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August 2000 Strong approximations for multiclass feedforward queueing networks
Hong Chen, Xinyang Shen
Ann. Appl. Probab. 10(3): 828-876 (August 2000). DOI: 10.1214/aoap/1019487511

Abstract

This paper derives the strong approximation for a multiclass queueing network,where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in first-out (FIFO) discipline is in force, and among groups, jobs are served under a preassigned preemptive priority discipline. We obtain the strong approximation for the network through an inductive application of an input–output analysis for a single-station queue. Specifically, we show that if the input data (i.e., the arrival and the service processes) satisfy an approximation (such as the functional law-of-iterated logarithm approximation or the strong approximation), then the output data (i.e., the departure processes) and the performance measures (such as the queue length, the workload and the sojourn time processes) satisfy a similar approximation. Based on the strong approximation, some procedures are proposed to approximate the stationary distribution of various performance measures of the queueing network. Our work extends and complements the existing work of Peterson and Harrison and Williams on the feedforward queueing network. The numeric examples show that strong approximation provides a better approximation than that suggested by a straightforward interpretation of the heavy traffic limit theorem.

Citation

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Hong Chen. Xinyang Shen. "Strong approximations for multiclass feedforward queueing networks." Ann. Appl. Probab. 10 (3) 828 - 876, August 2000. https://doi.org/10.1214/aoap/1019487511

Information

Published: August 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1083.60511
MathSciNet: MR1789981
Digital Object Identifier: 10.1214/aoap/1019487511

Subjects:
Primary: 60F17 , 60G17 , 60K25
Secondary: 60J70 , 90B10 , 90B22

Keywords: diffusion approximations , fluid approximations , heavy traffic , Multiclass queueing network , reflected Brownian motion and strong approximation

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August 2000
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