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

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.