Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T19:34:47.530Z Has data issue: false hasContentIssue false
  • English
  • Français

A sample path analysis of the delay in the M/G/C system

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Sridhar Seshadri
Sridhar Seshadri*
Affiliation:
New York University
*
∗Postal address: Department of Statistics and Operations Research, Leonard A. Stern School of Business, New York University, NY 10012, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Using sample path analysis we show that under the same load the mean delay in queue in the M/G/2 system is smaller than that in the corresponding M/G/1 system, when the service time has either the DMRL or NBU property and the service discipline is FCFS. The proof technique uses a new device that equalizes the work in a two server system with that in a single sterver system. Other interesting quantities such as the average difference in work between the two servers in the GI/G/2 system and an exact alternate derivation of the mean delay in the M/M/2 system from sample path analysis are presented. For the same load, we also show that the mean delay in the M/G/C system with general service time distribution is smaller than that in the M/G/1 system when the traffic intensity is less than 1/c.

Keywords

SAMPLE PATH ANALYSISMULTI-SERVER QUEUEBOUNDS FOR MEAN DELAY

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 256 - 266
Copyright
Copyright © Applied Probability Trust 1996 

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

Cox, D. R. and Smith, W. L. (1961) Queues. Wiley, New York.Google Scholar
Daley, D. J. and Rolski, T. (1984) Some comparability results for waiting times in single- and many-server queues. J. Appl. Prob. 21, 887–900.Google Scholar
Mori, M. (1975) Some bounds for queues. J. Operat. Res. Soc. Japan 18, 151–181.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Suzuki, T. and Yoshida, Y. (1970) Inequalities for the many-server queue and other queues. J. Operat. Res. Soc. Japan 13, 59–77.Google Scholar
Wolff, R. W. (1989) Stochastic Modeling and the Theory of Queues. Prentice Hall, New York.Google Scholar