The processor-sharing queue with bulk arrivals and phase-type services

Authors:
Jeongsim Kim;Bara Kim
Affiliations:
Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk 361-763, Republic of Korea;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea
Venue:
Performance Evaluation
Year:
2007

Citing 9
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Abstract

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.