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

• Published in: IEEE transactions on automatic control Vol. 42; no. 10; pp. 1442 - 1447
• Main Authors: TANG, Q.-Y, CHEN, H.-F, HAN, Z.-J
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.1997; Institute of Electrical and Electronics Engineers
• Subjects: Algorithm design and analysis; Applied sciences; Approximation algorithms; Automatic control; Computer science; control theory; systems; Control system analysis; Control systems; Control theory. Systems; Convergence of numerical methods; Discrete event systems; Exact sciences and technology; Laboratories; Operational research and scientific management; Operational research. Management science; Parameter estimation; Queuing theory. Traffic theory; Stochastic processes; Stochastic systems; Queueing system; Convergence rate; Stochastic approximation; Perturbation; Algorithm; Single server queue; Stochastic system; Discrete event system
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.633835

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.