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Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms

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  • Tetsuji Hirayama

Abstract

We consider multiclass Markovian polling systems with feedback and analyze their average performance measures. Scheduling in polling systems has many applications in computer and communication systems. We utilize the framework that has been effectively used to analyze various composite scheduling algorithms in many types of multiclass queues systematically in conjunction with the functional computation method (Hirayama in Naval Research Logistics 50:719–741, 2003 ; Journal of the Operations Research Society of Japan 48:226–255, 2005 ; Advances in queueing theory and network applications, pp. 119–146, Springer, New York, 2009a ; Journal of Industrial and Management Optimization 6:541–568, 2010 ). We define the conditional expected values of the performance measures such as the sojourn times as functions of the system state and find their expressions by solving some equations. Then from these expressions, we derive the average numbers of customers and the average sojourn times for all service stages of customers circulating the system. We consider their application to a packet scheduling problem where multiple categories of packets share a resource. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:83-123:10.1007/s10479-011-0910-7
    DOI: 10.1007/s10479-011-0910-7
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    References listed on IDEAS

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    1. Tetsuji Hirayama, 2003. "Mean sojourn times in multiclass feedback queues with gated disciplines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 719-741, October.
    2. Leonard Kleinrock & Hanoch Levy, 1988. "The Analysis of Random Polling Systems," Operations Research, INFORMS, vol. 36(5), pages 716-732, October.
    3. D. Sarkar & W. I. Zangwill, 1989. "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems---Exact Results and Applications," Management Science, INFORMS, vol. 35(12), pages 1463-1474, December.
    4. Mandyam M. Srinivasan, 1991. "Nondeterministic Polling Systems," Management Science, INFORMS, vol. 37(6), pages 667-681, June.
    5. R.D. van der Mei, 2002. "Waiting-Time Distributions in Polling Systems with Simultaneous Batch Arrivals," Annals of Operations Research, Springer, vol. 113(1), pages 155-173, July.
    6. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
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    Cited by:

    1. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    2. Jerim Kim & Bara Kim & Hsing Luh, 2019. "Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue," Annals of Operations Research, Springer, vol. 277(2), pages 137-159, June.

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