We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. An example is a generalized Jackson network with load less than unity and any work conserving policy. We find a simple diffusion limit for the inter-queue flows with an explicit computable expression for the covariance matrix. Specifically, we present a simple computable expression for the asymptotic variance of arrivals (or departures) of each of the individual queues and each of the flows in the network.
|Name||Memorandum of the Department of Applied Mathematics|
- Queueing networks
- Asymptotic variance
- Diffusion limits