Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T07:10:54.198Z Has data issue: false hasContentIssue false
  • English
  • Français

A model for queues in series

Published online by Cambridge University Press:  14 July 2016

O. P. Sharma
O. P. Sharma*
Affiliation:
Indian Institute of Technology, Delhi
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies the stationary behaviour of a finite space queueing model consisting of r queues in series with multi-server service facilities at each queue. Poisson input and exponential service times have been assumed. The model is suitable for phase-type service as well as service with waiting allowed before the different phases. In the case of single-server queues explicit expressions for certain probability distributions, parameters and a steady-state solution for infinite queueing space have been obtained.

Keywords

MULTI-SERVER SERVICE FACILITIESFINITE AND INFINITE QUEUEING SPACESSTEADY-STATE SOLUTIONSINGLE-SERVER QUEUESOCCUPATION TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 691 - 696
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research done while the author was visiting the University of Sheffield supported by a Technical Assistance Award from the Ministry of Overseas Development.

References

[1] Jackson, R. R. P. (1954) Queueing systems with phase type service. Operat. Res. Quart. 5, 109–120.10.1057/jors.1954.23Google Scholar
[2] Saaty, T. L. (1961) Elements of Queueing Theory. McGraw-Hill, New York.Google Scholar
[3] Prabhu, N. U. (1965) Queues and Inventories. John Wiley, New York.Google Scholar
[4] Arya, Krishan Lal (1972) Study of a network of serial and non-serial servers with phase type service and finite queueing space. J. Appl. Prob. 9, 198–201.10.2307/3212649Google Scholar