Stochastic Modeling and Analysis of Telecoms Networks

Chapter 10Spatial Point Processes

 

 

 

10.1. Preliminary

In radio communications, the distance between the transmitter and the receiver plays a crucial role. To evaluate the performance of radio-cellular protocols, it is customary to consider that the access points or base stations are evenly distributed in a hexagonal pattern; see Figure 10.1.

Figure 10.1. Hexagonal network of base stations

The mobile phones are often modeled by a continuum: a call can be transmitted from a point x with an infinitesimal probability dx. This approach which is very macroscopic prevents very precise and realistic calculations. For the last few years, under the influence of works of F. Baccelli, the models stemming from stochastic geometry are gaining more and more attention. They enable us to represent the reality more precisely and make calculations more rigorously.

10.2. Stochastic geometry

The concept of configuration is specified in example A.1. Let us recollect the definition, and see section A.1.2 for details.

DEFINITION 10.1.– A configuration is a locally finite set of points of a set E: there is a finite number of points in any bounded set. We denote as the set of configurations of E.

EXAMPLE 10.1 (BERNOULLI PROCESS).– The Bernoulli point process is a process based on a finite set E = { ...