Closed queueing networks

Question

When applying Norton's theorem to a closed queueing network, most documentation I found assumes same service rates for all queues. How do you calculate the throughput and delay if the service times are different for each queue? Does rate conservation apply?

Answer 1

This paper details how to apply Norton's theorem to a queueing network where (on the second page) "the service rate for the $i$th queue when there are $k$ custoers is $U_i(k)$, where $i=1,\ldots,M$ and $k=1,\ldots,N$." This therefore isn't assuming the same service rate for each queue.

• Chandy, K. M.; Herzog, U.; Woo, L. (Jan 1975). Parametric Analysis of Queuing Networks. IBM Journal of Research and Development 19 (1): 36–42. doi:10.1147/rd.191.0036.

I'm not sure what you mean by rate conservation.