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ASYMPTOTIC PROPERTIES OF SOJOURN TIMES IN MULTICLASS TIME-SHARED SYSTEMS

Published online by Cambridge University Press:  19 March 2008

Arzad A. Kherani
Arzad A. Kherani
Affiliation:
General Motors India Science LabBangalore, India E-mail: arzad.kherani@gm.com
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Abstract

We consider two multiclass discriminatory process sharing (DPS)-like time-shared M/G/1 queuing systems in which the weight assigned to a customer is a function of its class as well as (1) the attained service of the customer in the first system and (2) the residual processing time of the customer in the second system. We study the asymptotic slowdown, the ratio of expected sojourn time to the service requirement, of customers with very large service requirements. We also provide various results dealing with ordering of conditional mean sojourn times of any two given classes. We also show that the sojourn time of an arbitrary customer of a particular class in the standard DPS system (static weights) with heavy-tailed service requirements has a tail behavior similar to that of a customer from the same class that starts a busy period.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 2 , March 2008 , pp. 231 - 259
Copyright
Copyright © Cambridge University Press 2008

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