predictive power by adding to it other promising traffic variables that are easily obtained from traffic optimization models.

DATA COLLECTION

The study was conducted in the city of Al-Khobar, Saudi Arabia and is limited to four-legged signalized intersections with left turn bays. This type of intersection was selected because the majority of intersections in the study area are of this kind and also due to the fact that the previous model (model 1) was calibrated particularly for such intersections. The sample size needed was determined using the statistical formula shown below (9):

2

222/

E

zn

δ= α (1)

where: n = number of intersection approaches; E = error; δ2 = variance of conflict per hour; zα/2 = normal random variable, 1.96 at 95% confidence level.

The hourly variance in traffic conflict, δ, is assumed to be 3.5 conflicts per hour, which is the same value used in developing model 1 (9).

For a 95% confidence level, the above formula indicates that at least 21 intersection approaches are needed to ensure a margin of error not exceeding 1.5 conflicts per hour. This sample size is in agreement with the size needed for regression model validation reported in classical regression references (10). Conservatively, a total of 22 approaches were randomly selected in the study area. In addition to the hourly stops and rear-end conflicts, approach speed, hourly volume and signal timings were collected at each of the studied approaches. Data was collected during moderate volume periods (8:30–11:30 a.m.) to avoid saturation conditions where it is quite hard to collect reliable stop and conflict data.

The number of stops are defined as the total number of vehicles that come to a complete stop at or before the stopline of the intersection approach.

Approach speeds were measured using a radar gun at locations at an adequate distance from the stopline, so that the measured speeds were not influenced by the possibility of a standing queue at the approach. The procedure and sample size requirement for the speed study were in accordance with the recommendations listed in the Manual of Transportation Studies (11).

Traffic conflict is broadly defined as an interaction between two or more vehicles in which one vehicle undertakes a sudden action, forcing the other vehicle(s) to take evasive action such as braking or weaving to


Ratrout et al. 3

avoid a possible collision. Rear-end conflicts, as used in this study, are defined to be any one of the following types:

1. Left turn same direction conflict 2. Right turn same direction conflict 3. Slow vehicle same direction conflict 4. Lane change conflict

The exact operational definitions of these types of conflicts are well documented in many sources (2, 3, 4, 11). To ensure the quality of the collected conflict data, the relevant recommendations of the NCHRP 219 report (2) were strictly adhered to.

Traffic volume, conflict, and number of stops were all collected simultaneously at each studied intersection. MODEL VALIDATION

To assess the actual predictive capability of the original conflict model (model 1), this model was used to predict each case of the new validation data set and the result was used to calculate the Mean Squared Prediction Error

(MSPR) and the proportion of variability in the validation data explained by the model )( 2pR as follows:

n

yyn

iii∑

=−

= 1

2)ˆ(

MSPR (2)

∑

∑

=

−

−

−

−=n

ii

n

iii

p

yy

yy

R

1

2

1

2

2

)(

)ˆ(

1 (3)

where: yi = the value of the dependent variable in the ith validation case; iy = the predicted value for the ith validation case based on the model-building data set;

y = the average value of dependent variable in the validation data set.

The MSPR was then compared with the Error Mean Square (MSE) of model 1. Similarly, the 2pR was compared

with the coefficient of determination of the regression model R2 (12). The results of these comparisons are shown in Table 1.

It is clear from the previous table that the MSPR of the validation data is close to the MSE of the regression model. In fact, the MSPR is smaller than the MSE, indicating that the model describes the behavior of the validation data set better than the calibration data used in model building. The same conclusion can be

reached by comparing the proportions of variability in the validation data explained by the model 2pR with the

coefficient of determination of the regression model R2. In addition to that, the summation of the error terms

−∑

=

n

iii yy

1

ˆ of the validation data set is very close to zero. This suggests that the model seems to produce

unbiased predictions.

Another approach to check the validity of model 1 is to re-estimate its coefficients using the validation data set. Rebuilding the regression model using the validation data showed that the intercept coefficient is statistically not different from zero at a 95% confidence level. Forcing the model through the origin provides the following model (model 2):


Ratrout et al. 4

Conflict = (0.0109) Stops model (2)

The coefficient of the number of stops in model 2 is very close to model 1. The coefficient of determination of model 2 is only 0.506. This value is somewhat on the low side when compared to R2 of model 1. Nevertheless, the degradation in R2 is not severe enough to suspect a serious inconsistency in the behavior of model 1.

Finally, model 1 was used to predict the dependent variable of each case in the model-building data set (i.e. the data set used in building model 1). The correlation between the predicted dependent variable )ˆ( y and the observed one (y) in the same data set was calculated to be 0.796, as shown in Table 1. The same procedure was repeated on the validation data set where model 1 was used to predict the dependent variable in the validation data set, and then the correlation between the predicted dependent variable )ˆ( y and the observed one (y) in this validation data set was calculated and found to be 0.746. The degradation in the correlation coefficient from the model-building data set to the validation data set is minimal, indicating that model 1 is appropriate to predict the dependent variable of the new validation data set.

From all of the above, it can be safely concluded that model 1 is consistent and valid in the study area under the conditions in which it was calibrated and validated.

IMPROVEMENT OF THE ORIGINAL MODEL

An attempt to improve the prediction capabilities of the original rear-end conflict model was made by incorporating in it some new explanatory variables which were not initially considered in its development. In the calibration process of model 1, the volume, number of lanes, and overlapping phases in addition to the number of stops were taken as independent variables in the regression analysis. With the exception of the number of stops, all these variables were either insignificant or were highly correlated with the number of stops.

Three new explanatory variables were selected to investigate their significance in enhancing the prediction ability of model 1, namely the speed, number of signalized intersections per km, and the volume capacity ratio.

Approach speed is known to affect response time and stopping distance. As the speed increases, drivers become more tense and unpredictable, brake more often, and frequently change lanes to avoid accidents when approaching intersections. Thus, it can be expected that high speed is an indication of a high number of rear-end conflicts. The average speed, variance in speed and coefficient of variation in speed were examined to select the speed characteristic which is strongly correlated with rear-end conflict. The average speed (km/hr) was found to have the highest correlation with rear-end conflict, and consequently it was selected as one of the promising explanatory variables.

As the number of signalized intersections within one km increases, the number of rear-end conflicts is expected to decrease. When the intersections are closely spaced, the vehicles move uniformly in compact platoons eliminating the need for erratic maneuvers and therefore fewer conflicts are expected in such situation.

The volume to capacity ratio is a measure of the degree of friction and interaction between vehicles. As the interaction between vehicles increases, the number of rear-end conflicts are expected to increase. The capacity of each signalized approach was calculated based on the observed signal timing and the local saturation flow rates of 1780 vph and 1650 vph for through and turning traffic, respectively (13).

The Pearson-correlation matrix shown in Table 2 summarizes the relationships between the selected explanatory variables and rear-end conflict as well as the relationships between the explanatory variables themselves. Table 2 shows that in addition to the number of stops, the mean speed seems to be a promising predictor variable. On the contrary, the number of intersections per km looks to be a poor predictor of rear-end conflict. It is interesting to note that the number of stops is highly correlated with the volume to capacity ratio (r = 0.88). This indicates that the volume to capacity ratio might be used in lieu of the number of stops as a possible predictor of rear-end conflict.

All possible one, two, three, and four variable regression models were built and investigated. Out of the fifteen possible models, only five were relevant. The remaining models had at least one variable with a regression coefficient statistically not different from a zero to 95% confidence level. The relevant regression models are summarized in Table 3. The table shows that the number of stops in conjunction with the mean speed in regression model no. 5 produce the highest R2 (and adjusted R2) and the lowest MSE of all models. In fact, the


Ratrout et al. 5

MSE is reduced by more than 50% by adding the mean speed to the number of stops which was the only predictor variable used in model 1.

It is worth mentioning that the second best regression model in Table 3 in terms of R2 (and adjusted R2) and MSE is model no. 6, in which the mean speed and volume to capacity ratio are used as predictor variables. Since the volume to capacity ratio is much easier to collect than the number of stops, model 6 seems to be very practical. Although model 6 is not as good in terms of R2 and MSE as model 5, where the number of stops is used, it is much better than using the number of stops alone as was done in model 1.

The assumptions of normality, independence and equal variance of the regression models were checked graphically and appear to be reasonable.

PREDICTING CONFLICT BY TRANSYT MODEL

The TRANSYT-7F model is one of the most popular and widely used optimization packages. It has been subjected to extensive validation and calibration processes in many countries including Saudi Arabia (9, 13). The input used by this model is basically traffic volume, speed and the signal timing plan. One of the outputs of the model is the number of stops per link and/or approach. It is usually much easier to collect TRANSYT-7F input variables than observing the actual number of stops. From this point of view, it will be practical to use the TRANSYT-7F simulated number of stops, rather than the observed ones in predicting conflict by either model 1 or model 5. To examine if the observed and simulated number of stops produce a comparable number of conflicts, a practical experiment was undertaken. The TRANSYT-7F model was used to simulate the traffic between 9:15 and 10:15 a.m. at three four-leg intersections along a major arterial in the study area. At the same time, the actual number of stops at these intersections were observed.

The predicted number of conflicts was then calculated via model 1, first by using the actual number of stops, and a second time by using the simulated number of stops obtained from TRANSYT-7F, as shown in Table 4. The table clearly shows that the observed and simulated number of stops compare favorably. Furthermore, the predicted conflicts seem to be marginally affected by using the simulated number of stops in lieu of the observed number of stops.

The average difference in the predicted conflicts was tested. The paired t-test was used to test the null hypothesis (Ho) that the average difference in predicted conflicts is equal to zero as follows:

0: =dH o

0:1 =/dH

n

dt

d /

0

δ−

= (4)

where d is the mean of the difference between predicted conflicts and δd is the standard deviation of this difference. These values were calculated (from Table 4) to be –0.310 and 0.483, respectively. Using the above Equation (4), the “t” statistic is only –1.284 and consequently when compared to tα=.025, n=3 , Ho cannot be rejected. Thus, this simple experiment did not provide enough evidence to reject the null hypothesis (Ho), that the average of the difference between predicted conflicts is equal to zero. However, because of the small data set (n = 4), this finding should be taken conservatively and should not be generalized without additional larger experiments covering a wide spectrum of volume and stop values. Nevertheless, the TRANSYT-7F package looks to be a promising and convenient tool for facilitating the prediction of rear-end conflict.

CONCLUSION

For rear-end conflict prediction, model 1, namely conflict/hour = 0.01154 (no. stops/hour) was successfully validated in the study area. Consequently, traffic safety assessment can be more easily achieved using this model, obviating the need for the collection of actual conflict data. The predictive power of the model was shown to be dramatically improved by adding the mean speed as a second predictor. In particular, the best rear-end conflict model was found in this study to be: conflict/hour = –6.64 + 0.0066 (no. stops/hour) + 0.1737 (mean speed). However, the validity of this improved model has to be investigated in an independent study. It was also shown


Ratrout et al. 6

that the volume/capacity ratio is a good surrogate predictor for the number of stops in predicting rear-end conflict. The TRANSYT-7F software was found to be a promising tool in facilitating the prediction of rear-end conflict. The number of stops simulated by the TRANSYT-7F software and the actual number of stops observed in the field produced a similar number of conflicts when used in conflict prediction model 1.

In summary, this study showed that rear-end conflict can be successfully predicted using alternative and easily obtained traffic variables.

ACKNOWLEDGMENT

The authors would like to acknowledge the support of King Fahd University of Petroleum & Minerals in carrying out this research.

REFERENCES

1. Perkins, S. R., and J. I. Harris. Traffic Conflict Characteristics Accident Potential at Intersections. Highway Research Record, 1968.

2. Glauz, W. D., and D. J. Migletz. Application of Traffic Conflict and Analysis at Intersections. NCHRP 219, February 1980.

3. Paddock, R. D., and D. E. Spence. The Conflicts Technique: An Accident Prediction Method. Technical Report, Ohio Department of Transportation, August 1973.

4. Zegeer, C. V., and R. Deen. Traffic Conflicts as a Diagnostic Tool in Highway Safety. TRR 667, 1978, pp. 48–57.

5. Kittelson & Associates, Inc., and Texas Transportation Institute. Evaluation of Traffic Signal Displays for Protected-Permitted Left Turn Control. Traffic Conflict Studies Report, Working Paper 5, NCHRP Project 3-54, National Cooperative Highway Research Program, August 1999.

6. Bianli, L., H. Masaoka, T. Hagiwara, T. Nakatsuji, S. Tsuji, and M. Ueyama. Study on the Analysis of Intersection Traffic Accidents Using Real Traffic Accident Images. XIth PIARC International Winter Road Congress, Sapporo, Japan, 2002, http://www.ces.co.jp.piarc/ronbun/03.pdf .

7. Kaub, A. R., and J. A. Kaub. Predicting Annual Intersection Accidents with Conflict Opportunities. TRB Circular E-C019: Urban Street Symposium Conference Proceedings, Dallas, Texas, June 28-30, 1999, Transportation Research Board, Washington, D.C., December 2000, pp. H-2/1–H-2/12.

8. Gettman, D., and L. Head. Surrogate Safety Measures from Traffic Simulation Models. Final Report, Publication No. FHWA-RD-03-050, Office of Safety Research and Development, Turner-Fairbank Highway Research Center, U.S. Department of Transportation, Federal Highway Administration, 2003, http://www.tfhrc.gov/safety/pubs/03050/index.htm .

9. Al-Ofi, K. A. The Effect of Signal Coordination on Intersection Safety. Ph.D. Thesis, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 1994.

10. Montgomery, D. C., and E. A. Peck. Introduction to Linear Regression Analysis. John Wiley & Sons, Inc., USA, 1992.

11. Institute of Transportation Engineers. Manual of Transportation and Engineering Studies. Prentice-Hall, New Jersey, 1994.

12. Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Regression Models, Third Edition. Times-Mirror Higher Education Group, Inc., USA, 1996.

13. Ratrout, N. T. Assessment of the Applicability of TRANSYT-7F Optimization Model to the Traffic Conditions in the Cities of Al-Khobar and Dammam, Saudi Arabia. Ph.D. Thesis, Michigan State University, USA, 1989.


Ratrout et al. 7

List of Tables TABLE 1 Validation of Model No. 1 (Conflict = 0.0115 * Stops) TABLE 2 Correlation Matrix of Explanatory Variables TABLE 3 Relevant Regression Models

TABLE 4 Predicted Conflicts Using Observed and Simulated Stops


Ratrout et al. 8

TABLE 1 Validation of Model No. 1 (Conflict = 0.0115 * Stops)

Statistics

Regression Model (Model-building Data Set)

Validation Data Set

Coefficient of determination R2

0.634

Proportion of variability

2pR

0.675

Error Mean Square MSE

6.447

Mean Squared Prediction Error MSPR

3.266

Sum of error terms

∑=

−n

i

yy1

)ˆ(

0.356

Correlation coefficient between y & y

0.796

0.746

Number of observations (n)

38

22


Ratrout et al. 9

TABLE 2 Correlation Matrix of Explanatory Variables

Variable

No. Conflicts

No. Stops

Mean Speed

No. Inter- Sections/km

Volume/ Capacity

No. conflicts/hr 1.000a No. stops/hr 0.746 1.000 Mean speed (kph) 0.708 0.348 1.000 No. intersections/km –0 .328 –0.195 –0.375 1.000 Volume/capacity ratio

0.606

0.875

0.206

–0.085

1.000

aAll values are significant at 95% confidence.


Ratrout et al. 10

TABLE 3 Relevant Regression Models

Coefficient of Predictor Variables (α < 0.05)

Model No.

Intercept

No. Stops

Mean Speed

Volume/ Capacity

R2

Adjusted R2

MSE

2 a 0.0109 – – 0.506 3.326 3 –7.423 – 0.2411 – 0.501 3.531 4 a – – 8.6724 0.322 4.566 5 –6.641 0.0066 0.1737 – 0.785 0.762 1.601 6 –8.328 – 0.2074 5.2257 0.722 0.693 2.067

aIntercept is not different from zero at 95% confidence. Reported values are for model forced through origin.


Ratrout et al. 11

TABLE 4 Predicted Conflicts Using Observed and Simulated Stops Intersection No. and Traffic Direction

Observed No. Stops

Simulated No. Stops

Predicted Conflict Using Observed No. Stopsa

Predicted Conflict Using Simulated No. Stopsa

Difference in Predicted Conflicts

1, Northbound 300b 328b 3.46b 3.79b –0.33b 2, Northbound 305 378 3.52 4.36 –0.84 2, Southbound 153 125 1.77 1.44 +0.33 3, Southbound 251 286 2.90 3.30 –0.40 Average 252.25 279.25 2.91 3.22 –0.31

aUsing original model no.1. Conflict = 0.01154 ∗ stops. bAll values are per hour.


Ratrout et al. 12

FIGURE 1 Typical intersection in the study area.


trb2004-000051

Documents