The Probability Law of the Busy Period for Two Types of Queuing Processes

Lajos Takács

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

Abstract

A simple combinatorial method is given for the determination of the joint distribution of the length of the busy period and the number of customers served during this period for two types of single-Berver queuing processes. (1) Customers arrive at a counter according to a Poisson process and the service times have a general distribution, (2) customers arrive at a counter according to a recurrent process and the service times have an exponential distribution.

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1960Some Results for the Queue with Poisson Arrivals

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1963The stochastic law of the busy period for a single server queue with Poisson input 1995Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion 1975Combinatorial and analytic methods in the theory of queues 1962A Combinatorial Method in the Theory of Queues 1975Combinatorial and analytic methods in the theory of queues

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