A Stochastic Optimization Algorithm Minimizing Expected Flow Times on Uniforn Processors

Agrawala,; Coffman,; Garey,; Tripathi,

doi:10.1109/tc.1984.1676440

Cited by 51 publications

(37 citation statements)

References 2 publications

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“…It is seen that k > Sj **J ^ hAs argued by Agrawala et al [1], the threshold function gj is increasing in j . Thus J k is increasing in k. This property, together with the fact that the number of waiting jobs cannot increase as time progresses (no arrivals), implies that policy -K never newly activates any processors with indices higher than J k in x and all subsequent states of x.…”

Section: S H Xusupporting

confidence: 59%

“…For any given state, an available processor is utilized if and only if the threshold (the value of the threshold function evaluated at that state) exceeds the expected cost of processing a job on that processor. When the processing times have exponential distributions, the threshold function is often given by some simple explicit formula (Agrawala, Coffman, Garey, and Tripathi [1], Righter [4], Righter and Xu [6]); whereas when the processing times have IHR distributions, the threshold function can be obtained through recursive formulas (Xu [9], Righter and Xu [7]). 2.…”

mentioning

confidence: 99%

“…Thus the results reported in this paper can be considered as a generalization of Agrawala etal. [1].…”

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confidence: 99%

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Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

1991

Prob. Eng. Inf. Sci.

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This paper analyzes a scheduling system where a fixed number of nonpreemptive jobs is to be processed on multiple parallel processors with different processing speeds. Each processor has an exponential processing time distribution and the processors are ordered in ascending order of their mean processing times. Each job has its own deadline that is exponentially distributed with rate ß1, independent of the deadlines of other jobs and also independent of job processing times. A job departs the system as soon as either its processing completes or its deadline occurs. We show that there exists a simple threshold strategy that slochastically minimizes the total delay of all jobs. The policy depends on distributions of processing times and deadlines, but is independent of the rate of deadlines. When the rate of the deadline distribution is 0 (no deadlines), the total delay reduces to the flowtime (the sum of completion times of all jobs). If each job has its own probability of being correctly processed, then an extension of this policy stochastically maximizes the total number of correctly processed, nontardy jobs. We discuss possible generalizations and limitations of this result.

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Section: S H Xusupporting

confidence: 59%

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confidence: 99%

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Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

1991

Prob. Eng. Inf. Sci.

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“…and if a server is rejected, it is never used again [1]. Therefore, the same policy can be implemented even with secondary jobs, so must still be optimal in that case.…”

Section: Corollary 1 It Holds That T J (λ) Is Decreasing In λmentioning

confidence: 99%

Managing Queues with Heterogeneous Servers

2011

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We consider several versions of the job assignment problem for an M/M/m queue with servers of different speeds. When there are two classes of customers, primary and secondary, the number of secondary customers is infinite, and idling is not permitted, we develop an intuitive proof that the optimal policy that minimizes the mean waiting time has a threshold structure. That is, for each server, there is a server-dependent threshold such that a primary customer will be assigned to that server if and only if the queue length of primary customers meets or exceeds the threshold. Our key argument can be generalized to extend the structural result to models with impatient customers, discounted waiting time, batch arrivals and services, geometrically distributed service times, and a random environment. We show how to compute the optimal thresholds, and study the impact of heterogeneity in server speeds on mean waiting times. We also apply the same machinery to the classical slow-server problem without secondary customers, and obtain more general results for the two-server case and strengthen existing results for more than two servers.

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“…Agrawala, et al (1984) considered the problem of executing n identical jobs with exponential processing times on a set of m processors to minimize expected flowtime.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

Optimal dispatching of two-priority job streams to two nonidentical machines

Zhou

Mirchandani

Proceedings. IEEE International Symposium on Intelligent Control 1989

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The following control problem in manufacturing is addressed in this paper. Jobs of t;vc priority classes, C1 and C2, arrive at a system with two non-identical machines. Class C1 jobs with higher priority have dispatch preference aver C2 jobs with lower priority. The problem is to dispatch appropriate fractions of class C1 jobs to machines 1 and 2 so that the average flowtime of C1 jobs is minimized and neither C1 jobs nor C2 jobs are lost. The analytical soiution to the problem is derived for various system disciplines including 1) nonpreemptive priorities 2) preemptive priorities with resumption, 3) preemptive priorities with resumption and setup, and 4) nonpreemptive priorities with multiple vacations.

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A Stochastic Optimization Algorithm Minimizing Expected Flow Times on Uniforn Processors

Cited by 51 publications

References 2 publications

Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

Managing Queues with Heterogeneous Servers

Optimal dispatching of two-priority job streams to two nonidentical machines

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