Calculating MFPT for Processes Mapping into Random Walks in Inhomogeneous Networks

Abstract

Dynamic processes leading to natural disasters often translate into random walks in state spaces which are inhomogeneous in transport characteristics. In other words, such random walks will behave differently in different parts of a network which would have different values for transport properties ($d\!\!f$ and dw if using methods from Chap. 4). Thus, for such networks the application of $\textit{MFPT}$ calculation methods introduced in Chap. 4 along with many other methods described in literature are not straight forward. This chapter proposes that using the novel concept of dividing the node distribution into patches/clusters known as network primitives (NPs) where all nodes within each primitive share common transport variables, and adopting a ‘hop-wise’ approach to calculate $\textit{MFPT}$ between any source and target pair as an extension to the methods described under Chap. 4, can be a viable solution for predicting $\textit{MFPT}$ for random walks in inhomogeneous networks. This methodology’s potential is demonstrated through simulated random walks and with a case study using the dataset of past cyclone tracks over the North Atlantic Ocean. The predictions using the presented method are compared to real data averages and predictions assuming homogeneous transport properties.