Dobrushin's Mean-Field Approximation for a Queue with Dynamic Routing
1997, v.3, №4, 493-526
A queueing system is considered, with a large number $N$ of identical infinite-buffer FCFS single-servers. The system is fed by a Poisson flow of rate $\lambda N$, with i.i.d. service times, under the non-overload condition. Each arriving task joins a server by selecting it from an independently (and ``completely randomly'') chosen collection of $m \ll N$ servers, on the basis of some fixed dynamic routing policy. We discuss various properties of such a system as $N\to\infty$. In particular, a natural limiting random process describing statistical properties of the system turns out to be deterministic.
Keywords: queueing theory,single-server,dynamic routing,Markov process,generator,convergence,functional differential/difference equation,initial-boundary value problem,fixed points