In this paper we present an algorithmic approach to bounding the mean response time of a multi-server system in which the minimum expected delay routing policy issued, i.e., an arriving job will join the queue which has the minimal expected value of unfinished work. We assume the queueing system to have K servers, each with an infinite capacity queue. The arrival process is Poisson with parameter ॕ, and the service time of server i is exponentially distributed with mean 1/ॖ i , 1 ≤ i ≤ K . The computation algorithm we present allows one to tradeoff accuracy and computational cost. Upper and lower bounds on the expected response time and expected number of customers are computed; the spread between the bounds can be reduced with additional space and time complexity. Examples are presented which illustrate the excellent relative accuracy attainable with relatively little computation.
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Algorithmic approach to bounding the mean response time of a minimum expected delay routing system
Lui, John C. S.; Muntz, Richard R.
Follow ACM SIGMETRICS Performance Evaluation Review
, Volume 20 (1)
Association for Computing Machinery – Jun 1, 1992
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