On the spatial modeling of wireless networks by random packing models

In order to represent the set of transmitters simultaneously accessing a wireless network using carrier sensing based medium access protocols, one needs tractable point processes satisfying certain exclusion rules. Such exclusion rules forbid the use of Poisson point processes within this context. It has been observed that Matérn point processes, which have been advocated in the past because of their exclusion based definition, are rather conservative within this context. The present paper confirms that it would be more appropriate to use the point processes induced by the Random Sequential Algorithm in order to describe such point patterns. It also shows that this point process is in fact as tractable as the Matérn model. The generating functional of this point process is shown to be the solution of a differential equation, which is the main new mathematical result of the paper. In comparison, no equivalent result is known for the Matérn hard-core model. Using this differential equation, a new heuristic method is proposed, which leads to simple bounds and estimates for several important network performance metrics. These bounds and estimates are evaluated by Monte Carlo simulation.