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On a new formula for the transient state probabilities for M/M/1 queues and computational implications

Part of: Approximations and expansions Special processes

Published online by Cambridge University Press:  14 July 2016

B. W. Conolly  and
Christos Langaris
B. W. Conolly*
Affiliation:
Queen Mary and Westfield College
Christos Langaris*
Affiliation:
University of Ioannina
*
∗ Postal address: Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK.
∗∗ Postal address: University of Ioannina, Department of Mathematics, 45110 Ioannina, Greece.
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Abstract

Past work relating to the computation of time-dependent state probabilities in M/M/1 queueing systems is reviewed, with emphasis on methods that avoid Bessel functions. A new series formula of Sharma [13] is discussed and its connection with traditional Bessel function series is established. An alternative new series is developed which isolates the steady-state component for all values of traffic intensity and which turns out to be computationally superior. A brief comparison of our formula, Sharma's formula, and a classical Bessel function formula is given for the computation time of the probability that an initially empty system is empty at time t later.

Keywords

EXPONENTIAL QUEUESCOMPUTATIONAL FEATURES AND PERFORMANCE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 237 - 246
Copyright
Copyright © Applied Probability Trust 1993 

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