The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

Jacob Willem Cohen

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

Abstract

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

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1963Introduction to the Theory of Queues.1965On the maximum of the queue GI/M/1

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1971On the busy periods for the M/G/1 queue with finite and with infinite waiting room 1969The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System

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