Idle periods for the finite G/M/1 queue and the deficit at ruin for a cash risk model with constant dividend barrier

A.H. Lopker, D. Perry

Onderzoeksoutput: Boek/rapportRapportAcademic

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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 Vt of the queue plus the service time of an arriving customer exceeds 1, only 1-Vt of the service requirement is accepted. We are interested in the distribution of the idle period, which can be interpreted as the deficit ruin for a risk reserve process Rt 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 Rt reaches level 1. In the queueing context we further introduce a set-up time a 2e [0, 1]. After every idle period, when the queue is empty, an arriving customer has to wait for a time units until the server is ready to serve the customer.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's12
StatusGepubliceerd - 2008

Publicatie series

NaamReport Eurandom
Volume2008046
ISSN van geprinte versie1389-2355

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