The covariance function of the M/G/1 queuing system

Nils Blomqvist

14 citations0/0 files storedScandinavian Actuarial Journal

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

Abstract

The M/G/1 queuing system is defined in the following way (cf. Kendall [1]): Customers arrive at a single counter according to a Poisson process with constant arrival intensity. Customers arriving when the counter is occupied line up before the counter and are then served in order of arrival. Individual service-times are independent of each other and of the arrival process. No restrictions are made regarding the form of the service-time distribution function.

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References

1953Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain 1963Introduction to the Theory of Queues.1963Introduction to the Theory of Queues 1963Stochastic Service Systems.1955Stochastic Properties of Waiting Lines 1957On Queues with Poisson Arrivals

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1969Estimation of waiting-time parameters in the GI/G/1 queuing system 1970On the transient behaviour of the GI/G/1 waiting-times 1983Optimal Prediction of Times and Queue Lengths in the GI/M/1 Queue 2007Time-Dependent Behaviour of an Alternating Service Queue

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