Workload and Waiting Time Analyses of MAP/G/1 Queue under D-policy

Authors:
Ho Woo Lee;Sahng Hoon Cheon;Eui Yong Lee;K. C. Chae
Affiliations:
Department of Systems Management Engineering, Sungkyunkwan University, Su Won, Korea (South) 440-746 hwlee@skku.edu;Department of Systems Management Engineering, Sungkyunkwan University, Su Won, Korea (South) 440-746;Department of Statistics, Sookmyung Women's University, Seoul, Korea (South) eylee@sookmyung.ac.kr;Department of Industrial Engineering, KAIST, Taejon, Korea (South) kcchae@kaist.ac.kr
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

We study the workload (unfinished work) and the waiting time of the queueing system with MAP arrivals under D-policy. The D-policy stipulates that the idle server begin to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We first set up the system equations for workload and obtain the steady-state distributions of workloads at an arbitrary idle and busy points of time. We then proceed to obtain the waiting time distribution of an arbitrary customer based on the workload results. The M/G/1/D-policy queue will be investigated as a special case.