Copula Analysis of Temporal Dependence Structure in Markov Modulated Poisson Process and Its Applications

Abstract

The 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. Despite the rich literature on MMPP, very little is known on its intricate temporal dependence structure. No exact solution is available so far to capture the functional temporal dependence of MMPP at the stationary state over slotted times. This article tackles the above challenges with copula analysis. It not only presents a novel analytical framework to capture the temporal dependence of MMPP but also provides the exact copula-based solutions for single MMPP as well as the aggregate of independent MMPP. This theoretical contribution discloses functional dependence structure of MMPP. It also lays the foundation for many applications that rely on the temporal dependence of MMPP for adaptive control or predictive resource provisioning. We demonstrate case studies, with real-world trace data as well as simulation, to illustrate the practical significance of our analytical results.