Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

D. Perry, W. Stadje, S. Zacks

Research output: Contribution to journalArticlepeer-review


We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))t≥0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let τn be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[Sn, v*-V(τn-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τn-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.

Original languageEnglish
Pages (from-to)163-174
Number of pages12
JournalOperations Research Letters
Issue number4
StatePublished - Nov 2000

Bibliographical note

Funding Information:
This research was carried out while the first author (D. Perry) was a visiting professor at the University of Osnabrück. The support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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