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The Busy Period of a Queue with Batch Service

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  • M. F. Neuts

    (Purdue University, Lafayette, Indiana)

Abstract

In this paper, we study the distribution of the busy period for a queue with Poisson input, in which the customers are served m at the time if there are m or more present and all at once if there are less than m present. We show that the busy period is equal to the time between successive visits to the state 0 in an imbedded semi-Markov process, associated with the queuing process. Extending an argument of L. Takács for the M / G /1 queue, we obtain the transform of the distribution of the busy period. Explicit expressions in real time may in principle be obtained, using Lagrange's expansion.

Suggested Citation

  • M. F. Neuts, 1965. "The Busy Period of a Queue with Batch Service," Operations Research, INFORMS, vol. 13(5), pages 815-819, October.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:5:p:815-819
    DOI: 10.1287/opre.13.5.815
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    Cited by:

    1. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    2. Iwan Budihardjo & H. T. David, 1999. "Expected waiting time rankings in extended machine‐repair models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 864-870, October.
    3. Erhan Cinlar, 1973. "Markov Renewal Theory: A Survey," Discussion Papers 53, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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