Analysis of discrete-time MAP/G/1 queue under workload control

Authors:
Se Won Lee;Ho Woo Lee;Jung Woo Baek
Affiliations:
Department of Business Administration, Dongguk University-SEOUL, Seoul, Republic of Korea;Department of Systems Management Engineering, Sungkyunkwan University, 440-746 Suwon, Republic of Korea;Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada
Venue:
Performance Evaluation
Year:
2012

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Abstract

In this paper, we analyze the discrete-time MAP/G/1 queue under the D-policy in which the idle server resumes its service only when the accumulated workload exceeds the predetermined threshold D. We first derive the probability generating functions of the queue length, workload, waiting time, and sojourn time distributions. Then we derive the mean performance measures. Lastly we present our numerical experience. Through the numerical examples we show the effects of the threshold and the variability of the service times on the mean performance measures, and the effect of the correlation between arrivals.