On the busy periods for the M/G/1 queue with finite and with infinite waiting room

Jacob Willem Cohen

16 citations0/0 files storedJournal of Applied Probability

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

Abstract

Summary The Laplace-Stieltjes transform of the distribution of the busy period for the M/G/1 system with infinite waiting room can be obtained by using an argument from branching theory. In the present paper it is shown that by applying this argument it is rather easy to derive the expression for the joint distribution of the busy period and the maximum number of customers present simultaneously during this busy period for the M/G/1 system with infinite waiting room as well as the expression for the distribution of the busy period for the M/G/1 system with finite waiting room.

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1983The Single Server Queue.

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1976On the relationship between the distribution of maximal queue length in the M/G/1 queue and the mean busy period in the M/G/1/n queue 1976On the relationship between the distribution of maximal queue length in the M/G/ 1 queue and the mean busy period in the M/G /1/ n queue 1973On the length and number of served customers of the busy period of a generalised M / G /1 queue with finite waiting room

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