Abstract
We consider a multiclass closed queueing network model analogous to the open network models of Rybko and Stolyar and of Lu and Kumar. The closed network has two single-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 time distribution for each customer class is exponential, and attention is focused on the critical case where all four classes have the same mean service time. Letting n approach infinity, we prove a heavy traffic limit theorem that is unconventional in three regards. First, in our heavy traffic scaling of both queue-length processes and cumulative idleness processes, time is compressed by a factor of n rather than the factor of
Citation
J. M. Harrison. R. J. Williams. "A multiclass closed queueing network with unconventional heavy traffic behavior." Ann. Appl. Probab. 6 (1) 1 - 47, February 1996. https://doi.org/10.1214/aoap/1034968064
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