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Nondeterministic Polling Systems

Author

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  • Mandyam M. Srinivasan

    (Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2117)

Abstract

A nondeterministic polling system is considered in which a single server serves a number of stations. The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiexhaustive service discipline, then the next station polled is station j with probability p ij if there was service at station i. The service time at station i is a random variable which may depend on the station polled next. If no service is performed at station i, then the next station polled is station j with probability e ij . The time to switch between stations i and j is a random variable which may depend on whether service was performed at station i or not. If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not. Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained.

Suggested Citation

  • Mandyam M. Srinivasan, 1991. "Nondeterministic Polling Systems," Management Science, INFORMS, vol. 37(6), pages 667-681, June.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:6:p:667-681
    DOI: 10.1287/mnsc.37.6.667
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    Cited by:

    1. Boysen, Nils & de Koster, René & Weidinger, Felix, 2019. "Warehousing in the e-commerce era: A survey," European Journal of Operational Research, Elsevier, vol. 277(2), pages 396-411.
    2. Dieter Fiems & Eitan Altman, 2012. "Gated polling with stationary ergodic walking times, Markovian routing and random feedback," Annals of Operations Research, Springer, vol. 198(1), pages 145-164, September.
    3. Tetsuji Hirayama, 2012. "Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms," Annals of Operations Research, Springer, vol. 198(1), pages 83-123, September.
    4. Mahender P. Singh & Mandyam M. Srinivasan, 2007. "Performance Bounds for Flexible Systems Requiring Setups," Management Science, INFORMS, vol. 53(6), pages 991-1004, June.

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