Busy period, congestion analysis and loss probability in fluid queues

Stochastic fluid flow models and in particular those driven by Markov chains have been intensively studied in the last two decades. This chapter analyzes congestion when the buffer content is described by means of a Markov modulated fluid flow model in the stationary regime. It describes a methodology to compute exactly the loss probability of a finite-capacity system. The approach is based on the computation of hitting probabilities jointly with the peak level reached during a busy period, both in the infinite and finite buffer case. The chapter considers a classical fluid queue with infinite buffering capacity. This allows us to describe the buffer fluctuations and introduce the notation and the variables necessary to study the fluid queue when the buffer is finite.