Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T19:36:59.243Z Has data issue: false hasContentIssue false
  • English
  • Français

Decomposition property in a discrete-time queue with multiple input streams and service interruptions

Part of: Special processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Fumio Ishizaki
Fumio Ishizaki*
Affiliation:
Nanzan University
*
∗ Postal address: Department of Information and Telecommunication Engineering, Nanzan University, 27 Seirei, Aichi 489-0863, Japan. Email address: fumio@ieee.org
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

Keywords

Queueing theorymultiple input streamsstochastic decomposition

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 524 - 534
Copyright
Copyright © Applied Probability Trust 2004 

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.)

References

Cassandras, C. G., and Lafortune, S. (1999). Introduction to Discrete Event Systems. Kluwer, Boston, MA.Google Scholar
Chaudhry, M. L. (2000). On numerical computations of some discrete-time queues. In Computational Probability, ed. Grassmann, W. K., Kluwer, Dordrecht, pp. 365–408.CrossRefGoogle Scholar
Glasserman, P., and Gong, W.-B. (1991). Time-changing and truncating k-capacity queues from one k to another. J. Appl. Prob. 28, 647–655.CrossRefGoogle Scholar
Ishizaki, F., Takine, T., Takahashi, Y., and Hasegawa, T. (1994). A generalized SBBP/G/1 queue and its applications. Performance Evaluation 21, 163–181.Google Scholar
Ott, T. J. (1984). On the M/G/1 queue with additional inputs. J. Appl. Prob. 21, 129–142.CrossRefGoogle Scholar
Ott, T. J. (1987). The single-server queue with independent GI/G and M/G input streams. Adv. Appl. Prob. 19, 266–286.Google Scholar
Takagi, H. (1993). Queueing Analysis: A Foundation of Performance Evaluation, Vol. 3, Discrete-Time Systems. North-Holland, Amsterdam.Google Scholar
Takine, T., and Hasegawa, T. (1995). On the single-server queue with independent MAP/G and M/GI inputs streams. Commun. Statist. Stoch. Models 11, 227–234.Google Scholar