Avoiding the boundary effect: A sphere model for wireless multi-hop networks

The boundary effect emerges in random geometric graphs for modeling wireless multi-hop networks due to a given unit square in the model. That is, nodes close to the edges of the square have lower probability to connect other nodes than those nodes close to the center of the square. In this paper, the impact of the boundary effect on probability of node connecting to other nodes, and probability of network 1-connectivity is analyzed in a unit square. And then a sphere model which avoids the boundary effect is proposed to model a wireless multi-hop network. The simulation results show that the boundary effect does big harm to network connectivity when transmission range of nodes is considerable to side length of the unit square. And the sphere model is validated to be correct.