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Queue-Length Distribution for the Discriminatory Processor-Sharing Queue

Author

Listed:
  • Kiran M. Rege

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

  • Bhaskar Sengupta

    (NEC USA, Princeton, New Jersey)

Abstract

In this paper, we study a multiple class discriminatory processor-sharing queue. The queue is assumed to have Poisson input and exponentially distributed service times. In this discipline there are K classes of customers. When there are n i customers present in the system of class i ( i = 1, …, K ), each member of class j receives a fraction of the server's capacity given by α j /∑ i =1 K n i α i . Thus, associated with class i customers is a weight α i which determines the level of service discrimination. For this problem, we find the moments of the queue-length distribution as a solution of linear simultaneous equations. We also prove a heavy traffic limit theorem for the joint queue-length distribution for this queue.

Suggested Citation

  • Kiran M. Rege & Bhaskar Sengupta, 1996. "Queue-Length Distribution for the Discriminatory Processor-Sharing Queue," Operations Research, INFORMS, vol. 44(4), pages 653-657, August.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:4:p:653-657
    DOI: 10.1287/opre.44.4.653
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    Citations

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    Cited by:

    1. Haviv, Moshe & van der Wal, Jan, 2008. "Mean sojourn times for phase-type discriminatory processor sharing systems," European Journal of Operational Research, Elsevier, vol. 189(2), pages 375-386, September.
    2. Florian Simatos & Alain Simonian, 2020. "Mobility can drastically improve the heavy traffic performance from $$\frac{1}{1-\varrho }$$11-ϱ to $$\log (1/(1-\varrho ))$$log(1/(1-ϱ))," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 1-28, June.
    3. 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.
    4. H. Thorsdottir & I. M. Verloop, 2016. "Markov-modulated M/G/1-type queue in heavy traffic and its application to time-sharing disciplines," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 29-55, June.
    5. I. M. Verloop & U. Ayesta & R. Núñez-Queija, 2011. "Heavy-Traffic Analysis of a Multiple-Phase Network with Discriminatory Processor Sharing," Operations Research, INFORMS, vol. 59(3), pages 648-660, June.

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