Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T05:13:33.213Z Has data issue: false hasContentIssue false
  • English
  • Français

The Downs-Thomson Effect in a Markov Process

Published online by Cambridge University Press:  27 July 2009

Bruce Calvert
Bruce Calvert
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose customers pass through a network of two queues in parallel. A statedependent routing policy gives individuals their quickest journey. The Downs-Thomson effect is any increase in the long-run expected journey time caused by an increase in the service rates. This effect may occur.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 327 - 340
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Abraham, H. & Mahoney, O. (1994). Road pricing and public transport provision in London. Traffic Engineering and Control 35: 666–670.Google Scholar
2.Arnott, R. & Small, K. (1994). The economics of traffic congestion. American Scientist 82: 447–455.Google Scholar
3.Bly, P.H., Johnston, R.H., & Webster, F.V. (1987). A panacea for road congestion? Traffic Engineering and Control 28: 8–12, 19–20.Google Scholar
4.Brady, M.E. (1993). Dynamic stability, traffic equilibrium and the law of peak-hour expressway congestion. Transportation Research 27B: 229–236.CrossRefGoogle Scholar
5.Calvert, B., Solomon, W., & Ziedins, I. (to appear). Braess's paradox in a queueing network with state dependent routing. Journal of Applied Probability.Google Scholar
6.Cohen, J.E. & Kelly, F.P. (1990). A paradox of congestion in a queuing network. Journal of Applied Probability 27: 730–734.CrossRefGoogle Scholar
7.Downs, A. (1962). The law of peak-hour expressway congestion. Traffic Quarterly 16: 393–409.Google Scholar
8.Hickling-Lewis-Brod, , Inc. (1994). Unsticking traffic: When transit works and why. Washington, D.C.: Federal Transport Administration, U.S. Department of Transportation.Google Scholar
9.Holden, J. (1989). Wardrop's third principle. Journal of Transport Economics and Policy 23: 239–262.Google Scholar
10.Kanafani, A. (1983). Transportation demand and analysis. New York: McGraw Hill.Google Scholar
11.Mackie, P.J. & Bonsall, P.W. (1989). Traveller response to road improvements: Implications for user benefits. Traffic Engineering and Control 30: 411–416.Google Scholar
12.May, A.D., Guest, P.W., & Gardner, K. (1990). Can rail-based policies relieve urban congestion? Traffic Engineering and Control 31: 406–407.Google Scholar
13.Mogridge, M.J.H. (1988). Jams and superjams: A systems approach to congested traffic networks. Civil Engineering Systems: Decision Making and Problem Solving 5(4): 181–193.CrossRefGoogle Scholar
14.Mogridge, M.J.H. (1990). Planning for optimum urban efficiency; the relationship between congestion on the roads and public transport. Transportation Planning Systems 1(1): 11–19.Google Scholar
15.Mogridge, M.J.H. & Holden, D.J. (1989). A panacea for road congestion: A riposte. Traffic Engineering and Control 28: 13–19.Google Scholar
16.Mogridge, M.J.H., Holden, D.J., Bird, J., & Terzis, G.C. (1987). The Downs-Thomson paradox and the transportation planning process. International Journal of Transport Economics 14: 283–311.Google Scholar
17.Olszewski, P. & Suchorzewski, W. (1987). Traffic capacity of the city centre. Traffic Engineering and Control 28: 336–337, 339–343, 348, 647.Google Scholar
18.Ross, S.M. (1980). Introduction to probability models. New York: Academic Press.Google Scholar
19.Thomson, J.M. (1977). Great cities and their traffic. London: Gollancz, Peregrine Edition.Google Scholar
20.Wardrop, J.G. (1952). Some theoretical aspects of road traffic research. Proceedings, Institution of Civil Engineers 1(11): 325–378.CrossRefGoogle Scholar
21.Williams, H.C.W.L., Lam, W.M., Austin, J. & Sims, K.S. (1991). Transport policy appraisal with equilibrium models III: Investment benefits in multi-modal systems. Transportation Research 25B: 293–316.CrossRefGoogle Scholar
22.Younes, B. (1993). Roads in urban areas: To build or not to build? Transport Reviews 13: 99–117.CrossRefGoogle Scholar