On the transient behaviour of the GI/G/1 waiting-times

Nils Blomqvist

12 citations0/0 files storedScandinavian Actuarial Journal

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

Abstract

Consider a single-server queuing system, where the arrival intervals Ti and the service-times Ui of consecutive customers form two independent sequences of independent and equally distributed random variables. Assume that customers arriving when the server is busy line up and that they are then served in order of arrival. Let Wn be the waiting-time of the nth customer and suppose that the server is idle at the start, i.e. W1 = 0. Put W = lim n ∞ Wn when the limit exists. Furthermore, let Fn (⋅) be the c.d.f. of Wn and put EWn =ω n .

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References

1953Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain 1962Some Inequalities for the Queue GI/G/1 1953On the distribution of queueing times 1968The serial correlation coefficients of waiting times in a stationary single server queue 1967The covariance function of the M/G/1 queuing system 1969Estimation of waiting-time parameters in the GI/G/1 queuing system 1968Monte Carlo Estimation of the Mean Queue Size in a Stationary GI/M/1 Queue

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