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The Analysis of Random Polling Systems

Author

Listed:
  • Leonard Kleinrock

    (University of California, Los Angeles, California)

  • Hanoch Levy

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

In this paper, we analyze the behavior of random polling systems . The polling systems we consider consist of N stations, each equipped with an infinite buffer and a single server who serves them in some order. In contrast to previously studied polling systems, where the order of service used by the server is periodic (and usually cyclic ), in the systems we consider the next station to be served after station i is determined by probabilistic means . More specifically, according to the model we consider in this paper, after serving station i , the server will poll (i.e., serve) station j ( j = 1, 2, …, N ) with probability p j . The main results of this paper are expressions for the expected response time in a random polling system operated under a variety of service disciplines. The results are compared to the response time in the equivalent cyclic polling systems. Also in this paper, we analyze the cycle time and the number of customers found in the system.

Suggested Citation

  • Leonard Kleinrock & Hanoch Levy, 1988. "The Analysis of Random Polling Systems," Operations Research, INFORMS, vol. 36(5), pages 716-732, October.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:5:p:716-732
    DOI: 10.1287/opre.36.5.716
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    Citations

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    Cited by:

    1. Chydzinski, Andrzej, 2016. "Analysis of the scheduling mechanism for virtualization of links with partial isolation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 39-54.
    2. Germs, Remco & Van Foreest, Nicky D., 2011. "Admission policies for the customized stochastic lot scheduling problem with strict due-dates," European Journal of Operational Research, Elsevier, vol. 213(2), pages 375-383, September.
    3. Mahender P. Singh & Mandyam M. Srinivasan, 2007. "Performance Bounds for Flexible Systems Requiring Setups," Management Science, INFORMS, vol. 53(6), pages 991-1004, June.
    4. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. 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.
    6. Jelmer P. Gaast & Ivo J. B. F. Adan & René B. M. Koster, 2017. "The analysis of batch sojourn-times in polling systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 313-335, April.
    7. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case," Economics Working Papers 302, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998.
    8. Christos Langaris, 1999. "Markovian polling systems with mixed service disciplines and retrial customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 305-322, December.
    9. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    10. 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.

    More about this item

    Keywords

    queues: random polling;

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