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CONDITIONAL SOJOURN TIMES OF PROCESSOR-SHARING QUEUES

Published online by Cambridge University Press:  20 December 2012

Wei-Yi Lee  and
Chia-Li Wang
Wei-Yi Lee
Affiliation:
Department of Applied Mathematics National Dong Hwa University, Hualien, Taiwan, ROC E-mail: cwang@mail.ndhu.edu.tw
Chia-Li Wang
Affiliation:
Department of Applied Mathematics National Dong Hwa University, Hualien, Taiwan, ROC E-mail: cwang@mail.ndhu.edu.tw
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Abstract

Queues operated by a processor-sharing mode have important applications in many modern systems. However, because of the simultaneous sharing of service capacity by all customers, the distribution function and moments of the sojourn time are difficult to derive, even with a given initial condition. In addition, when a limit on the number of customers in the system is enforced to ensure the quality of service, the sojourn time becomes more complicated. In recent literature, the distribution function is obtained via the Laplace–Stieltjes transform. In this paper, we take a pure algebraic approach to derive the moments of the sojourn time. We obtain an iterative formula and use it to investigate properties of the conditional sojourn time. The approach is simple and intuitive, and applies to queues with multiple class customers as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 99 - 114
Copyright
Copyright © Cambridge University Press 2013

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