Analysis of Constrained Random WayPoint Mobility Model on Graph

Graph traversal is one of fundamental problems in discrete mathematics since it has a broad range of applications in diverse research areas such as computer science and information networking. In the last decade, the characteristics of random-walk-based mobility models have been extensively studied by many researchers through mathematical analyses as well as computer simulations. One of the popular mobility models on a graph is the Constrained Random WayPoint (CRWP) mobility model, which is a natural extension of the Random WayPoint (RWP) mobility model. It has been known that the RWP mobility model on a continuous space has many favorable properties (e.g., fast mixing time and wide range of positional distribution) over random-walk-based mobility model on a continuous space. The RWP mobility model has always a specific goal so that the agent is likely to deviate from the current position. Such deviating property of the RWP mobility model has positive impact on many applications. However, to the best of our knowledge, the superiority of such mobility model on a graph has not been well understood. In this paper, we derive the two major indices of the CRWP mobility model on an arbitrary graph G (i.e., the recurrence time and the first hitting time). Furthermore, through several numerical examples, we investigate the effect of the structure of a graph on the characteristics of the CRWP mobility model. Our findings include that the characteristics of the CRWP mobility model are determined by betweenness centralities of nodes.