On the Optimal and Decentralized Control of Stochastic Loss Network Systems
Zhongjing Ma
Department of Electrical and Computer Engineering
McGill University
Date: Wednesday, March 5, 2pm
Location: BA 5256
Abstract:
In this work call admission and routing control in (stochastic) loss networks
with semi-Markovian, multi-class call arrivals and general connection
durations, are formulated as optimal stochastic control (OSC) problems. The
associated hybrid dynamic programming (DP) equations correspond to a
collection of coupled first-order PDEs which reduce to the piecewise linear
equations of Markov decision formulations whenever call arrivals are Poisson
and connection durations are exponentially distributed.
The solution of the hybrid DP equations associated with optimal admission and
routing in loss networks of any significant size is computationally
intractable. This leads us to consider an alternative, suboptimal, game
theoretic formulation. In this framework, a class of large-population network
call admission problems is formulated as a set of decentralized OSC problems
via the so-called Point Process Nash Certainty Equivalence (PPNCE) (Mean
Field) Principle; this is an extension to the network point process context of
the NCE Principle originally formulated in the LQG framework by M. Huang et.
al. [IEEE TAC 2007, CDC 2006]. Computational examples will be presented for
both parts of the talk.
Bio:
Zhongjing Ma is a PhD candidate in the Systems and Control Group in the
Electrical and Computer Engineering Department of McGill University with
Professor Peter Caines at McGill University and Professor Roland Malhame who
is with the Department of Electrical Engineering of the Ecole Polytechnique de
Montreal. He received the M.Eng. degree in Systems and Control from McGill
University in 2005, and the B. Eng. degree in Automatic Control from Nankai
University, China, in 1997. His work experience includes analysis of the
toll-collection system for highway networks in China during 1998-2001.
Host of the talk
Peter Marbach (marbach@cs.toronto.edu)