The Markov modulated regulated Brownian motion: A second-order fluid flow model of a finite buffer

A second-order fluid flow model of a queue with finite capacity buffer and variable net input process is presented, based on the previous work of Kara ndikar and Kulkarni (1995). Queue length is modelled as a Brownian motion w hose parameters are controlled by a finite state Markov chain. The process, termed a Markov modulated regulated Brownian motion (MMRBM), provides anal ytical solutions for steady state queue length distributions, overflow loss es and idleness probabilities using boundary regulators. Applications of th e model include queues with failure-prone servers and ATM statistical multi plexers with variable traffic loads.