Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing

Authors:
Jeongsim Kim;Bara Kim
Affiliations:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea
Venue:
Performance Evaluation
Year:
2004

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Abstract

In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are ni class i jobs in the system, i = 1,...,K, each class j job receives a fraction αj/Σi=1k αini of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.