Justifying diffusion approximations for multiclass queueing networks under a moment condition

Heng Qing Ye, David D. Yao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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, t→∞and k→∞, with t being the time index and k, the scaling parameter. Here, we show this interchange of limits is justified under a p∗th 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.

Original languageEnglish
Pages (from-to)3652-3697
Number of pages46
JournalAnnals of Applied Probability
Volume28
Issue number6
DOIs
Publication statusPublished - Dec 2018

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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