Reflecting diffusions and queueing networks
Let \(Z(t)\) be the \(K\)-vector of numbers of customers at time \(t\) in an open queueing network with \(J\) stations and \(K\) customer classes and \(W(t)\) be the \(J\)-vector of workloads at the \(J\) stations. This paper surveys recent progress on a classical problem, when these processes after appropriate scaling have multidimensional reflected Brownian motion in an orthant as their heavy-traffic limit. The conditions involve multiplicative state space collapse as discussed by Bramson in the paper reviewed above.
scientific article; zbMATH DE number 1184371