University of Calgary

A computationally tractable theory of performance analysis in stochastic systems

Submitted by ccameron on Wed, 05/23/2012 - 3:33pm.
May 28 2012 - 10:00am
May 28 2012 - 11:00am

Dr. Dimitris Bertsimas

MS 325

Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is  currently the major tool for performance analysis  in stochastic systems. While it offers insights in understanding such systems, probability theory is really not a  computationally tractable theory. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, network information theory, pricing multi-dimensional financial contracts, auction design in multi-item, multi-bidder auctions among others.

 We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms as primitives of probability theory, with some   of the asymptotic  implications of probability theory: the central limit theorem and law of large numbers and to define appropriate robust optimization problems to perform performance analysis. In this way, the performance analysis questions become highly structured optimization problems (linear, conic, mixed integer) for which there exist efficient, practical algorithms that are capable of solving truly large scale systems.

 We demonstrate that  the proposed approach achieves computationally tractable methods for  (a) analyzing multiclass queueing networks, (b)  characterizing the capacity region of network information theory and associated coding and decoding methods generalizing the work of Shannon, (c) pricing multi-dimensional  financial contracts generalizing the work of Black, Scholes and Merton, (d)  designing multi-item, multi-bidder auctions generalizing the work of Myerson.

 This is joint work with my doctoral student  at MIT Chaithanya Bandi.