Scheduling networks of queues: heavy traffic analysis of a simple open network
Queueing Systems: Theory and Applications
Optimal load balancing and scheduling in a distributed computer system
Journal of the ACM (JACM)
Multiclass queueing systems: polymatroidal structure and optimal scheduling control
Operations Research - Supplement to Operations Research: stochastic processes
Monotone structure in discrete-event systems
Monotone structure in discrete-event systems
Monotone optimal control of permutable GSMPs
Mathematics of Operations Research
Mathematics of Operations Research
Optimization over Time
Analysis and Synthesis of Computer Systems: Texts)
Analysis and Synthesis of Computer Systems: Texts)
Polymatroid Optimization, Submodularity, and Joint Replenishment Games
Operations Research
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Dynamic scheduling of multi-class jobs in queueing systems has wide ranging applications, but in general is a very difficult control problem. Here we focus on a class of systems for which conservation laws hold. Consequently, the performance space becomes a polymatroid - a polytope witha matroid-like structure, withall the vertices corresponding to the performance under priority rules, and all the vertices are easily identified. This structure translates the optimal control problem to an optimization problem, which, under a linear objective, becomes a special linear program; and the optimal schedule is a priority rule. In a more general setting, conservation laws extend to so-called generalized conservation laws, under which the performance space becomes more involved; however, the basic structure that ensures the optimality of priority rules remains intact. This tutorial provides an overview to the subject, focusing on the main ideas, basic mathematical facts, and computational implications.