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The Remaining Busy Period for a Single Server Queue with Poisson Input

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  • Sven Erlander

    (Stockholm University, Stockholm 23, Sweden)

Abstract

Consider a single-server queuing process with Poisson input and general service time distribution. Define the remaining busy period χ( t ) as the time from a given instant t until the server becomes idle for the first time. Let ξ( t ) be the number of customers in the system at time t . Let χ 1 ( t ) be the remaining service time for the customer being served at time t . In this paper we shall study the stochastic law of the remaining service time χ 1 ( t ) given that ξ(0) = i and ξ( t ) = r . The result will then be applied to the problem of finding the joint distribution of the remaining busy period χ( t ) and the number of customers served during χ( t ) given that ξ(0) = i and ξ( t ) = r .

Suggested Citation

  • Sven Erlander, 1965. "The Remaining Busy Period for a Single Server Queue with Poisson Input," Operations Research, INFORMS, vol. 13(5), pages 734-746, October.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:5:p:734-746
    DOI: 10.1287/opre.13.5.734
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