Capacity Drop Estimation Based on Stochastic Approach Applied to Tehran-Karaj Freeway

Document Type: Research Paper


Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran


Existence of capacity drop phenomenon, as the difference between pre-queue and queue discharge flow rates, has been one of the controversial concepts of traffic engineering. Several researches have focused on capacity drop existence and also its estimation issues. This paper aims to estimate capacity drop based not only on a comparison between breakdown and queue discharge flow rates, but also on the estimation of the capacity distribution function before and after breakdown. In the empirical case, speed and flow rate data are collected in a section of Iran’s most crowded freeway for four months, based on which the threshold speed as the boundary between congested and non-congested flow is determined, and breakdown flow rates and their subsequent queue discharge flows are detected. Paired t-test between pre-queue and queue discharge flow rates is conducted to find the mean difference. Also, the distribution function of capacity under non-congested and congested flow is estimated using maximum likelihood and product limit methods. Based on the 11,600-record data set, it was observed that end results of both methods are consistent, revealing roughly five percent drop in capacity for the section under investigation.


- Banks, J. H. (2006) “Flow processes at a freeway bottleneck”, Transportation Research Record: Journal of the Transportation Research Board, 1278, pp.20-28.

-Brilon, W., Geistefeldt, J. and Regler, M. (2005) “Reliability of freeway traffic flow: a stochastic concept of capacity”, Transportation and Traffic Theory: Flow, Dynamics and Human Interaction, Proceedings of the 16th International Symposium on Transportation and Traffic Theory, Elsevier Ltd., Oxford, pp.125-144.

-Di Cristoforo, R., Hood, C. and Sweatman, P. F. (2004) “Acceleration and deceleration testing of combination vehicles”, Report to Main Roads Western Australia, Document Number RUS-04-1075-01-05.

-El-Metwally, M. and Rakha, H. (2009) “Analysis of capacity drop at congestion toward better environment”, IRF Educational Foundation 2009 Student Essay Competition.

-Geistefeldt, J. and Brilon, W. (2009) “A comparative assessment of stochastic capacity estimation methods”, Transportation and Traffic Theory 2009, Proceedings of the18th International Symposium on Transportation and Traffic Theory, Springer, pp.583-602.

-Hall, F.L. and Agyemang-Duah, K. (1991) “Freeway capacity drop and the definition of capacity”, Transportation Research Record: Journal of the Transportation Research Board, 1320, 20-28.

-Hall, F. L. and Hall, L. M. (1990) “Capacity and speed-flow analysis of the Queen Elizabeth way in Ontario”, Transportation Research Record: Journal of the Transportation Research Board, 1287, pp.108-118.
-Highway Capacity Manual (2000) Transportation Research Board, Washington, D.C.

-Kaplan, E.L. and Meier, P. (1958) “Nonparametric estimation from incomplete observations”, Journal of the American Statistical Association, Vol. 53, No. 282, pp.457-481.

-Lorenz, M. and Elefteriadou L. (2000) “A probabilistic approach to defining freeway capacity and breakdown”, Proceedings of the 4th International Symposium on Highway Capacity, TRB-Circular E-C018, Transportation Research Board, Washington, D.C., pp.84-95.

-Maze, T. H., Schrock, S.D. and Kamyab, A. (2000) “Capacity of freeway work zone lane closures”, Mid-Continent Transportation Symposium 2000 Proceedings, Iowa State University, Ames, pp.178-183.

-Milella, P.P. (2012) “Fatigue and corrosion in metals”, Springer, Milan.

-Myung, J. (2002) “Tutorial on maximum likelihood estimation”, Journal of Mathematical Psychology, 47, pp.90–100.

-Oh, S. and Yeo, H. (2012) “Estimation of capacity drop in highway merging sections”, TRB Annual Meeting, Transportation Research Board, Washington, D.C.

-Persaud, B., Yagar, S. and Brownlee, R. (1998) “Exploration of the breakdown phenomenon in freeway traffic”, Transportation Research Record: Journal of the Transportation Research Board, 1643, pp.64-69.

-Qin, L. and Smith, B.L. (2001) “Characterization of accident capacity reduction”, A Research Project Report for the National ITS Implementation Research Center, UVA Center for Transportation Studies.

-Shojaat, S. (2012) “Stochastic model of freeway capacity and its application to times of disaster”, M.S Thesis, Islamic Azad University-South Tehran Branch, Tehran.

-Washington, S.P., Karlaftis, M.G. and Mannering, F.L. (2003) “Statistical and econometric methods for transportation data analysis”, Chapman & Hall., CRC Press, Florida.

-Wu, N. (2004) “Determination of stochastic bottlenecks capacity on freeways and estimation of congestion probabilities”, Proceedings of the International Conference on Traffic and Transportation Studies 2004, Dalian, China.

-Zhong-zhong, T. (2006) “Ramp metering and the two-capacity phenomenon in freeway operations”, Journal of Transportation Systems Engineering and Information Technology, Vol. 6, pp.11-20.

-Chung, K., Rudjanakanoknad, J. and Cassidy M.J. (2007) “Relation between traffic density and capacity drop at three freeway bottlenecks”, Transportation Research Part B: Methodological, Vol. 41, No. 1, pp. 82-95.

9. Endnotes
1- 15-minute observation intervals
2- To define capacity under congested situation, the word “breakdown” could be substituted by the word “recovery” in this definition.
3- Time series is based on real data gathered in one of the most crowded days of the freeway.