Uniformization based sensitivity estimation for a class of discrete-event systems

Abstract

Infinitestimal Perturbation Analysis (IPA) estimators are based on particular couplings of parameteric families of discrete event systems where “small” changes in the parameter value, typically, cause “small” changes in the timing of events and, for finite horizons, the sequence of states visisted remains the same. We consider another coupling approach based on the uniformization procedure and a simple generalization of it. In our case any “small” change in the parameter value causes a change in the state of the system; our parameterization of trajectories keeps them highly synchronized, hence the effect of such changes can be estimated, sometimes efficiently. In this framework, we define three tupes of performance sensitivity estimators for a broad class of performance measures and with respect to a range of parameter values. Performance measures on finite deterministic horizons are considered and it is shown that they are unbiased under mild conditions. We show that for some systems the derivative estimators can be calculated from a nominal sample path of the system.