Williams, R. J. Reflecting diffusions and queueing networks. (English) Zbl 0933.60102 Doc. Math. Extra Vol. ICM Berlin 1998, vol. III, 321-330 (1998). 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. Reviewer: S.Asmussen (Lund) Cited in 5 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 60J65 Brownian motion Keywords:Brownian motion; customer class; fluid limit; heavy traffic; multiclass networks; semimartingale; state space collapse Citations:Zbl 0933.60101 PDFBibTeX XMLCite \textit{R. J. Williams}, Doc. Math. Extra Vol., 321--330 (1998; Zbl 0933.60102) Full Text: EuDML EMIS