An exhaustive Lévy storage process with intermittent output

Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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 languageAmerican English
Pages (from-to)979-992
Number of pages14
JournalCommunications in Statistics. Part C: Stochastic Models
Issue number4
StatePublished - 1998

Bibliographical note

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


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


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