Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T23:56:59.802Z Has data issue: false hasContentIssue false
  • English
  • Français

A paradox of congestion in a queuing network

Published online by Cambridge University Press:  14 July 2016

Joel E. Cohen  and
Frank P. Kelly
Joel E. Cohen*
Affiliation:
Rockefeller University
Frank P. Kelly*
Affiliation:
University of Cambridge
*
∗Postal address: Rockefeller University, 1230 York Avenue, Box 20, New York, NY 10021, USA.
∗∗Postal address: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

In an uncongested transportation network, adding routes and capacity to an existing network must decrease, or at worst not change, the average time individuals require to travel through the network from a source to a destination. Braess (1968) discovered that the same is not true in congested networks. Here we give an example of a queuing network in which added capacity leads to an increase in the mean transit time for everyone. Self-seeking individuals are unable to refrain from using the additional capacity, even though using it leads to deterioration in the mean transit time. This example appears to be the first queuing network to demonstrate the general principle that in non-co-operative games with smooth payoff functions, user-determined equilibria generically deviate from system-optimal equilibria.

Keywords

BRAESS'S PARADOXNASH EQUILIBRIANON-CO-OPERATIVE GAME
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 730 - 734
Copyright
Copyright © Applied Probability Trust 1990 

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

Bertsekas, D. P. (1982) Optimal routing and flow control methods for communication networks. In Analysis and Optimization of Systems, ed. Bensoussan, A. and Lions, J. L. Lecture Notes in Control and Information Sciences 44, Springer-Verlag, Berlin, 615–643.Google Scholar
Braess, D. (1968) über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258–268.Google Scholar
Dafermos, S. and Nagurney, A. (1984a) On some traffic equilibrium theory paradoxes. Transportation Res. B 18, 101–110.Google Scholar
Dafermos, S. and Nagurney, A. (1984b) Sensitivity analysis for the asymmetric network equilibrium problem. Math. Programming 28, 174–184.Google Scholar
Dubey, P. (1986) Inefficiency of Nash equilibria. Math. Operat. Res. 11, 1–8.Google Scholar
Gallager, R. G. (1977) A minimum delay routing algorithm using distributed computation. IEEE Trans. Comm. 25, 73–85.Google Scholar
Knödel, W. (1969) Graphentheoretische Methoden und ihre Anwendungen, Springer-Verlag, Berlin, pp. 56–59.Google Scholar
Steinberg, R. and Zangwill, W. I. (1983) The prevalence of Braess' paradox. Transportation Sci. 17, 301–318.Google Scholar