Stream of Overflows from a Finite Queue

Erhan Çinlar and Ralph L. Disney
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Erhan Çinlar: Northwestern University, Evanston, Illinois
Ralph L. Disney: University of Michigan, Ann Arbor, Michigan

Operations Research, 1967, vol. 15, issue 1, 131-134

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.

Date: 1967
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