Abstract
Conditions at a freeway bottleneck are predicted with a two-dimensional stochastic differential equation (SDE) model of flow and speed. Stochastic behavior is assumed to be standard Brownian motion. To fully describe conditions observed in the field, it is necessary to couple the SDE model with a stochastic capacity model, thus forming a stochastic capacity-differential equation (SCDE) model. The model contains mechanisms to (1) trigger a breakdown event when the traffic flow reaches or exceeds the freeway capacity, and (2) identify when recovery takes place. Measures of freeway performance are derived from SCDE model predictions. They include breakdown probability, expressed as a function of traffic flow and time-of-day, and recovery time, i.e., the length of time the freeway remains in a congested state before returning to a free-flow state. To achieve dependable model forecasts, it is necessary to impose constraints when fitting the stochastic capacity model. The constraint condition consists of matching the breakdown and prebreakdown flow distributions derived from field data and stochastic capacity model forecasts. Sensitivity analyses are performed to test validity of the model-fitting procedure and to test the dependability of the SCDE model forecasts. An empirical study of recurrent workday freeway congestion on I-93 in Salem, NH is used to demonstrate the approach. The approach demonstrates the need to treat breakdown as a random process.
Get full access to this article
View all available purchase options and get full access to this article.
References
Agresti, A. (1990). Categorical data analysis, 1st Ed., Wiley, New York.
Brilon, W., Geistefeldt, J., and Regler, M. (2005). “Reliability of freeway traffic flow: A stochastic concept of capacity.” Proc., 16th Int. Symp. on Transportation and Traffic Theory, College Park, MD, 125–144.
Brilon, W., Geistefeldt, J., and Zurlinden, H. (2007). “Implementing the concept of reliability for highway capacity analysis.” Transp. Res. Rec., 2027, 1–8.
Brouste, A., et al. (2014). “The yuima project: A computational framework for simulation and inference of stochastic differential equations.” J. Stat. Software, 57(4), 1–51.
Eisele, B., Schrank, D., and Lomax, T. (2011). “TTT’s 2011 congested corridors report, powered by INRIX traffic data.” 〈http://d2dtl5nnlpfr0r.cloudfront.net/tti.tamu.edu/documents/corridors-report-2011.pdf〉 (Nov. 2011).
GAO (Government Accountability Office). (2015). “Surface transpiration, DOT is progressing toward a performance-based approach. But states and grantees report potential implementation challenges.” 〈http://www.gao.gov/assets/670/667939.pdf〉 (Jan. 2015).
Geistefeldt, J. (2009). “Estimation of passenger car equivalents based on capacity variability.” Transp. Res. Rec., 2130, 1–6.
Geistefeldt, J. (2010). “Consistency of stochastic capacity estimations.” Transp. Res. Rec., 2173, 89–95.
Glickman, T. S., and Gough, M. (1991). “Readings in risk.” Environ. Int., 17(4), 391.
Haldar, A., and Mahadevan, S. (2000). Probability, reliability and statistical methods in engineering design, Wiley, New York.
Hosmer, D., and Lemeshow, S. (1989). Applied logistic regression, Wiley, New York.
Iacus, S. (2008). Simulation and inference for stochastic differential equations: With R examples, Springer, Berlin.
Ishak, S., Mamidala, C., and Qi, Y. (2010). “Stochastic characteristics of freeway traffic speed during breakdown and recovery periods.” Transp. Res. Rec., 2178, 79–89.
Kittelson, W. K., and Roess, R. P. (2001). “Highway capacity analysis after Highway Capacity Manual 2000.” Transp. Res. Rec., 1776, 10–16.
Kuhne, R., Mahnke, R., Lubashevsky, I., and Kaupuzs, J. (2002). “Probabilistic description of traffic breakdowns.” Phys. Rev. E (Statistical, Nonlinear, and Soft Matter Physics), 65(6), 066125.
Lorenz, M. R., and Elefteriadou, L. (2001). “Defining freeway capacity as function of breakdown probability.” Transp. Res. Rec., 1776, 43–51.
Mahnke, R., Kaupuzs, J., and Lubashevsky, I. (2005). “Probabilistic description of traffic flow.” Phys. Rep., 408(1–2), 1–130.
Qiu, T. Z., Lu, X.-Y., Chow, A. H., and Shladover, S. E. (2010). “Estimation of freeway traffic density with loop detector and probe vehicle data.” Transp. Res. Rec., 2178, 21–29.
R Core Team. (2014). “R: A language and environment for statistical computing.” R Foundation for Statistical Computing, Vienna, Austria.
Tebaldi, C., West, M., and Karr, A. F. (2002). “Statistical analyses of freeway traffic flows.” J. Forecasting, 21(1), 39–68.
TRB (Transportation Research Board). (2000). Highway capacity manual, Washington, DC.
U.S. DOT. (2012). “Moving ahead for progress in the 21st century act (P.L. 112-141) (MAP-21).” 〈http://www.fhwa.dot.gov/map21/〉.
Yeon, J., Hernandez, S., and Elefteriadou, L. (2009). “Differences in freeway capacity by day of the week, time of day, and segment type.” J. Transp. Eng., 416–426.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 142 • Issue 7 • July 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: May 21, 2015
Accepted: Jan 7, 2016
Published online: Mar 18, 2016
Published in print: Jul 1, 2016
Discussion open until: Aug 18, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.