A process is said to be long-range dependent if its autocovariance function decays hyperbolically (slower than exponentially) and the area under it is infinite.
Published in Chapter:
Modeling IP Traffic Behavior through Markovian Models
Antóniol Nogueira (University of Aveiro/Institute of Telecommunications Aveiro, Portugal), Paulo Salvador (University of Aveiro/Institute of Telecommunications Aveiro, Portugal), Rui Valadas (University of Aveiro/Institute of Telecommunications Aveiro, Portugal), and António Pacheco (Instituto Superior Técnico – UTL, Portugal)
Copyright: © 2008
|Pages: 11
DOI: 10.4018/978-1-59140-993-9.ch044
Abstract
This article addresses the use of Markovian models, based on discrete time MMPPs (dMMPPs), for modeling IP traffic. In order to describe the packet arrival process, we will present three traffic models that were designed to capture self-similar behavior over multiple time scales. The first model is based on a parameter fitting procedure that matches both the autocovariance and marginal distribution of the counting process (Salvador 2003). The dMMPP is constructed as a superposition of two-state dMMPPs (2-dMMPPs), designed to match the autocovariance function, and one designed to match the marginal distribution. The second model is a superposition of MMPPs, each one describing a different time scale (Nogueira 2003a). The third model is obtained as the equivalent to a hierarchical construction process that, starting at the coarsest time scale, successively decomposes MMPP states into new MMPPs to incorporate the characteristics offered by finer time scales (Nogueira 2003b). These two models are constructed by fitting the distribution of packet counts in a given number of time scales.