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A Markov Game Approach For Optimal Routing Into A Queueing Network


  • Eitan ALTMAN

    (INRIA, 2004 Route des Lucioles, BP93, 06902 Sophia-Antipolis Cedex, France)


We study a dynamic optimal routing problem, where a controller has to decide to which of two queues should arriving customers (representing packets, messages, call etc...) be sent. The service rate in each queue may depend on the state of the system, may change in time and is unknown to the controller. The goal of the controller is to design a strategy that guarantees the best performance under the worst case service conditions. The payoff is composed of a holding cost, an admission cost, and a cost that depends on the quality of the service. We consider both the finite and infinite horizon discounted cost and the expected average cost. The problem is studied in the framework of zero-sum Markov games where the server, called player 1, is assumed to play against the router, called player 2. Each player is assumed to have the information of all previous actions of both players as well as the current and past states of the system. We show that there exist pure optimal strategies for both players. A value iteration algorithm is used to establish properties of the value of the game, which are related to supermodularity and to convexity. This is then shown to imply the existence of optimal strategies described by

Suggested Citation

  • Eitan ALTMAN, 1994. "A Markov Game Approach For Optimal Routing Into A Queueing Network," Game Theory and Information 9401002, EconWPA.
  • Handle: RePEc:wpa:wuwpga:9401002
    Note: 12 pages, LateX file

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    References listed on IDEAS

    1. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
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    Cited by:

    1. Arie Hordijk & Olaf Passchier & Floske Spieksma, 1997. "Optimal service control against worst case admission policies: A multichained stochastic game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 281-301, June.
    2. repec:spr:compst:v:45:y:1997:i:2:p:281-301 is not listed on IDEAS

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty


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