Networks and Spatial Economics

, Volume 10, Issue 1, pp 93–112

Simultaneous Departure Time/Route Choices in Queuing Networks and a Novel Paradox


DOI: 10.1007/s11067-007-9026-7

Cite this article as:
Zhang, X. & Zhang, H.M. Netw Spat Econ (2010) 10: 93. doi:10.1007/s11067-007-9026-7


In this paper, we establish an exact expression of the dynamic traffic assignment (DTA) problem with simultaneous departure time and route (SDR) choices in transportation networks with bottlenecks, where both link and path capacities are time-dependent. Using this expression, closed form of dynamic user equilibrium solutions can be obtained in some special networks. Furthermore, we investigate the DTA-SDR problem in the classical Braess’s network with closed form equilibrium solutions. The explicit results show that an inappropriately added new link could deteriorate the existing network in terms of the increase of individual and system travel costs. The mechanism of this new paradox is quite different from that of the previously discovered ones, and it is the first paradox caused by the simultaneous departure time/route competitions among individuals.


Dynamic traffic assignment (DTA)Simultaneous departure time and route (SDR) choicesBraess’s paradoxFirst-In-First-Out (FIFO)Bottleneck models

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Key Laboratory of Road and Traffic Engineering of the Ministry of EducationTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Department of Civil and Environment EngineeringUniversity of CaliforniaDavisUSA