Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-10T14:01:49.099Z Has data issue: false hasContentIssue false
  • English
  • Français

Response times in M/M/1 time-sharing schemes with limited number of service positions

Published online by Cambridge University Press:  14 July 2016

Benjamin Avi-Itzhak  and
Shlomo Halfin
Benjamin Avi-Itzhak*
Affiliation:
Bell Communications Research
Shlomo Halfin*
Affiliation:
Bell Communications Research
*
∗ Present address: RUTCOR, Rutgers University Center for Operations Research, New Brunswick, NJ 08903, USA.
∗∗ Postal address: Bell Communications Research, 435 South Street, Morristown, NJ 07960-1961, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Two service schemes for an M/M/1 time-sharing system with a limited number of service positions are studied. Both schemes possess the equilibrium properties of symmetric queues; however, in the first one, a preempted job is placed at the end of the waiting line; while in the second one, it is placed at the head of the line. Methods for calculating the Laplace transforms and moments of the response times are presented. The variances of the response times are then compared numerically to indicate that the first scheme is superior to the second scheme. It is also indicated that in both cases the response time variance decreases when the number of service positions increases.

Keywords

RESPONSE TIME VARIANCESPROCESSOR SHARINGQUEUE DISCIPLINESYMMETRIC QUEUES
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 579 - 595
Copyright
Copyright © Applied Probability Trust 1988 

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

[1] Avi-Itzhak, B. and Halfin, S. (1987) Server sharing with a limited number of service positions and symmetric queues. J. Appl. Prob. 24, 990–1000.Google Scholar
[2] Coffman, E. G., Muntz, R. R. and Trotter, H. (1970) Waiting time distributions for processor-sharing systems. J. Assoc. Comp. Mach. 17, 123–130.Google Scholar
[3] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[4] Kleinrock, L. (1975) Queuing Systems, Volume 1: Theory. Wiley, New York.Google Scholar
[5] Ott, T. J. (1984) The sojourn-time distribution in the M/G/1 queue with processor sharing. J. Appl. Prob. 21, 360–378.Google Scholar
[6] Yashkov, S. F. (1980) Properties of invariance of probabilistic models and adaptive scheduling in shared-use systems. Autom. Control Computer Sci. 12, 56–62.Google Scholar
[7] Yashkov, S. F. (1983) A derivation of response time distribution for M/G/1 processor-sharing queue. Prob. Control Inf. Theory 12, 122–148.Google Scholar