Structured Markovian models for discrete spatial mobile node distribution
 Fernando Luís Dotti,
 Paulo Fernandes,
 Cristina M. Nunes
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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 threedimensional models are presented. For the twodimensional 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.
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 Title
 Structured Markovian models for discrete spatial mobile node distribution
 Journal

Journal of the Brazilian Computer Society
Volume 17, Issue 1 , pp 3152
 Cover Date
 20110301
 DOI
 10.1007/s131730100026y
 Print ISSN
 01046500
 Online ISSN
 16784804
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Structured stochastic modeling formalisms
 Mobile nodes
 Markovian models
 Authors

 Fernando Luís Dotti ^{(1)}
 Paulo Fernandes ^{(1)}
 Cristina M. Nunes ^{(1)}
 Author Affiliations

 1. FACIN–PUCRS, Av. Ipiranga, 6681, Porto Alegre, Brazil