Long-memory statistical models in telecommunication networks

Recent studies of measurements from packet networks have demonstrated that the arrival process of packets (packet network traffic) is self similar or long memory. In this paper, statistical models for packet network traffic are presented. They provide a physical explanation for the occurrence of self similarity based on new convergence results for processes that exhibit high variability. The key result states that the superposition of many strictly alternating ON/OFF sources whose ON and/or OFF periods exhibit the Noah Effect (i.e. have high variability or infinite variance) produces (aggregate) network traffic that exhibits the Joseph Effect (i.e. is self similar with long memory increments). The implications of self similarity on performance evaluation are presented. Statistical inference in the presence of self similarity is described.