Characterizing a lumping heuristic for a Markov network reliability model

Abstract

Network reliability models are plagued by large state spaces. When combinatorial models are inapplicable, Markov models are generally used to evaluate network reliability. Standard numerical methods of Markov chain solution are not applicable due to the size of the state space. Alternate solution methods through state space reduction by lumping or a solution by simulation are required. The authors characterize a lumping heuristic which derives a smaller Markov model from the original Markov reliability model for a network with an alternate-routing capability and link repair facility. In an empirical evaluation, this heuristic is seen to yield very good approximations: in all the experiments the reliability function obtained by solving the derived Markov chain using a standard Markov solver closely tracked the function obtained through simulation of the original Markov chain over a range of parameters. The theory of lumpability is used to investigate the characteristics of the heuristically constructed Markov chain.