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Journal of Optimization Theory and Applications

, Volume 68, Issue 1, pp 181–202 | Cite as

Consistency of perturbation analysis for a queue with finite buffer space and loss policy

  • Y. Wardi
  • M. A. Zazanis
  • M. Luo
Contributed Papers

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.

Key Words

Perturbation analysis discrete-event dynamical systems 

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Y. Wardi
    • 1
  • M. A. Zazanis
    • 2
  • M. Luo
    • 1
  1. 1.School of Electrical EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Department of Industrial EngineeringNorthwestern UniversityEvanston

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