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The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Queueing Systems volume 49, pages 321–334 (2005)Cite this article

Abstract

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.

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Authors and Affiliations

  1. Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Heti Afimeimounga, Wiremu Solomon & Ilze Ziedins

Authors
  1. Heti Afimeimounga
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  2. Wiremu Solomon
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  3. Ilze Ziedins
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Correspondence to Ilze Ziedins.

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AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13

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Afimeimounga, H., Solomon, W. & Ziedins, I. The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria. Queueing Syst 49, 321–334 (2005). https://doi.org/10.1007/s11134-005-6970-0

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  • DOI: https://doi.org/10.1007/s11134-005-6970-0

Keywords

  • queueing networks
  • routing
  • Downs-Thomson paradox
  • Wardrop equilibrium
  • transportation networks