Lumping Partially Symmetrical Stochastic Models

The performance and dependability evaluation of complex systems by means of dynamic stochastic models (e.g. Markov chains) may be impaired by the combinatorial explosion of their state space. Among the possible methods to cope with this problem, symmetry-based ones can be applied to systems including several similar components. Often however these systems are only partially symmetric: their behavior is in general symmetric except for some local situation when the similar components need to be differentiated. In this paper two methods to efficiently analyze partially symmetrical models are presented in a general setting and the requirements for their efficient implementation are discussed. Some case studies are presented to show the methods' effectiveness and their applicative interest.