Mean-field Limit for General Queueing Networks on Infinite Graphs

We study the sequences of Markov processes defining the evolution of a general symmetric queueng network with the number of nodes tending to infinity. These sequences have limits which are nonlinear Markov processes. Time evolution of these nonlinear Markov processes are sometimes simpler and easier to analyze than the evolution of corresponding prelimit Markov processes on finite graphs. This fact give the possibility to find good approximation for the behavior of symmetric queueing networks on large graphs. Examples will be discussed.

The talk is based on a joint work with S. Shlosman.