Reliability-based network flow estimation with day-to-day variation: A model validation on real large-scale urban networks

ABSTRACT

Day-to-day variation in the travel times of congested urban transportation networks is a frustrating phenomenon to the users of these networks. These users look pessimistically at the path travel times, and learn to spend additional time to safeguard against serious penalties that await late arrivals at the destinations. These additional expenses are charges similar to the tolls in system equilibrium flow problem, but may not be collected. With this conjecture, the user equilibrium (UE) formulation of congested network flow problem would lack some necessary factors in addressing appropriate path choices. This study, following a previous work proposing pessimistic UE (PUE) flow, aims to show how to measure this additional travel cost for a link, and investigates how different is PUE from UE, and when such differences are pronounced. Data are collected from the peak-hour travel times for the links of paths in the city of Tehran, to estimate the variance of travel times for typical links. Deterministic functions are obtained by calibrating the standard deviation of the daily variations of link travel times, and probabilistic functions by the technique of copula. UE and PUE traffic assignment models are built and applied to three large cities of Mashhad, Shiraz, and Tehran in Iran. The results show that the estimated flows by PUE model replicate the observed flows in screen lines much better than the UE model, particularly for longer trips. Since PUE is computationally equivalent to UE, this improvement is attained virtually at no cost.

KEYWORDS:

• copula
• pessimistic user equilibrium
• travel time standard deviation
• travel time reliability

Acknowledgments

The authors wish to thank Prof. H. Z. Aashtiani, of Sharif University of Technology, for his helpful comments, and Dr. A. Babazadeh of Tehran University, and Ms. M. Zakeri Sohi, for their help in running some of the computer programs. They also appreciate the insightful comments by the anonymous reviewers, very much, that enhanced the content and presentation of the article appreciably. The authors, however, remain solely responsible for the content of this article.