TY - JOUR

T1 - The idle period of the finite G/M/1 queue with an interpretation in risk theory

AU - Lopker, A.H.

AU - Perry, D.

PY - 2010

Y1 - 2010

N2 - 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-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¿[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.

AB - 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-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¿[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.

U2 - 10.1007/s11134-010-9168-z

DO - 10.1007/s11134-010-9168-z

M3 - Article

VL - 64

SP - 395

EP - 407

JO - Queueing Systems: Theory and Applications

JF - Queueing Systems: Theory and Applications

SN - 0257-0130

IS - 4

ER -