Large loss networks

Abstract

A general loss network is considered in the limit as the arrival rates and link capacities become large with their ratio held fixed. We show that the network obeys a functional law of large numbers (along a subsequence) and that the free circuit process acts as a control for the network. The network exhibits a separation of time-scales, with the free circuit process operating on the fast time-scale as a random walk on Z + J , and this leads to an interesting conjecture for transient random walks. The techniques used to prove the results are of independent interest and can be applied to a wide range of models in which a similar separation of time-scale occurs, or in which the transition rates of the process undergo a discontinuity at or near a boundary. Finally, we give examples and show that commonly employed fixed point approximations are not valid in this limit.