## Abstract

We consider a Lévy storage model in which the output is shut off every time the system reaches zero, for a length of time which is determined by an arbitrary stopping time with respect to a filtration which may be richer than the one generated by the Lévy process. The main contribution is in showing that under suitable conditions, the steady state distribution associated with such a model exhibits a new decomposition property. Namely it can be written as an independent sum of two random variables. One has the distribution associated with a standard reflected Lévy process and the other has the steady state distribution of some clearing process (in contrast to excess lifetime or excess number of customers arriving during a vacation). A special case of such a model is the workload process in an M/G/1 queue, in particular with the well known T, N and D-policies.

Original language | American English |
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Pages (from-to) | 979-992 |

Number of pages | 14 |

Journal | Communications in Statistics. Part C: Stochastic Models |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - 1998 |

### Bibliographical note

Funding Information:Acknowledgement: This work is supported in part by grant 92-00035 from the United States Israel Binational Science Foundation.

## Keywords

- Clearing process
- Decomposition
- Intermittent service
- Lévy process
- Removable server
- Service interruptions
- Vacations