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

  • Bruce Calvert (a1), Wiremu Solomon (a1) and Ilze Ziedins (a1)
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.

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Corresponding author
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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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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