Algorithms for the generation of state-level representations of stochastic activity networks with general reward structures

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Abstract
Stochastic Petri nets and extensions are a popular method for evaluating a wide variety of systems. In most cases, their numerical solution requires generating a state-level stochastic process, which captures the behavior of the SPN with respect to a set of specified performance measures. These measures are commonly defined at the net level by means of a reward variable. We discuss issues regarding the generation of state-level reward models for systems specified as stochastic activity networks with "step-based reward structures." Step-based reward structures are a generalization of previously proposed reward structures for SPNs, and can represent all reward variables that can be defined on the marking behavior of a net. While discussing issues related to the generation of the underlying state-level reward model, we provide an algorithm to determine whether a given SAN is "well specified." A SAN is well specified if choices about which instantaneous activity completes among multiple simultaneously enabled instantaneous activities do not matter, with respect to the probability of reaching next possible stable markings, and distribution of reward obtained upon completion of a timed activity. The fact that a SAN is well specified is both a necessary and sufficient condition for its behavior to be completely probabilistically specified, and hence an important property to determine.