Slowdown in the M/M/1 discriminatory processor-sharing queue

Authors:
Sing-Kong Cheung;Bara Kim;Jeongsim Kim
Affiliations:
University of Twente, Department of Applied Mathematics, Stochastic Operations Research Group, P.O. Box 217, 7500 AE Enschede, The Netherlands;Korea University, Department of Mathematics, Telecommunication Mathematics Research Center, Anam-dong, Seongbuk-ku, Seoul 136-713, Republic of Korea;Chungbuk National University, Department of Mathematics Education, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk, 361-763, Republic of Korea
Venue:
Performance Evaluation
Year:
2008

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Abstract

We consider a queue with multiple K job classes, Poisson arrivals, and exponentially distributed required service times in which a single processor serves according to the discriminatory processor-sharing (DPS) discipline. For this queue, we obtain the first and second moments of the slowdown, which is a measure for queueing fairness. We then provide numerical examples and discuss aspects of the slowdown in the DPS queue.