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

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 at 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∈[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.

• Publication year

  2010

• Venue

  Queueing Syst. Theory Appl.

• Publication date

  2010-04-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s11134-010-9168-z
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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