Name
Abstract | ||
|---|---|---|
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks. In this paper we consider a natural extension of the random geometric graph model to the mobile setting by allowing nodes to move in space according to Brownian motion. We study three fundamental questions in this model: detection (the time until a given target point---which may be either fixed or moving---is detected by the network), coverage (the time until all points inside a finite box are detected by the network), and percolation (the time until a given node is able to communicate with the giant component of the network). We derive precise asymptotics for these problems by combining ideas from stochastic geometry, coupling and multi-scale analysis. We also give an application of our results to analyze the time to broadcast a message in a mobile network. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00440-012-0428-1 | Probability Theory and Related Fields |
Keywords | DocType | Volume |
Poisson point process,Brownian motion,Coupling,Minkowski dimension | Conference | 156 |
Issue | ISSN | ISBN |
1-2 | 0178-8051 | 978-1-61197-251-1 |
Citations | PageRank | References |
25 | 1.05 | 22 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuval Peres | 1 | 523 | 53.68 |
| Alistair Sinclair | 2 | 1506 | 308.40 |
| Perla Sousi | 3 | 33 | 2.44 |
| Alexandre O. Stauffer | 4 | 130 | 11.34 |