Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-13T19:01:59.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of an M/G/1 queue with two types of impatient units

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

M. Martin  and
J. R. Artalejo
M. Martin*
Affiliation:
Universidad Complutense de Madrid
J. R. Artalejo*
Affiliation:
Universidad Complutense de Madrid
*
* Postal address: Department of Statistics and O.R., Faculty of Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain.
* Postal address: Department of Statistics and O.R., Faculty of Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later.

We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.

Keywords

QUEUES WITH IMPATIENT UNITS AND REPEATED ATTEMPTSTAKÁCS'EQUATIONMATRICES OF M/G/L TYPEMARKOV RENEWAL PROCESSES

MSC classification

Primary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 840 - 861
Copyright
Copyright © Applied Probability Trust 1995 

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

The second author was supported by the Universidad Complutense of Madrid, grant PR161/93-4777.

References

[1] Artalejo, J. R. and Martin, M. (1994) A maximum entropy analysis of the M/G/1 queue with constant repeated attempts. In Selected Topics on Stochastic Modelling. World Scientific, Singapore.Google Scholar
[2] ÇInlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[3] Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[4] Falin, G., Artalejo, J. R. and Martin, M. (1993) On the single server retrial queue with priority customers. Queueing Systems 14, 439–455.CrossRefGoogle Scholar
[5] Farahmand, K. (1990) Single line queue with repeated demands. Queueing Systems 6, 223–228.CrossRefGoogle Scholar
[6] Fayolle, G. (1986) A simple telephone exchange with delayed feedbacks. In Teletraffic Analysis and Computer Performance Evaluation, ed. Boxma, O. J., Cohen, J. W. and Tijms, H. C.. Elsevier Science. Amsterdam.Google Scholar
[7] Hammond, J. L. and O'Reilly, P. J. P. (1986) Performance Analysis of Local Computer Networks. Addison-Wesley, Reading, MA.Google Scholar
[8] Neuts, M. F. and Ramalhoto, M. F. (1984) A service model in which the server is required to search for customers. J. Appl. Prob. 21, 157–166.Google Scholar
[9] Neuts, M. F. (1989) Structured Stochastic Matrices of M/G/1 Type and their Applications. Marcel Dekker, New York.Google Scholar