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This paper provides an introductory discussion for an importantconcept, the performance potentials of Markov processes, and its relationswith perturbation analysis (PA), average-cost Markov decision processes(MDP), Poisson equations, &agr;-potentials, the fundamentalmatrix, and the group inverse of the transition matrix (or the infinitesimalgenerators). Applications to single sample path-based performancesensitivity estimation and performance optimization are also discussed.On-line algorithms for performance sensitivity estimates and on-line schemesfor policy iteration methods are presented. The approach is closely relatedto reinforcement learning algorithms.