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Some New Results for the M/M/1 Queue

Author

Listed:
  • Claude Dennis Pegden

    (The Pennsylvania State University)

  • Matthew Rosenshine

    (The Pennsylvania State University)

Abstract

New results are obtained for the single server queue with Poisson arrivals and exponential service times. A closed form solution involving only finite sums is obtained for the probability that exactly i arrivals and j services occur over a time interval of length t in a queueing system that is idle at the beginning of the interval. Since many applications of queueing theory involve queues which are emptied and restarted periodically and thus not susceptible to analysis using the well-known equilibrium results, there are many potential applications for results obtained. Some ways in which the results obtained may be applied are discussed.

Suggested Citation

  • Claude Dennis Pegden & Matthew Rosenshine, 1982. "Some New Results for the M/M/1 Queue," Management Science, INFORMS, vol. 28(7), pages 821-828, July.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:7:p:821-828
    DOI: 10.1287/mnsc.28.7.821
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    Cited by:

    1. Don Towsley, 1987. "An application of the reflection principle to the transient analysis of the M/M/1 queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 451-456, June.
    2. Britt Mathijsen & Bert Zwart, 2017. "Transient error approximation in a Lévy queue," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 269-304, April.

    More about this item

    Keywords

    queues; transient behavior;

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