A fluid model analysis of streaming media in the presence of time-varying bandwidth

This paper is motivated by the increasing popularity of streaming media applications that are offered via the Internet. Packet streams generated by media application servers are distorted due to variability in the available bandwidth; at the receiving end, a play-out buffer compensates for the distortion. We study the dynamics of this system in a queueing-theoretical setting, using fluid analysis. To this end, we consider a model in which a constant bit-rate (CBR) media application is streamed 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 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 playout-buffer level that provides a probabilistic guarantee for undisturbed playback.