A spectral theory approach for extreme value analysis in a tandem of fluid queues

We consider a model to evaluate performance of streaming media over an unreliable network. Our model consists of a tandem of two fluid queues. The first fluid queue is a Markov modulated fluid queue that models the network congestion, and the second queue represents the play-out buffer. For this model the distribution of the total amount of fluid in the congestion and play-out buffer corresponds to the distribution of the maximum attained level of the first buffer. We show that, under proper scaling and when we let time go to infinity, the distribution of the total amount of fluid converges to a Gumbel extreme value distribution. From this result, we derive a simple closed-form expression for the initial play-out buffer level that provides a probabilistic guarantee for undisturbed play-out

Fluid Queue Driven by an M

This paper deals with the stationary analysis of a fluid queue driven by an M/M/1 queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions