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 Karandikar and Kulkarni. Queue length is modelled as a Brownian motion whose parameters are controlled by a finite state Markov chain. The process, termed a Markov modulated regulated Brownian motion, provides analytical solutions for steady state queue length distributions, overflow losses and idleness probabilities using boundary regulators. Applications of the model include queues with failure-prone servers and ATM statistical multiplexers with variable traffic loads.