Abstract
The subject of discrete-event dynamical systems has taken on a new direction with the advent of perturbation analysis (PA), an efficient method for estimating the gradients of a steady-state performance measure, by analyzing data obtained from a single-simulation experiment in the time domain. A crucial issue is whether PA gives strongly consistent estimates, namely, whether average time-domain-based gradients converge, over infinite horizon, to the steady-state gradients. In this paper, we investigate this issue for a queue with a finite buffer capacity and a loss policy. The performance measure in question is the average amount of lost customers, as a function of the buffer's capacity, which is assumed to be continuous in our work. It is shown that PA gives strongly consistent estimates. The analysis uses a new technique, based on busy period-dependent inequalities. This technique may have possible extensions to analyses of consistency of PA for more general queueing systems.
Similar content being viewed by others
References
Ho, Y. C.,Performance Evaluation and Perturbation Analysis of Discrete Event Dynamic Systems, IEEE Transactions on Automatic Control, Vol. AC-32, pp. 563–572, 1987.
Suri, R., andZazanis, M. A.,Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue, Management Science, Vol. 34, pp. 39–63, 1988.
Zazanis, M. A., andSuri, R.,Estimating First and Second Derivatives of Response Time for GI/G/1 Queues from a Single Sample Path, Queueing Systems (to appear).
Wardi, Y.,Interchangeability of Expectation and Differentiation of Waiting Times in GI/G/1 Queues (submitted).
Fu, M. C., andHu, J. Q.,Consistency of Infinitesimal Perturbation Analysis for the GI/G/m Queue (submitted).
Cao, X. R.,Realization Probability in Closed Jackson Queueing Networks and Its Application, Advances in Applied Probability, Vol. 19, pp. 708–738, 1987.
Cao, X. R.,Convergence of Parameter Sensitivity Estimates in a Stochastic Experiment, IEEE Transactions on Automatic Control, Vol. AC-30, pp. 845–885, 1985.
Author information
Authors and Affiliations
Additional information
Communicated by Y. C. Ho
Rights and permissions
About this article
Cite this article
Wardi, Y., Zazanis, M.A. & Luo, M. Consistency of perturbation analysis for a queue with finite buffer space and loss policy. J Optim Theory Appl 68, 181–202 (1991). https://doi.org/10.1007/BF00939941
Issue Date:
DOI: https://doi.org/10.1007/BF00939941