The M/G/1 queue with finite workload capacity

D. Perry, W. Stadje, S. Zacks

Research output: Contribution to journalArticlepeer-review


We consider the M/G/1 queueing system in which customers whose admission to the system would increase the workload beyond a prespecified finite capacity limit are not accepted. Various results on the distribution of the workload are derived; in particular, we give explicit formulas for its stationary distribution for M/M/1 and in the general case, under the preemptive LIFO discipline, for the joint stationary distribution of the number of customers in the system and their residual service times. Furthermore, the Laplace transform of the length of a busy period is determined. Finally, for M/D/1 the busy period distribution is derived in closed form.

Original languageEnglish
Pages (from-to)7-22
Number of pages16
JournalQueueing Systems
Issue number1
StatePublished - Sep 2001

Bibliographical note

Funding Information:
W. Stadje was supported by the Volkswagen Foundation.


  • Busy period
  • Finite capacity
  • M/D/1
  • M/G/1 queue
  • Restricted access
  • Stationary distribution
  • Workload

ASJC Scopus subject areas

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


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