Translator Disclaimer
December 2018 Justifying diffusion approximations for multiclass queueing networks under a moment condition
Heng-Qing Ye, David D. Yao
Ann. Appl. Probab. 28(6): 3652-3697 (December 2018). DOI: 10.1214/18-AAP1401

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, $t\to\infty$ and $k\to\infty$, 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.

Citation

Download Citation

Heng-Qing Ye. David D. Yao. "Justifying diffusion approximations for multiclass queueing networks under a moment condition." Ann. Appl. Probab. 28 (6) 3652 - 3697, December 2018. https://doi.org/10.1214/18-AAP1401

Information

Received: 1 August 2015; Revised: 1 January 2018; Published: December 2018
First available in Project Euclid: 8 October 2018

zbMATH: 06994403
MathSciNet: MR3861823
Digital Object Identifier: 10.1214/18-AAP1401

Subjects:
Primary: 60K25, 90B15
Secondary: 60F17, 60J20

Rights: Copyright © 2018 Institute of Mathematical Statistics

JOURNAL ARTICLE
46 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 6 • December 2018
Back to Top