## 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.

Original language | English |
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Pages (from-to) | 395-407 |

Number of pages | 13 |

Journal | Queueing Systems |

Volume | 64 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2010 |

## Keywords

- Deficit at ruin
- Finite G/M/1
- Finite M/G/1
- Idle period
- Level crossing
- Risk process
- Sample path analysis
- Workload

## ASJC Scopus subject areas

- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics