Stochastic Models for Network Traffic

Abstract

This chapter introduces several stochastic models largely used to describe traffic processes. It is concerned with point processes. With reference to the unidimensional real line, often interpreted as the time axis, a point process specifies a sequence of instantaneous events that occur on the time axis. The chapter addresses mainly unidimensional point processes, since those are mostly used in network traffic engineering applications. Relevant information for a point process is the counting of the events occurring in a given interval and the probability distribution of the inter‐event times. The chapter review four classes of stochastic processes largely used in network traffic engineering applications: the Poisson process and its variants (spatial Poisson processes, modulated Poisson processes); renewal processes; birth‐death processes; and branching processes. The extension to inhomogeneous Poisson process, i.e., one where the arrival rate is a function of time, is also introduced.