A New Dependence Model for Heterogeneous Markov Modulated Poisson Processes

Markov Modulated Poisson Process (MMPP) has been extensively studied in random process theory and widely applied in various applications involving Poisson arrivals whose rate varies following a Markov process. The most general form of aggregated MMPP is the superposition of heterogeneous MMPPs (HeMMPP), in which each constituent MMPP has different parameters. Due to the generality of HeMMPP, studying its temporal dependence will benefit network traffic monitoring and traffic prediction. Modeling the temporal dependence of HeMMPP, however, is extremely hard because the total number of states in a HeMMPP increases exponentially with the number of states in constituent MMPPs. This paper tackles the above challenge with copula analysis. It not only presents a novel framework to capture the functional dependence structure of HeMMPP, but also provides a recursive algorithm to effectively calculate HeMMPP copula values. The theoretical analysis and the algorithms together offer a complete solution for modeling the temporal dependence of HeMMPP. Another contribution of the paper is the application of HeMMPP copula for traffic prediction.