Management Science Vol. 21 No. 5 1975
The Steady-State Queueing Time Distribution for the M/G/1 Finite Capacity Queue
Abstract
We derive an expression for the Laplace-Stieltjes transform of the steady-state distribution of the queueing time for the M/G/1 finite capacity queue. The derivation proceeds in terms of a related 2-stage closed cyclic queueing network. The resulting expression is a rational function of the steady-state probabilities of the imbedded Markov chain at departure epochs and of the Laplace-Stieltjes transform of the service time distribution. The expression can be differentiated readily in order to obtain moments of the steady-state queueing time and some numerical results for the mean and coefficient of variation are presented.
- DOI
- 10.1287/mnsc.21.5.501
- Volume
- 21
- Issue
- 5
- Pages
- 501-506
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref