Introduction to Perturbation Analysis

Abstract

To facilitate the discussion of Perturbation Analysis (PA), let us introduce some notations for DEDS. Let

• θ = system parameter(s)

• x(t) = a time history of the evolution of the DEDS, i.e., the (state, holding time) sequence as illustrated in Fig.1.1 In more physical terms, this may consist of the content of all the queues as a function of time, durations of all service intervals, etc. Since DEDS are often stochastic, x(t) will in general be dependent on the actual realized values of various random variables in the system.

• ξ= a vector of random variables, defined on the underlying probability space, that represents all the random phenomena of the DEDS or a particular realization of all the random variables in the system.