Structured Markovian models for discrete spatial mobile node distribution

摘要

The study and characterization of node mobility in wireless networks is extremely important to foresee the node distribution in the network, enabling the creation of suitable models, and thus a more accurate prediction of performance and dependability levels. In this paper we adopt a structured Markovian formalism, namely SAN (Stochastic Automata Networks), to model and analyze two popular mobility models for wireless networks: the Random Waypoint and Random Direction. Our modeling considers mobility over a discrete space, i.e., over a space divided in a given number of slots, allowing a suitable analytical representation of structured regions. We represent several important aspects of mobility models, such as varying speed and pause times, and several border behaviors that may take place. One, two, and three-dimensional models are presented. For the two-dimensional models, we show that any regular or irregular convex polygon can be modeled, and we describe several routing strategies in two dimensions. In all cases, the spatial node distribution obtained from the steady state analysis is presented and whenever analogous results over continuous spaces were available in the literature, the comparison with the ones obtained in this paper is shown to be coherent. Besides showing the suitability of SAN to model this kind of reality, the paper also contributes to new findings for the modeled mobility models over a noncontinuous space.