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A Gambler's Ruin Type Problem in Queuing Theory

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  • Julian Keilson

    (Applied Research Laboratory, Sylvania Electronic Systems, Waltham, Massachusetts)

Abstract

The Takács process, X ( t ) describing the virtual waiting time or server backlog for a single-server queue with Poisson arrivals and general service time distribution, is discussed with two absorbing boundaries. The process terminates at x = 0 when the server becomes idle or at x = T when a given backlog level is exceeded. The probabilities (Gamma) T ( x 0 ) that absorption will occur at x = 0 if the process starts at x 0 , and (Gamma) T ( x 0 , t ) that absorption will occur at zero before time t , are exhibited. The process is also of interest to the theory of collective risk.

Suggested Citation

  • Julian Keilson, 1963. "A Gambler's Ruin Type Problem in Queuing Theory," Operations Research, INFORMS, vol. 11(4), pages 570-576, August.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:4:p:570-576
    DOI: 10.1287/opre.11.4.570
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