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Finite capacity vacation models with non-renewal input

Published online by Cambridge University Press:  14 July 2016

C. Blondia
C. Blondia*
Affiliation:
Philips Research Laboratory
*
∗Postal address: Philips Research Laboratory, Av. Albert Einstein 4, B-1348 Louvain-la-Neuve, Belgium.
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Abstract

This paper studies a single server queue with finite waiting room where the server takes vacations according to two different strategies: (i) an exhaustive service discipline, where the server takes a vacation whenever the system becomes empty and these vacations are repeated as long as there are no customers in the system upon return from a vacation, i.e. a repeated vacation strategy; (ii) a limited service discipline, where the server begins a vacation either if K customers have been served in the same busy period or if the system is empty and then a repeated vacation strategy is followed. The input process is a general Markovian arrival process introduced by Lucantoni, Meier-Hellstern and Neuts, which as special cases includes the Markov modulated Poisson process and the phase-type renewal process. The service times and vacation times each are generally distributed random variables. For both models, we obtain the queue length distribution at departures, at an arbitrary time instant and at arrival time. We also derive the loss probability of an arriving customer. We obtain formulae for the LST of the virtual waiting time distribution and for the LST of the waiting time distribution at arrival epochs.

Keywords

SINGLE SERVER QUEUEFINITE CAPACITY QUEUESERVER VACATIONLIMITED SERVICE DISCIPLINEEXHAUSTIVE SERVICE DISCIPLINEGENERAL MARKOVIAN ARRIVAL PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 174 - 197
Copyright
Copyright © Applied Probability Trust 1991 

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