Poisson Processes

Poisson processes are particular types of random point processes. A random point process on the line (resp. in space) is, roughly speaking, a countable random set of points of the real line (resp. in some space1). In most applications to engineering and operations research, a point of a point process on the line is the time of occurrence of some event, and this is why points are also called events. For instance, the arrival times of customers at the desk of a post office or of jobs at the central processing unit of a computer are point process events. In biology the time of birth of an organism and in physiology the firing time of a neuron are events. In applications to ecology, a point of a spatial point process could be the location of a tree in a forest, or of a source of pollution. In a communications context, it may represent the position of a cellphone or of a relay antenna.