Copula-based parameter estimation for Markov-modulated Poisson Process

Fang Dong, Kui Wu, Venkatesh Srinivasan

Abstract: Markov-modulated Poisson Process (MMPP) has been extensively studied in random process theory and widely used as a network traffic model. Most methods for estimating MMPP parameters are based on the exact arrival times. Nevertheless, in many applications it is costly to record the exact time of each arrival. Instead, we only record the number of arrivals in fixed-length time slots, which is called arrival count. Since arrival count data does not maintain detailed arrival times, it is non trivial to develop effective methods for MMPP parameter estimation with arrival counts only. Very few existing works deal with this challenge. This paper tackles the above challenge with copula analysis. The theoretical marginal distribution and copula of arrival counts in MMPP are applied to develop a new estimation method, MarCpa, which is a two-step estimation method involving marginal matching followed by copula matching. Our evaluation results demonstrate that the proposed method is fast and accurate.