Mathematical Modelling of Network Traffic

ncreasing access to the Internet is producing profound influence around the World. More and more people are taking advantage of the Internet to obtain information, communicate with each other far away and enjoy various recreations. This largely increased demand for the Internet requires better and more effective models. During the 1990s, a number of studies show that due to a different nature from telephonic traffic, in particular a bursty nature, traditional queuing models are not applicable in modeling of modern traffic. This work presents some alternative rigorous models that can be used in studying the behavior of the Internet traffic.
In the thesis, we propose several new models to explain bursty nature of network traffic.
Many practical problems in computer science, natural science and insurance are highly complex, since they typically involve a huge amount of random factors. Con- ventional queuing theory cannot handle such problems and the high variance and long memory features are not yet well understood.
In the first part of our research, we start with investigation of random sum as well as random product and derive a single path model of network traffic and a multiple path model of network traffic.In the second part of this thesis, we present a homotopic approach to model network traffic.