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A note on sojourn times in M/G/1 queues with instantaneous, bernoulli feedback

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  • Ralph L. Disney

Abstract

Queueing systems which include the possibility for a customer to return to the same server for additional service are called queueing systems with feedback. Such systems occur in computer networks for example. In these systems a chosen customer will wait in the queue, be serviced and then, with probability p, return to wait again, be serviced again and continue this process until, with probability (1 – p) = q, it departs the system never to return. The time of waiting plus service time, the nth time the customer goes through, we will call his nth sojourn time. The (random) sum of these sojourn times we will call the total sojourn time (abbreviated, sojourn time when there is no confusion which sojourn time we are talking about). In this paper we study the total sojourn time in a queueing system with feedback. We give the details for M/G/1 queues in which the decision to feedback or not is a Bernoulli process. While the details of the computations can be more difficult, the structure of the sojourn time process is unchanged for the M/G/1 queue with a more general decision process as will be shown. We assume the reader is familiar with Disney, McNickle and Simon [1].

Suggested Citation

  • Ralph L. Disney, 1981. "A note on sojourn times in M/G/1 queues with instantaneous, bernoulli feedback," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 679-684, December.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:4:p:679-684
    DOI: 10.1002/nav.3800280415
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    Cited by:

    1. Mark Fackrell & Peter Taylor & Jiesen Wang, 2021. "Strategic customer behavior in an M/M/1 feedback queue," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 223-259, April.
    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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