Some Further Results in the Non-Equilibrium Theory of a Simple Queue

Norman T. J. Bailey

21 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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

Abstract

Summary A number of new results are obtained in the non-equilibrium theory of a simple single-server queue with random arrival and departure, involving both the frequency distribution and distribution function of queue length, the derivation of exact and asymptotic expressions for means and variances, and the distribution of the time taken to reach a pre-assigned state.

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References

1954A Continuous Time Treatment of a Simple Queue using Generating Functions 1956An Elementary Method of Solution of the Queueing Problem with a Single Server and Constant Parameters 1956A Waiting Line Process of Markov Type

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1988Simple spectral representations for the M/M/1 queue 1992Transient analysis of multi-server queues with Markov-modulated Poisson arrivals and overload control 2018Robust transient analysis of multi-server queueing systems and feed-forward networks

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