Some Relationships Between the Distributions of Waiting Time, Idle Time and Interoutput Time in the $GI/ G/1$ Queue

K. T. Marshall

22 citations0/0 files storedSIAM Journal on Applied Mathematics

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

Abstract

Some known results on the waiting time distribution in the $GI/G/1$ queue are summarized, and a generalization of the Pollaczek-Khintchine formula is derived from these. The author gives a.direct derivation of this result and demonstrates the role played by the idle time distribution in finding the distribution of wait. The results lead to two representations of the Laplace transform of the output distribution.

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1952The theory of queues with a single server 1967An introduction to probability theory and its applications, Vol. II 1953On the distribution of queueing times 1966Queues and Inventories, a Study of Their Basic Stochastic Processes

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1983Technical Note—Simulating the GI/G/1 Queue in Heavy Traffic 1987A generalized pollaczek-khinchine formula for the gi/gi/1/k queue and its application to approximation 2003Efficient simulation of queues in heavy traffic 1983Analysis of the GI/G/1 queue by the supplementary variables approach

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