Technical Note—Approximations for Overflows from Queues with a Finite Waiting Room

John H. Rath · Diane Dwan Sheng

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

We report in this note a study of the use of the interrupted Poisson process (IPP) as an approximation to the overflow process from a M/M/C/K queue (a queue with a Poisson arrival process, C servers each with exponentially distributed service times, and a maximum of K customers in the system). The IPP has been used successfully by Kuczura to approximate the overflow from a M/M/C/C queue. Numerical comparisons are made for a number of examples and both the maximum absolute errors and percent errors are plotted.

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1973The Interrupted Poisson Process As An Overflow Process

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1982Approximating a Point Process by a Renewal Process, I: Two Basic Methods 1985A stochastic recirculation system with random access 1989Nonstationary queues with Interrrupted Poisson arrivals and unreliable/repairable servers 1984On a two-server finite queuing system with ordered entry and deterministic arrivals 1987Approximation of the Overflow Process from a G/M/N/K Queueing System

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