JUSTIFYING DIFFUSION APPROXIMATIONS FOR MULTICLASS QUEUEING NETWORKS UNDER A MOMENT CONDITION

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)3652-3697
Journal / PublicationAnnals of Applied Probability
Volume28
Issue number6
Online published8 Oct 2018
Publication statusPublished - Dec 2018
Externally publishedYes

Abstract

Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, → ∞ and → ∞, with t being the time index and k, the scaling parameter. Here, we show this interchange of limits is justified under a pth moment condition on the primitive data, the interarrival and service times; and we provide an explicit characterization of the required order (p), which depends naturally on the desired order of moment of the workload process.

Research Area(s)

  • Diffusion limit, Interchange of limits, Multiclass queueing network, Uniform stability