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−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.
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Löpker, A., Perry, D. The idle period of the finite G/M/1 queue with an interpretation in risk theory. Queueing Syst 64, 395–407 (2010). https://doi.org/10.1007/s11134-010-9168-z
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DOI: https://doi.org/10.1007/s11134-010-9168-z
Keywords
- Finite G/M/1
- Finite M/G/1
- Workload
- Idle period
- Sample path analysis
- Level crossing
- Risk process
- Deficit at ruin