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The Relationship Between Bernoulli and Fixed Feedback Policies for the M/G/1 Queue

Author

Listed:
  • Vikram S. Adve

    (University of Wisconsin, Madison, Wisconsin)

  • Randolph Nelson

    (IBM T. J. Watson Research Center, Yorktown Heights, New York)

Abstract

We consider an M / G /1 queue with feedback, in which customers, after receiving service, either return to the tail of the queue or depart the system, according to some feedback policy. We derive simple expressions for the expected response time for feedback policies that include Bernoulli feedback and feeding back a fixed number of times. Our results reveal some interesting and nonintuitive properties of the behavior of such feedback policies when the coefficient of variation of service time is varied. One result shows that for the Bernoulli feedback and fixed feedback policies with an equal mean number of visits to the queue, the expected response time for the Bernoulli policy is smaller than for the fixed policy if the coefficient of variation of service time is greater than 1. The relationship reverses if the coefficient of variation is less than 1.

Suggested Citation

  • Vikram S. Adve & Randolph Nelson, 1994. "The Relationship Between Bernoulli and Fixed Feedback Policies for the M/G/1 Queue," Operations Research, INFORMS, vol. 42(2), pages 380-385, April.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:2:p:380-385
    DOI: 10.1287/opre.42.2.380
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    Cited by:

    1. 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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    Keywords

    queues: feedback;

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