Fitting MMPP to IP Stream

Markov Modulated Posson Process (MMPP) is a good model of Internet traffic. We take an IP trace and fit an MMPP to it using an algorithm recently published in a Journal. It is observed that trace generated using the MMPP model of the original trace has a distribution similar to the original trace. This is seen in the form of a linear quantile-quantile plot. Average queuing delay with data trace as input is close to the average queuing delay with model generated trace as input at low loads. At high loads, queuing delay of original data trace is much greater than queuing delay of generated trace. This is because original trace has longer durations when arrival rate exceeds service rate. Lloyd-Max algorithm, commonly used in digital communications systems for non uniform quantization is used here to determine arrival rate at each state. Levels generated at the end of the sixth iteration of the Lloyd max algorithm are used as arrival rates. The resultant MMPP model is used to generate a traffic trace. This trace has a very different distribution than the original data trace. The Quantile-Quantile plot of trace generated using Lloyd-Max and the original trace is not linear.