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Limit theorems for generalized single server queues

Published online by Cambridge University Press:  01 July 2016

Austin J. Lemoine
Austin J. Lemoine*
Affiliation:
University of Texas at Austin
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Abstract

For the generalized single server queueing system described herein weak convergence results are obtained for the processes {Wa, n ≧ 0}, {W(t), t ≧ 0}, and {Q (t), t ≧ 0}, where Wn is the waiting time of customer n, W(t) is the workload of the server at time t, and Q(t) is the number of customers present in the system at time t. We also provide a functional strong law, a functional central limit theorem, and a functional law of the iterated logarithm for various cumulative processes in the system.

Keywords

GENERALIZED SINGLE SERVER QUEUESWAITING TIMEWORKLOADQUEUE-LENGTHWEAK CONVERGENCEDELAYED RANDOM WALKSOPTIONAL RANDOM VARIABLESCUMULATIVE PROCESSESFUNCTIONAL LIMIT THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 159 - 174
Copyright
Copyright © Applied Probability Trust 1974 

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