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Braess's paradox in a queueing network with state-dependent routing

Part of:Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bruce Calvert,
Wiremu Solomon and
Ilze Ziedins
Bruce Calvert*
Affiliation:
University of Auckland
Wiremu Solomon*
Affiliation:
University of Auckland
Ilze Ziedins*
Affiliation:
University of Auckland
*
∗ Postal address: Department of Mathematics, School of Mathematical and Information Sciences, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
∗ Postal address: Department of Mathematics, School of Mathematical and Information Sciences, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
∗∗ Postal address: Department of Statistics, School of Mathematical and Information Sciences, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
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Abstract

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential.

We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them.

We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Keywords

BRAESS'S PARADOXQUEUEING NETWORK

MSC classification

Primary:90B15: Network models, stochastic90B22: Queues and service90C35: Programming involving graphs or networks

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997, pp. 134 - 154
Copyright
Copyright © Applied Probability Trust 1997 

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