Reliability modeling of structured systems: exploring symmetry in state-space generation

A large number of systems are implemented using regular interconnected topologies. Markov analysis of such systems results in large state spaces. We explore symmetry, in particular rotational and permutational, of such systems to achieve a significant reduction in the size of the state space required to analyze them. The resulting much smaller state spaces allow analyses of very large systems. We define equivalent classes of states and develop an algorithm to generate small state spaces and the corresponding Markov chain for systems with permutation symmetries. The state space generation process is also simplified. We demonstrate our technique using several examples. Our technique is very useful in the exact analysis of large systems.