Fixed utilization perturbation analysis

A simple example of a discrete event dynamic system is used to show that given that an interevent time has a distribution function that is a function of t/τ, where τ is the mean interarrival time and t is the interdeparture time, one cannot conclude that a perturbation of δτ, which is the parameter perturbation, would cause every interevent time to stretch by the factor δτ/τ. This example is used to illustrate the fact that, to ensure that the constructed perturbed path is physically possible, when performing general perturbation analysis one must keep track of events in both the nominal and perturbed paths; but when performing infinitesimal perturbation analysis (IPA) one must employ interevent distribution functions given the event sequence observed in the nominal path. One implication of the latter observation is that IPA estimates are independent of the representation