On-line estimation and algorithms for performance sensitivities of discrete event systems

In this paper we study the sensitivities of the performance measures in discrete event dynamic systems. The model used is closed queueing networks with exponential service requirements and load-dependent service rates. The performance measures have two general forms: customer average and time average. We derive formulae for the elasticities of the performance measures with respect to the system parameters and develop efficient algorithms for the calculation of these formulae. We show that the steady-state probabilities of the network with one less customer can be determined by the steady-state performance of the original network. We also develop recursive procedures for the online estimation of the elasticities, as well as the steady-state probabilities of the network consisting of one less customer. The estimation procedures require no knowledge of the system parameters and are based on a single sample path of the underlying stochastic process