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Server sharing with a limited number of service positions and symmetric queues

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
*
∗Postal address for both authors: Bell Communications Research, 435 South Street, Morristown, NJ 07960, USA.
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Abstract

A class of M/G/1 time-sharing queues with a finite number of service positions and unlimited waiting space is described. The equilibrium distribution of symmetric queues belonging to this class is invariant under arbitrary service-independent reordering of the customers at instants of arrivals and departures. The delay time distribution, in the special case of one service position where preempted customers join the end of the line, is provided in terms of Laplace transforms and generating functions. It is shown that placing preempted customers at the end of the line rather than at the beginning of the line results in a reduction of the delay time variance. Comparisons with the delay time variance of the case of unlimited number of service positions (processor sharing system) are presented.

Keywords

INSENSITIVE QUEUESPROCESSOR SHARINGWAITING-TIME VARIANCESLIFO AND FIFO DISCIPLINES
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 990 - 1000
Copyright
Copyright © Applied Probability Trust 1987 

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References

Asare, B. K. Foster, F. G. (1983) Conditional response times in the M/G/1 processor sharing system. J. Appl. Prob. 20, 910–915.Google Scholar
Coffman, E. G. Muntz, R. R. Trotter, H. (1970) Waiting time distributions for processor-sharing systems. J. Assoc. Comput. Mach. 17, 123–130.CrossRefGoogle Scholar
Conway, R. W. Maxwell, W. L. Miller, L. W. (1967) Theory of Scheduling. Addison-Wesley, Reading, Mass.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Kleinrock, L. (1967) Time-shared systems: A theoretical treatment. J. Assoc. Comput. Mach. 14, 242–261.Google Scholar
Kleinrock, L. (1975) Queueing Systems. Volume 1: Theory. Wiley, New York.Google Scholar
Ott, T. J. (1984) The sojourn-time distribution in the M/G/1 queue with processor sharing. J. Appl. Prob. 21, 360–378.CrossRefGoogle Scholar
Rege, K. M. Sengupta, G. (1985) Sojourn time distribution in a multiprogrammed computer system. AT&T Tech. J. 64, 1077–1090.Google Scholar
Schassberger, R. (1984) A new approach to the M/G/1 processor-sharing queue. Adv. Appl. Prob. 16, 202–213.Google Scholar
Yashkov, S. F. (1980) Properties of invariance of probabilistic models of adaptive scheduling in shared-use systems. Autom. Control. Computer Sci. 12, 56–62.Google Scholar
Yashkov, S. F. (1983) A derivation of response time distribution for M/G/1 processor-sharing queue. Problems Control. Inf. Theory 12, 122–148.Google Scholar