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AutoCAT: Automated Product-Form Solution of Stochastic Models

  • Giuliano Casale
  • Peter G. Harrison
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 27)

Abstract

We introduce AutoCAT, a class of algorithms to automatically generate exact and approximate product-form solutions for large Markov processes that cannot be solved by direct numerical methods. Focusing on models that can be described as cooperating Markov processes, which include queueing networks and stochastic Petri nets as special cases, it is shown that finding a global optimum for a nonconvex quadratic program is sufficient for determining a product-form solution. Such problems are notoriously hard to solve due to the inherent difficulty of searching over nonconvex sets. Using a potential theory for Markov processes, convexification techniques, and a class of linear constraints that follow from stochastic characterization of product-form solutions, we obtain a family of linear programming relaxations that can be solved efficiently. A sequence of these linear programs is solved under increasingly tighter constraints to determine the exact product-form solution of a model when one exists. This approach is then extended to obtain approximate solutions for non-product-form models. Finally, our new techniques are validated with examples and increasingly complex case studies that show the effectiveness of the method on both conventional and novel performance models.

Keywords

Markov Process Linear Programming Relaxation Linear Relaxation Reversed Rate Convex Envelope 
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 Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK

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