Algorithm for Constructing Ergodic Location Networks using Discrete Markov Chains

Abstract

Abstract For a region's tourism strategy, connecting famous locations to the surrounding locations can activate the entire area. Connections between locations can be obtained by calculating the central locations of the area and creating routes to other locations from there. This study proposes an algorithm to obtain ergodicity in discrete Markov chains using network centrality relations. The number of calculations to obtain ergodicity was compared using several definitions of network centrality, making it possible to select a type of network centrality for the target network. The proposed method clarifies the network’s central locations and how transition probabilities between locations can be adjusted to achieve an ergodic network. If the location network holds ergodicity, a stationary distribution of the Markov chain exists and optimization applications are expected. Numerical calculations were used to demonstrate the method’s applicability to various networks. Furthermore, using a Wi-Fi log, we observed that the proposed method can reconstruct a network with ergodicity for networks that use access points as locations, indicating the social applicability of the proposed method. The proposed method can be used to analyze various networks in modern society, such as facility operations and tourism stimulation. This method applies to human traffic management and stay analysis in facility operations. To promote tourism, by considering tourist sites as network locations, the method clarifies which routes should be prioritized to construct an uninterrupted tourist network, making the construction and operation of an extensive tourist network possible.