Diffusion parameters of flows in stable multi-class queueing networks

Sarat Babu Moka (), Yoni Nazarathy and Werner Scheinhardt
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Sarat Babu Moka: Macquarie University
Yoni Nazarathy: The University of Queensland
Werner Scheinhardt: University of Twente

Queueing Systems: Theory and Applications, 2023, vol. 103, issue 3, No 4, 313-346

Abstract: 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. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

Keywords: Queueing networks; Diffusion limits; Asymptotic variance; 60K25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-022-09869-1

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