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Scheduling two classes of exponential jobs on parallel processors: structural results and worst-case analysis
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- Journal:
- Advances in Applied Probability / Volume 23 / Issue 4 / December 1991
- Published online by Cambridge University Press:
- 01 July 2016, pp. 925-944
- Print publication:
- December 1991
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- Article
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In this paper, we consider scheduling problems with m machines in parallel and two classes of job. We assume that all jobs are present at time 0 and there are no further arrivals. The service times of class 1 (2) jobs are independent and exponentially distributed with mean
. Each class 1 (2) job incurs a cost c1 (c2) per unit of time until it leaves the system. The objective is to minimize the expected total cost, that is the expected weighted sum of completion times. We show that the optimal policy among all preemptive policies is of threshold type. Based on these structural results, we also show that the ratio of the expected weighted sum of completion times under the cµ-rule to that under the optimal rule is less than 1·71.
. Each class 1 (2) job incurs a cost 