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 -