Sample-path conservation laws, with applications to scheduling queues and fluid systems

Sample-path conservation laws, with applications to scheduling queues and fluid systems

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Article ID: iaor20013088
Country: Netherlands
Volume: 36
Issue: 1/3
Start Page Number: 175
End Page Number: 200
Publication Date: Jan 2000
Journal: Queueing Systems
Authors: ,
Keywords: scheduling
Abstract:

The achievable-region approach, based on strong conservation laws, has most often been applied to stochastic scheduling and other control problems in the context of performance measures that are steady-state expected quantities. For some problems, however, strong conservation laws hold for performance measures at every time point on every sample path. We exploit this property to study optimal control for certain scheduling problems on a sample-path basis. Examples include preemptive scheduling to minimize a weighted sum of work in the system in each class, nonpreemptive scheduling to minimize a weighted sum of the number of customers in each class (when all classes have the same service-time distribution), and scheduling the processing of fluid in a multiclass fluid system operating in a random environment. The last problem is solved by considering the related Skorohod problem and its minimal solution.

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