Diffusion parameters of flows in stable queueing networks

Yoni Nazarathy, Willem R.W. Scheinhardt

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Abstract

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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages24
Publication statusPublished - 16 Jan 2015

Publication series

NameMemorandum of the Department of Applied Mathematics
No.2040
ISSN (Print)1874-4850

Keywords

  • Queueing networks
  • METIS-312481
  • Asymptotic variance
  • Diffusion limits
  • IR-93880
  • EWI-25619

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