Multiclass queueing systems: polymatroidal structure and optimal scheduling control
Operations Research - Supplement to Operations Research: stochastic processes
Mathematics of Operations Research
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
A heavy traffic limit theorem for a class of open queueing networks with finite buffers
Queueing Systems: Theory and Applications
Optimal control of single-server fluid networks
Queueing Systems: Theory and Applications
Conservation Laws for Single-Server Fluid Networks
Queueing Systems: Theory and Applications
Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload
Queueing Systems: Theory and Applications
A survey on discriminatory processor sharing
Queueing Systems: Theory and Applications
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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.