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The Queue M/G/1 With Feedback to Lower Priority Queues

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  • L. E. Schrage

    (Stanford University)

Abstract

The queue M/G/1 with a round-robin type queueing discipline is considered. The overall processing time of a job is assumed to consist of a sequence of "simple" processing times. There are a countably infinite number of waiting queues, 1,2,..., but a single processing facility. A job upon arrival enters the first, or highest priority waiting queue. When a job in the n th queue gains the processor, it receives its n th simple processing time in an uninterrupted fashion and then either departs or enters the n + 1 st queue. The processor upon completion of a simple processing time selects the job to be next processed from the highest priority (lowest index number) non-empty queue. Laplace transforms and expressions for the moments of the time in system distributions are obtained.

Suggested Citation

  • L. E. Schrage, 1967. "The Queue M/G/1 With Feedback to Lower Priority Queues," Management Science, INFORMS, vol. 13(7), pages 466-474, March.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:7:p:466-474
    DOI: 10.1287/mnsc.13.7.466
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    Cited by:

    1. B. Houdt & J. Velthoven & C. Blondia, 2008. "QBD Markov chains on binomial-like trees and its application to multilevel feedback queues," Annals of Operations Research, Springer, vol. 160(1), pages 3-18, April.

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