In many situations, the arrival rate or service rate is determined by a Poisson process whose parameter varies as a function of time. For example, if the arrival rate to a fast food restaurant varies ...

A Markov-modulated Poisson Process (MMPP) is a Poisson process that has its parameter controlled by a Markov process. These arrival processes are typical in communications modeling where time-varying ...

Fractional Poisson processes and stochastic modeling are important areas of study in probability theory and statistics, particularly in understanding complex systems that exhibit random behavior ...

Poisson processes: counting processes, definition as counting process with independent and stationary increments, compensated Poisson process as martingale, distribution of number of events in a given ...