COVARIANCE STRUCTURE OF INTERRUPTED MARKOV MODULATED POISSON PROCESS

Estimating the parameters of a seasonal Markov-modulated Poisson process

The Markov Modulated Poisson Process and Markov Poisson Cascade with Applications to Web Traffic Modeling

A Markov modulated Poisson Process (MMPP) is a Poisson process whose rate varies according to a Markov process. The nonhomogeneous MMPP developed in this article is a natural model for point processes whose events combine irregular bursts of activity with predictable (e.g. daily and hourly) patterns. We show how the MMPP may be viewed as a superposition of unobserved Poisson processes that are ...

Detecting Network Intrusion Using a Markov Modulated Nonhomogeneous Poisson Process

Network intrusion occurs when a criminal gains access to a customer's telephone, computer, bank, or other type of account. Detecting network intrusion is an important problem that has received little attention in the statistics literature. This article proposes a Markov modulated nonhomogeneous Poisson process (MMNHPP) to monitor transactions on a customer's account for deviations from the cust...

Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process

a NTT Information Sharing Platform Laboratories 3-9-11 Midori-cho, Musashino-shi, Tokyo 180-8585, Japan E-mail: [email protected] b Graduate School of Information Science, Nara Institute of Science and Technology 8916-5 Takayama, Ikoma, Nara 630-0101, Japan E-mail: [email protected] c Graduate School of Informatics, Kyoto University Kyoto 606-8501, Japan E-mail: taka...

Anomaly Detection in the WIPER System Using Markov Modulated Poisson Process

Cell phone call activity records the behavior of individuals, which reflects underlying human activity over time. Therefore this data displays multi-level periodicity, such as weekly, daily, hourly, etc. Simple stochastic models that rely on aggregate statistics are not able to differentiate between normal daily variations and legitimate anomalous (and potentially crisis) events. In this paper ...