Fixed point iteration using stochastic reward nets

Stochastic Petri net models of large systems that are solved by generating the underlying Markov chain pose the problem of largeness of the state-space. Hierarchical and iterative models of systems have been used extensively to solve this problem. A problem with models which use fixed point iteration is the theoretical proof of existence, uniqueness, and convergence of the fixed point equations, which still remains an “art”. We establish conditions, in terms of the net structure and the characteristics of the iterated variables, under which existence of a solution is guaranteed when fixed point iteration is used in stochastic Petri nets