Markov Network Model with Unreliable Edges

Abstract

Network topologies representing the relationships among nodes in supply chain network should be dynamic in time, partly because the relationships are unreliable. Existing network analysis methods such as the Markov network, however, do not consider the time-dependency of the unreliable edges, and therefore these methods cannot consider the dynamics of networks precisely. In order to consider the unreliable edges in Markov network analysis, we suggest a Markov Network with Time-Varying Edge algorithm in this paper, where the discrete time Markov chain is employed to express the time-dependency of the edges. The algorithm consists of: finding unreliable edges for maximal cliques; developing a discrete time Markov chain 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 and limiting probability with this algorithm and numerical application to the supply chain network is provided.