The M/G/1 queue with finite workload capacity

D. Perry; W. Stadje; S. Zacks

doi:10.1023/A:1017931515538

The M/G/1 queue with finite workload capacity

D. Perry, W. Stadje, S. Zacks

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	7-22
Number of pages	16
Journal	Queueing Systems
Volume	39
Issue number	1
DOIs	https://doi.org/10.1023/A:1017931515538
State	Published - Sep 2001

Bibliographical note

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

Keywords

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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10.1023/A:1017931515538

Cite this

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The M/G/1 queue with finite workload capacity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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