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, Extreme value theory, Spectral analysis, Tandem of fluid queues, Gumbel distribution, Binet-Cauchy formula, Time varying service rates
Network models, stochastic (msc 90B15)
Logistics (theme 3)
Queueing Systems
Service Optimization and Quality

Bosman, J.W, & Núñez Queija, R. (2014). A spectral theory approach for extreme value analysis in a tandem of fluid queues. Queueing Systems, 78(2), 121–154. doi:10.1007/s11134-014-9395-9