Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T06:15:28.905Z Has data issue: false hasContentIssue false
  • English
  • Français

GI/G/1 processor sharing queue in heavy traffic

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Sergei Grishechkin
Sergei Grishechkin*
Affiliation:
Moscow State University
*
* Postal address: Warshavskoje shosse, d.88 kv. 43, Moscow 113556, Russia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider GI/G/1 processor sharing queues with traffic intensity tending to 1. Using the theory of random measures and the theory of branching processes we investigate the limiting behaviour of the queue length, sojourn time and random measures describing attained and residual processing times of customers present.

Keywords

RANDOM MEASURESBRANCHING PROCESSES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 539 - 555
Copyright
Copyright © Applied Probability Trust 1994 

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 supported by ISF.

References

Asmussen, S. (1987) Applied Probability and Queues. Wiley, Chichester.Google Scholar
Baccelli, F. and Towsley, D. (1990) The customer response times in the processor sharing queue are associated. QUESTA 7, 269–282.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Grishechkin, S. A. (1991) Crump-Mode-Jagers branching processes as a method of investigating M/G/1 systems with processor sharing. Theory Prob. Appl. 36, 19–35.Google Scholar
Grishechkin, S. A. (1992) On a relationship between processor-sharing queues and Crump-Mode-Jagers branching processes. Adv. Appl. Prob. 24, 653–698.Google Scholar
Jagerman, D. and Sengupta, B. (1991) The GI/M/1 processor-sharing queue and its heavy traffic analysis. Stoch. Models 7, 379–395.Google Scholar
Jagers, P. and Nerman, O. (1984) The growth and composition of branching populations. Adv. Appl. Prob. 16, 221–259.Google Scholar
Kallenberg, O. (1983) Random Measures. Academie-Verlag, Berlin.CrossRefGoogle Scholar
Prokhorov, Yu. V. (1956) Convergence of random processes and limit theorems in probability theory. Theory Prob. Appl. 1, 157–214.CrossRefGoogle Scholar
Sengupta, B. (1992) An approximation for the sojourn-time distribution for the GI/G/1 processor-sharing queue. Stoch. Models 8, 35–57.Google Scholar
Skorokhod, A. V. (1956) Limit theorems for stochastic processes. Theory Prob. Appl. 1, 261–290.Google Scholar
Yashkov, S. F. (1987) Processor-sharing queues: some progress in analysis. QUESTA 2, 1–17.Google Scholar