Networks and Spatial Economics

, Volume 10, Issue 1, pp 93–112

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

Article

Abstract

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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akamatsu T (2000) A dynamic traffic equilibrium assignment paradox. Transp Res 34B:515–531CrossRefGoogle Scholar
  2. Akamatsu T (2001) An efficient algorithm for dynamic traffic equilibrium assignment with queues. Transp Sci 35:389–404CrossRefGoogle Scholar
  3. Arnott R, Small K (1994) The economics of traffic congestion. Am Sci 82:446–455Google Scholar
  4. Arnott R, Palma AD, Lindsey R (1993) Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering. Transp Sci 27:148–160CrossRefGoogle Scholar
  5. Ben-Akiva M, Bierlaire M, Koutsopoulos H, Mishalani R (1998) Dynamit: a simulation-based system for traffic prediction. Paper presented at the DACCORD short-term forecasting workshop, Delft, The NetherlandsGoogle Scholar
  6. Braess D (1968) Uber ein paradoxen der verkehrsplaning. Unternehmensforschung 12:258–268CrossRefGoogle Scholar
  7. Carey M (1986) A constraint qualification for a dynamic traffic assignment model. Transp Sci 20:55–58CrossRefGoogle Scholar
  8. Carey M (1987) Optimal time-varying flows on congested networks. Oper Res 35:58–69CrossRefGoogle Scholar
  9. Chen H-K, Hsueh C-F (1998) A model and an algorithm for the dynamic user optimal route choice problem. Transp Res 32B:219–234CrossRefGoogle Scholar
  10. Daganzo C (1996) Two paradoxes of traffic flow on networks with physical queues. II Symposium Ingenieria de los Transportes. Madrid, 22–24 May 1996, pp 55–62Google Scholar
  11. Daganzo C (1998) Queue spillovers in transportation networks with a route choice. Transp Sci 32:3–11CrossRefGoogle Scholar
  12. Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res 41:179–191CrossRefGoogle Scholar
  13. Heydecker BG, Addison JD (1996) An exact expression of dynamic traffic equilibrium. In Lesort J-B (ed) Proceeding of 13th international. Symposium on transportation and traffic theory. Elsevier, pp 359–383Google Scholar
  14. Heydecker BG, Addison JD (2005) Analysis of dynamic traffic equilibrium with departure time choice. Transp Sci 39(1):39–57CrossRefGoogle Scholar
  15. Huang HJ, Lam WHK (2002) Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues. Transp Res 36B:253–273CrossRefGoogle Scholar
  16. Hurdle VF (1974) The effect of queuing on traffic assignment in a simple road network. In Proceedings of the 6th international symposium on transportation and traffic theory, Elsevier Science, Amsterdam, The Netherlands, pp 519–540Google Scholar
  17. Janson BN (1991) Dynamic traffic assignment for urban road networks. Transp Res 25B:143–161CrossRefGoogle Scholar
  18. Janson BN, Robles J (1995) A quasi-continuous dynamic traffic assignment model. Transp Res Rec 1493:199–206Google Scholar
  19. Jayakrishnan R, Hu HSMTU (1994) An evaluation tool for advanced traffic information and management systems in urban networks. Transp Res 2C:129–147Google Scholar
  20. Lo HK, Szeto WY (2002) A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transp Res 36B:421–443CrossRefGoogle Scholar
  21. Luque FJ, Friesz TL (1980) Dynamic traffic assignment considered as a continuous time optimal control problem. In: Paper presented at the TIMS/ORSA Joint National Meeting. May 5–7Google Scholar
  22. Mahmassani H, Sbayti H, Chiu Y (2002) Dynasmart-p version 0.930.0 user’s guide, Technical report, Maryland Transportation Initiative, University of MarylandGoogle Scholar
  23. Merchant DK, Nemhauser GL (1978a) A model and an algorithm for the dynamic traffic assignment problems. Transp Sci 12:183–199CrossRefGoogle Scholar
  24. Merchant DK, Nemhauser GL (1978b) Optimality conditions for a dynamic traffic assignment model. Transp Sci 12:200–207CrossRefGoogle Scholar
  25. Pas EI, Principio SL (1997) Braess’s paradox: some new insights. Transp Res 31B:265–276CrossRefGoogle Scholar
  26. Penchina CM (1997) Braess paradox: maximum penalty in a minimal critical network. Transp Res 31A:379–388Google Scholar
  27. Ran B, Boyce D (1996) A link-based variational inequality formulation of ideal dynamic user optimal route choice problem. Transp Res 4C:1–12Google Scholar
  28. Ran B, Hall RW, Boyce D (1996) A link-based variational inequality model for dynamic departure time/route choice. Transp Res 30B:31–46CrossRefGoogle Scholar
  29. Small KA (1982) The scheduling of consumer activities: work trips. Am Econ Rev 72:467–479Google Scholar
  30. Smith MJ (1993) A new dynamic traffic model and the existence and calculation of dynamic user equilibrium on congested capacity-constrained road networks. Transp Res 27B:49–63CrossRefGoogle Scholar
  31. Szeto WY, Lo HK (2004) A cell-based simultaneous route and departure time choice model with elastic demand. Transp Res 38B:593–612CrossRefGoogle Scholar
  32. Wie BW, Friesz TL, Tobin RL (1990) Dynamic user optimal traffic assignment on congested multi-destination networks. Transp Res 24B:431–442CrossRefGoogle Scholar
  33. Wie BW, Tobin RL, Carey M (2002) The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation. Transp Res 36B:897–918CrossRefGoogle Scholar
  34. Yagar S (1970) Analysis of the Peak Period Travel in a Freeway-Arterial Corridor. Ph.D. Dissertation, University of California, BerkeleyGoogle Scholar
  35. Yagar S (1971) Dynamic traffic assignment by individual path minimization and queueing. Transp Res 5:179–196CrossRefGoogle Scholar
  36. Yagar S (1974) Emulation of dynamic equilibrium in traffic networks. In Florian MA (ed) Traffic equilibrium methods, Lecture notes in economics and mathematical systems, volume 118, Springer-VerlagGoogle Scholar
  37. Yang H (1997) Sensitivity analysis for the elastic-demand network equilibrium problem with applications. Transp Res 31B:55–70CrossRefGoogle Scholar
  38. Yang H, Bell MGH (1998) A capacity paradox in network design and how to avoid it. Transp Res 32A:539–545Google Scholar
  39. Zhang XN, Zhang HM (2005) Paradoxes of network expansion considering dynamic user response. Transportation research board 84th annual meeting. Washington D.C., 12–16 January 2005Google Scholar

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

Personalised recommendations