Conservation Laws

• Hong Chen
• David D. Yao
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 46)

Abstract

Conservation laws belong to the most fundamental principles that govern the dynamics, or law of motion, of a wide range of stochastic systems. Under conservation laws, the performance space of the system becomes a polymatroid, that is, a polytope with a matroid-like structure, with all the vertices corresponding to the performance under priority rules, and all the vertices are easily identified. Consequently, the optimal control problem can be translated into an optimization problem. When the objective is a linear function of the performance measure, the optimization problem becomes a special linear program, for which the optimal solution is a vertex that is directly determined by the relative order of the cost coefficients in the linear objective. This implies that the optimal control is a priority rule that assigns priorities according to exactly the order of the cost coefficients.

Keywords

Busy Period Priority Rule Submodular Function Performance Vector 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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