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Journal of Inforamtion Science and Engineering, Vol.7 No.3, pp.347-366 (September 1991)
Time Analysis of a Heterogeneous Multi-Server Queue
with a General Service Time Requirement

Jau-Hsiung Huang and Jun-Song Lee
Department of Computer Science and Information Engineering
National Taiwan University
Taipei, Taiwan 10764, Republic of China

In this paper we consider a queueing system with Poisson arrivals and heterogeneous servers with a single queue. The disciplines studied are (1) Preemptive Resume Policy, (2) Fastest Available Server Policy and (3) Threshold Policy. In dissecting the mean system delay of customers into two crucial ingredients, mean waiting time and mean service time, we derive our approximations for each component individually. A single rule based on the ratio of the mean waiting time of an M/G/1 system to an M/M/1 system is applied to all of the three policies to approximate the mean waiting time. Compared to our simulation study, the approximation thus derived shows a satisfying result. In addition, we adopt Linear approximations resulting from measures of system utilization and of queuelength probabilities to estimate mean service time. The results of this paper can be applied to distributed computing systems involving load balancing problems.

Keywords: heterogeneous servers, general distribution, preemptive resume, fastest available server, threshold

Received November 20, 1990; revised April 30, 1991.
Communicated by Ferng-Ching Lin.