Addendum to "Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework"

Under a very general framework, both in terms of finite-time performance measures and system structure, the authors derive smoothed perturbation analysis (SPA) estimators and prove their unbiasedness. The commuting condition, which has been key in previous work, is not required a priori, and thus the framework includes such systems as the GI/G/1/K queue and multiclass queueing networks, which do not satisfy the commuting condition. The generality achieved is traded off against the fact that the estimator is not always easily implementable on a single sample path. The use of the commuting condition in a local sense is proposed to help simplify the estimators derived: queueing and multiclass queueing networks are used as illustrative examples. For a simple multiclass closed queueing network, some simulation results are provided. When the commuting condition is satisfied globally, the framework allows the recovery of previous results on IPA and SPA estimators as corollaries of the main theorems. >