Markov Network Model with Unreliable Edges

Abstract

Network topologies representing the relations among nodes in the supply chain network should be dynamic in time partly because the relationships are unreliable. But existing network analysis methods such as Markov network do not consider time-dependency of the edges (unreliable edge), and therefore these methods cannot consider the dynamics of networks and express real world network precisely. In order to consider the unreliable edges in Markov network analysis, we suggest a MN-TVE algorithm in this paper, where the discrete time Markov chain (DTMC) is employed to express time-dependency of the edges. The algorithm consists of: finding unreliable edges for maximal cliques; developing a DTMC model for each unreliable edge which composes any maximal cliques and composition; and analyzing the Markov network. We explain how to calculate the transient probabilities of an observation unit and limiting probability with this algorithm.