Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T20:25:35.706Z Has data issue: false hasContentIssue false
  • English
  • Français

A perturbation method for solving some queues with processor sharing discipline

Published online by Cambridge University Press:  14 July 2016

Bhaskar Sengupta
Bhaskar Sengupta*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: HO 3L-309, AT&T Bell Laboratories, Holmdel, NJ 07733, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we present a perturbation method of solving a second-order difference equation with variable coefficients with some additional assumptions. This method can be used to devise an algorithmic solution for the moments of sojourn times in some processor sharing queues. In particular, we examine three queues. The first has exponential service and a fairly general interrupted arrival mechanism. The second is a cyclic queue. The third is a model for a computer system in which finite and infinite sources interact.

Keywords

SOJOURN TIMESCOMMUNICATIONS SYSTEMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 209 - 214
Copyright
Copyright © Applied Probability Trust 1989 

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

Bellman, R. (1960) Introduction to Matrix Analysis. McGraw-Hill, New York.Google Scholar
Bellman, R. (1964) Perturbation Techniques in Mathematics, Physics and Engineering. Holt, Reinhart and Winston, New York.Google Scholar
Boxma, O. J. (1983) The cyclic queue with one general and one exponential server. Adv. Appl. Prob. 15, 857–873.Google Scholar
Coffman, E. G., Muntz, R. R. and Trotter, H. (1970) Waiting time distributions for processor sharing systems. JACM 17, 123–130.Google Scholar
Daduna, H. (1986) Cycle time in two-stage closed queueing networks: applications to multiprogrammed computer systems with virtual memory. Operat. Res. 34, 281–288.Google Scholar
Kleinrock, L. (1976) Queueing Systems , Vols I and II. Wiley, New York.Google Scholar
Neuts, M. F. (1981) Matrix Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore.Google Scholar
Ott, T. J. (1984) The sojourn time in an M/G/1 queue with processor sharing. J. Appl. Prob. 21, 360–378.Google Scholar
Rege, K. M. and Sengupta, B. (1988) Response time distribution in a multiprogrammed computer with terminal traffic. Performance Evaluation 8, 41–50.Google Scholar
Schassberger, R. (1984) A new approach to the M/G/1 processor-sharing queue. Adv. Appl. Prob. 16, 202–213.Google Scholar
Sengupta, B. and Jagerman, D. L. (1985) A conditional response time of the M/M/1 processor sharing queue. AT&T Tech. J. 64, 409–421.Google Scholar
Yashkov, S. F. (1983) A derivation of response time distribution for an M/G/1 processor sharing queue. Problems of Control and Information Theory 12, 133–148.Google Scholar