Nondifferentiability of the steady-state function in discrete event dynamic systems

Abstract

This paper suggests that expected-value performance functions in discrete-event dynamic systems can be nondifferentiable at dense sets of points in the parameter space, when the sample performance functions are convex and the distributions of events' times contain atoms. A general result is first proved for regenerative processes and then applied to simple queueing examples where nondifferentiability at dense sets is established. >