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The Price of Anarchy for a Network of Queues in Heavy Traffic

In: Essays in Production, Project Planning and Scheduling

Author

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  • Shaler Stidham

    (University of North Carolina at Chapel Hill)

Abstract

The price of anarchy (POA) in a congestion network refers to the ratio of the individually optimal total cost to the socially optimal total cost. An extensive literature on this subject has focussed mostly on deriving upper bounds on the POA that are independent of the topology of the network and (to a lesser extent) the form of the cost functions at the facilities of the network. This paper considers congestion networks in which the cost functions at the facilities display qualitative characteristics found in the waiting-time function for queue with an infinite waiting room. For a network of parallel M/M/1 queues an explicit expression exists for the POA, which, unlike the bounds in the literature, remains finite in heavy traffic. We show that a similar explicit expression holds in heavy traffic for parallel GI/GI/1 queues and, in some cases, in more general networks as well.

Suggested Citation

  • Shaler Stidham, 2014. "The Price of Anarchy for a Network of Queues in Heavy Traffic," International Series in Operations Research & Management Science, in: P. Simin Pulat & Subhash C. Sarin & Reha Uzsoy (ed.), Essays in Production, Project Planning and Scheduling, edition 127, chapter 5, pages 91-121, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-9056-2_5
    DOI: 10.1007/978-1-4614-9056-2_5
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    Cited by:

    1. Ghosh, Souvik & Hassin, Refael, 2021. "Inefficiency in stochastic queueing systems with strategic customers," European Journal of Operational Research, Elsevier, vol. 295(1), pages 1-11.
    2. N. Hemachandra & Kishor Patil & Sandhya Tripathi, 2020. "Equilibrium points and equilibrium sets of some $$\textit{GI}/M/1$$ GI / M / 1 queues," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 245-284, December.
    3. Riccardo Colini-Baldeschi & Roberto Cominetti & Panayotis Mertikopoulos & Marco Scarsini, 2020. "When Is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic," Operations Research, INFORMS, vol. 68(2), pages 411-434, March.

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