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Stream of Overflows from a Finite Queue

Author

Listed:
  • Erhan Çinlar

    (Northwestern University, Evanston, Illinois)

  • Ralph L. Disney

    (University of Michigan, Ann Arbor, Michigan)

Abstract

A finite queuing system with a recurrent arrival process and a single negative exponential server is considered. A customer who, upon his arrival, finds the system full departs never to return, i.e., he “overflows.” The process of overflows is shown to be a recurrent process and the distribution of the time between overflows is derived as a recurrence time distribution in a semi-Markov process. In the special case where the maximum number of customers allowed in the system is one, the problem is known as Palm's overflow problem.

Suggested Citation

  • Erhan Çinlar & Ralph L. Disney, 1967. "Stream of Overflows from a Finite Queue," Operations Research, INFORMS, vol. 15(1), pages 131-134, February.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:1:p:131-134
    DOI: 10.1287/opre.15.1.131
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