A New Model Reduction Method for Traffic Described by Markov Modulated Poisson Processes

The Markov modulated poisson processes (MMPP) are very powerful in describing general network traffic. The main hindrance to the application of MMPP is the state-space explosion problem, that is, the superposition of two traffic processes, described by MMPP with orders of n₁ and n₂, respectively, is also an MMPP process with orders of n₁ times n₂. In this paper, we propose a new method to reduce the state-space of the MMPP traffic models based on the clustering structure of the decaying time constants of the variance-time curve of the counting process. It is found that the time constants of the aggregated traffic equal one minus the product of the eigenvalues of the transition matrix of the individual traffic. If some time constants, e.g., those can be merged time constants (MTCs), are well clustered around a representative time constant (RTC), the states corresponding to these time constants can be merged into the state of the RTC. By defining a condition of matrix product approximation (MPA), we find a new model with reduced dimensions. Our numerical examples and simulations have demonstrated the effectiveness of the proposed technique.