Distributed control for radial loss network systems via the ash Certainty Equivalence (mean field) principle

Abstract

The computational intractability of the dynamic programming (DP) equations associated with optimal admission and routing in stochastic loss networks of any non-trivial size (Ma et al., 2006, 2008) leads to the consideration of suboptimal distributed game theoretic formulations of the problem. This work presents a formulation of loss network admission control problems in terms of a class of systems composed of a large population of weakly coupled competitive individual agent networks. The resulting distributed dynamic stochastic game problem is solved and analyzed by application of the so-called point process Nash certainty equivalence (PPNCE) 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., (2006, 2007). This methodology has close connections with the mean field models studied by Lasry and Lions (2006, 2007) and the notion of oblivious equilibrium proposed by Weintraub, Benkard, and Van Roy (2005, 2007) via a mean field approximation.