Convergence rates of perturbation-analysis-Robbins-Monro-single-run algorithms for single server queues

Author

Tang, Qian-Yu ; Chen, Han-Fu ; Han, Zeng-jin

Author_Institution

Dept. of Autom., Tsinghua Univ., Beijing, China

Volume

42

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

1442

Lastpage

1447

Abstract

In this paper the perturbation-analysis-Robbins-Monro-single-run algorithm is applied to estimating the optimal parameter of a performance measure for the GI/G/1 queueing systems, where the algorithm is updated after every fixed-length observation period. Our aim is to analyze the limiting behavior of the algorithm. The almost sure convergence rate of the algorithm is established. It is shown that the convergence rate depends on the second derivative of the performance measure at the optimal point

Keywords

convergence; optimisation; perturbation techniques; queueing theory; GI/G/1 queueing systems; almost sure convergence rate; fixed-length observation period; optimal parameter estimation; performance measure; perturbation-analysis-Robbins-Monro-single-run algorithms; single server queues; Algorithm design and analysis; Approximation algorithms; Automatic control; Control systems; Convergence of numerical methods; Discrete event systems; Laboratories; Parameter estimation; Stochastic processes; Stochastic systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.633835

Filename

633835