Dynamic Scheduling via Polymatroid Optimization

  • David D. Yao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2459)


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.


Priority Rule Dynamic Schedule Performance Vector Complementary Slackness Priority Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • David D. Yao
    • 1
  1. 1.Columbia UniversityNew YorkUSA

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