Alternative Simulation Methods

Abstract

The previous chapter concerns SPNs in which regeneration points exist for the marking process or underlying chain or both. For such nets, regenerative methods often can be used to obtain strongly consistent point estimates and asymptotic confidence intervals for time-average limits of the form $r\, = \,\text{lim}_{\text{t} \to \infty } \bar r\left( t \right),$ where $\bar r\left( t \right)\, = \,(1/t)\,\int\limits_0^t f (X(u))$ du for some function f. This chapter deals with methods for estimation of time-average limits when regenerative methods are not applicable. This situation can occur either because there is no apparent sequence of regeneration points or because regenerations occur so infrequently that the method is impractical—in Section 7.1 we give examples of both types of scenario.