Stochastic transportation networks and stability of dynamical systems. (English. Russian original) Zbl 1002.60090

Oseledets, V. I.; Khmelev, D. V.

Theory Probab. Appl. 46, No. 1, 154-161 (2001); translation from Teor. Veroyatn. Primen. 46, No. 1, 147-154 (2001).

A certain closed Markovian queueing network with \(N\) servers, \(rN\) customers, and time-dependent service rates is studied. It is shown that, as \(N\) tends to infinity, a suitably defined Markovian state process tends to a deterministic process. The latter is the solution of a system of differential (mean-field) equations which possess the property of global asymptotic stability. Analogous results are obtained for a similar network studied previously in the literature.

Reviewer: R.Schassberger (Braunschweig)

MSC:

60K25	Queueing theory (aspects of probability theory)
37N99	Applications of dynamical systems

Keywords:

Markov processes; nonlinear dynamical systems; global asymptotic stability; generating operator; convergence; mean field approximation; queueing network; dynamical systems