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The continuity of the single server queue

Published online by Cambridge University Press:  14 July 2016

Douglas P. Kennedy
Douglas P. Kennedy*
Affiliation:
University of Sheffield
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Abstract

In many applications of queueing theory assumptions of either Poisson arrivals or exponential service times are made. The implicit assumption is that if the actual arrival process approximates a Poisson process and the service times are close to exponential, then the quantities of interest in the real queueing system (viz. the virtual waiting time, queue length, idle times, etc.), will approximate those of the idealized model. The continuity of the single server queue acting as functionals of the arrival and service processes is established. The proof involves an application of the theory of weak convergence of probability measures on metric spaces.

Keywords

WEAK CONVERGENCEQUEUESFUNCTIONAL LIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 370 - 381
Copyright
Copyright © Applied Probability Trust 1972 

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References

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