The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Fluid models for single buffer systems
Frontiers in queueing
A TANDEM FLUID QUEUE WITH GRADUAL INPUT
Probability in the Engineering and Informational Sciences
Mean first passage times in fluid queues
Operations Research Letters
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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 queuing-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 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 buffers 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.