Stochastic Processes and Statistical Methods

In this chapter we introduce stochastic processes and the statistical methods for analysing them. Specifically, we focus on processes with long-memory, which have been subject to much research in relation to data networks [6, 16] and are considered to be more representative of network traffic (particularly in packet networks) than traditional Markovian models. We introduce the concept of short-range and long-range dependence and how these can be simulated in J.

The long-range dependence property is often accompanied by self-similarity. We will refer to short-range dependent and long-range dependent self-similar processes as “srd” and “lrd-ss,” respectively. Whereas srd traffic processes tend to smooth rapidly as we “zoom in,” lrd-ss processes retain their burstiness.

In this chapter, we develop a number of functions in J for generating and analysing both srd and lrd-ss stochastic processes. We also show how srd and lrd-ss properties can be identified.