A multiclass closed queueing network with unconventional heavy traffic behavior
This paper discusses a closed network with two-server stations and a fixed customer population of size \(n\). Customers are routed in cyclic fashion through four distinct classes, two of which are served at each station, and each server uses a preemptive resume priority discipline. The service times follow exponential law. When \(n\) approaches infinity, this paper discusses a heavy traffic limit theorem which involves a mixture of Brownian scaling and fluid scaling. The interesting part of the result is the limit process that is not an ordinary reflected Brownian motion (as in conventional heavy traffic theorems). But the limit process is related to Brownian motion process.
scientific article; zbMATH DE number 920835
scientific article