Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T06:41:57.040Z Has data issue: false hasContentIssue false
  • English
  • Français

The sojourn-time distribution in the M/G/1 queue by processor sharing

Published online by Cambridge University Press:  14 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
Bell Communications Research, Inc.
*
∗ Postal address: Room HO, 4L435, Bell Communications Research, Inc., Holmdel, NJ 07733, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers in the general M/G/1 queue with processor sharing (M/G/1/PS).

Explicit formulas are given for a number of conditional and unconditional moments, including the variance of the sojourn time of an ‘arbitrary' customer.

Keywords

WAITING TIMEINFINITE DIVISIBILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 360 - 378
Copyright
Copyright © Applied Probability Trust 1984 

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

Asare, B. K. and Foster, F. G. (1983) Conditional response times in the M/G/1 processor-sharing system. J. Appl. Prob. 20, 910–915.CrossRefGoogle Scholar
Aven, O., Coffman, E. G. Jr, Kogan, Y. A. and Yashkov, S. F. (to appear) Resource Allocation in Computer Systems. Eugene Gross, London.Google Scholar
Coffman, E. G. Jr, Muntz, R. R. and Trotter, H. (1970) Waiting time distributions for processor-sharing systems. J. Assoc. Comput. Mach. 17, 123–130.CrossRefGoogle Scholar
Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
Gross, D. and Harris, C. M. (1974) Fundamentals of Queueing Theory. Wiley, New York.Google Scholar
Jagerman, D. L. (1978) An inversion technique for the Laplace transform with application to approximation. Bell System Tech. J. 57, 669–710.CrossRefGoogle Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Kleinrock, L. (1976) Queueing Systems, II. Computer Applications. Wiley, New York.Google Scholar
Lukacs, E. (1970) Characteristic Functions, 2nd edn. Hafner, New York.Google Scholar
Mitra, D. and Morrison, J. A. (1983) Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes. Adv. Appl. Prob. 15, 813–839.CrossRefGoogle Scholar
Ramaswami, V. (1984) The sojourn time in the GI/M/1 queue with processor sharing. J. Appl. Prob. 21, 445–450.CrossRefGoogle Scholar
Schassberger, R. (1984) A new approach to the M/G/1 processor-sharing queue. Adv. Appl. Prob. 16, 202–213.CrossRefGoogle Scholar
Yashkov, S. F. (1983) A derivation of response time distribution for a M/G/1 processor-sharing queue. Problems of Control and Information Theory 12, 133–148.Google Scholar