Thermodynamic Limit for the Mean Field Model of Simple Symmetrical Closed Queueing Network

#### F.I. Karpelevich, A.N. Rybko

2000, v.6, №1, 89-105

ABSTRACT

The thermodynamic limit for the mean field dynamics of simple closed queueing network is investigated. It is proved that in the thermodynamical limit the corresponding random process converges to a deterministic dynamical system. The main result of the paper is the theorem about the convergence of this infinite dimensional dynamical system to its unique stable point. This stable point corresponds to the invariant measure of $M/ M/ 1/ \infty$ queue.

Keywords: mean field models,thermodynamic limit,queueing network