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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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