Control of fluid queues

We study fluid queues from the perspective of dynamical systems. Following an approach outlined in [Bro] and [BGG99], the dynamics are described with stochastic differential equations driven by Poisson arrival processes. One advantage of this approach is that it allows us to employ techniques from optimal stochastic control to solve queueing problems. We make connections between these subjects explicit through concrete applications in traffic shaping, admission control, and dynamic round-robin scheduling. In the process, we will develop a new stochastic differential equation model for fluid circular buffers and well as synchronization primitives like the binary semaphore. We consider stability and consistency concerns associated with numerically approximating optimal controls when a closed form solution is unavailable. Finally, we introduce a concept of conditional optimal control which when paired with a classical traffic modeling approach, allows us to develop queueing controls for fluid queues which are driven by traffic with general statistics and are optimal in a restricted sense.