This chapter presents an analytical performance analysis method based on arbitrary stochastic Petri nets (ASPN) and moment generating functions and presents it by deriving closed-form performance characteristics for a machine-repairman model and a robotic assembly system. It describes a moment generating function based methodology for ASPN. The chapter presents future research directions for the Petri net and MGF combined performance analysis methodology. Combination of Petri nets and moment generating functions results in a symbolic performance analysis method. Petri nets can be used to generate control codes and validate software designs. Many applications of Petri net modeling and control are reported in flexible manufacturing and advanced automation To reduce the computational effort for large computer-integrated systems, a reduction method is always desired. When conducting analysis of large ordinary Petri nets, researchers have found many useful reduction rules.