JISE


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Journal of Information Science and Engineering, Vol. 7 No. 3, pp. 347-366


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

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