Dobrushin's Mean-Field Approximation for a Queue With Dynamic Routing

N. D. Vvedenskaya · Yuri Suhov

43 citations0/0 files storedOpenGrey (Institut de l'Information Scientifique et Technique)

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Interconnection Networks and Systems

Abstract

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 $\l N$, 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.

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