The idle period of the finite G/M/1 queue with an interpretation in risk theory

Authors:
Andreas Löpker;David Perry
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB;Department of Statistics, University of Haifa, Haifa, Israel 31905
Venue:
Queueing Systems: Theory and Applications
Year:
2010

Citing 4
Cited 0

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Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

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Abstract

We consider a G/M/1 queue with restricted accessibility in the sense that the maximal workload is bounded by 1. If the current workload V t of the queue plus the service time of an arriving customer exceeds 1, only 1驴V t of the service requirement is accepted. We are interested in the distribution of the idle period, which can be interpreted as the deficit at ruin for a risk reserve process R t in the compound Poisson risk model. For this risk process a special dividend strategy applies, where the insurance company pays out all the income whenever R t reaches level 1. In the queueing context we further introduce a set-up time a驴[0,1]. At the end of every idle period, an arriving customer has to wait for a time units until the server is ready to serve it.