The Annals of Applied Probability

Strong approximations for multiclass feedforward queueing networks

Hong Chen and Xinyang Shen

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 10, Number 3 (2000), 828-876.

Dates
First available in Project Euclid: 22 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1019487511

Digital Object Identifier
doi:10.1214/aoap/1019487511

Mathematical Reviews number (MathSciNet)
MR1789981

Zentralblatt MATH identifier
1083.60511

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60K25: Queueing theory [See also 68M20, 90B22] 60G17: Sample path properties
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 90B10: Network models, deterministic 90B22: Queues and service [See also 60K25, 68M20]

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

Citation

Chen, Hong; Shen, Xinyang. Strong approximations for multiclass feedforward queueing networks. Ann. Appl. Probab. 10 (2000), no. 3, 828--876. doi:10.1214/aoap/1019487511. https://projecteuclid.org/euclid.aoap/1019487511


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