Dynamical Analysis of an Internet-Based Video System

The dissemination of video applications across the Internet still remains the driving force for Internet traffic growth. Generally, video streaming systems are characterized with irregular transmitting pattern and fluctuation which usually leads to transmission delay and frame loss. Furthermore, the democratic platform created by peer-to-peer (P2P) network for video streaming suggests complex dynamical behaviour with difficult predictable performance. The existence of flash crowd and peer churn situations in P2P streaming systems obtained from random arrival and departure of peers exhibits chaotic attributes. In this paper, a P2P streaming system(UStream) was modelled using a system of first order differential equations. The dynamics of UStream were analysed using equilibrium points and eigenvalues structure. Instability region was tracked through numerical investigation. The numerical simulation conducted using the Mathematica package software showed that UStream exhibits spiral fixed point and strange attractors with certain initial conditions which confirms experimental measurement and observations. Also, the system responds exponentially with time and reflects instability pattern for the first 20 seconds and 500 seconds when investigated with client-to-server(CS)and P2P network models respectively.