Abstract
Discrete-event systems to which the technique of infinitesimal perturbation analysis (IPA) is applicable are natural candidates for optimization via a Robbins-Monro type stochastic approximation algorithm. We establish a simple framework for single-run optimization of systems with regenerative structure. The main idea is to convert the original problem into one in which unbiased estimators can be derived from strongly consistent IPA gradient estimators. Standard stochastic approximation results can then be applied. In particular, we consider the GI/G/1 queue, for which IPA gives strongly consistent estimators for the derivative of the mean system time. Convergence (w.p.1) proofs for the problem of minimizing the mean system time with respect to a scalar service time parameter are presented.
Similar content being viewed by others
References
Suri, R., andZazanis, M. A.,Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue, Management Science, Vol. 34, pp. 39–64, 1988.
Suri, R., andLeung, Y. T.,Single-Run Optimization of Discrete-Event Simulations: An Empirical Study Using the M/M/1 Queue, IIE Transactions (to appear).
Zazanis, M. A., andSuri, R.,Perturbation Analysis of the G/G/1 Queue, Department of Industrial Engineering, University of Wisconsin, Working Paper No. 89–121, 1989.
Glynn, P. W.,Stochastic Approximation for Monte Carlo Optimization, Proceedings of the Winter Simulation Conference, Washington, DC, pp. 356–364, 1986.
Fu, M. C., andHo, Y. C.,Using Perturbation Analysis for Gradient Estimation, Averaging, and Updating in a Stochastic Approximation Algorithm, Proceedings of the Winter Simulation Conference, San Diego, California, pp. 509–517, 1988.
Zazanis, M. A., andSuri, R.,Comparison of Perturbation Analysis with Conventional Estimates for Regenerative Stochastic Systems, Department of Industrial Engineering, University of Wisconsin, Working Paper No. 86–123, 1986.
Crane, M. A., andIglehart, D. L.,Simulating Stable Stochastic Systems, III: Regenerative Processes and Discrete-Event Simulations, Operations Research, Vol. 23, pp. 33–45, 1975.
Kushner, H. J., andClark, D. C.,Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer-Verlag, New York, New York, 1978.
Fu, M. C.,Optimization of Queueing Systems Using Perturbation Analysis, PhD Thesis, Division of Applied Sciences, Harvard University, 1989.
Shanthikumar, J. G., andYao, D. D.,Second-Order Stochastic Properties in Queueing Systems, Proceedings of the IEEE, Vol. 77, pp. 162–170, 1989.
Author information
Authors and Affiliations
Additional information
Communicated by P. Varaiya
Rights and permissions
About this article
Cite this article
Fu, M.C. Convergence of a stochastic approximation algorithm for the GI/G/1 queue using infinitesimal perturbation analysis. J Optim Theory Appl 65, 149–160 (1990). https://doi.org/10.1007/BF00941166
Issue Date:
DOI: https://doi.org/10.1007/BF00941166