Fluid flow models with state-dependent service rate for data-handling systems

The fluid-flow model with a Markov-modulated source is widely used to describe queueing systems with bursty input traffic. Many systematic analyses concerning the cases of constant service rate have appeared in the literature recently. We propose a general model in which the service rate is a function of the queue length. A new set of differential equations including the drift-distribution relationship, the boundary equations, and the drift conservation law is developed based on this model. Applying these results to a system with two-state on-off source traffic, a general solution for the queue length distribution can be obtained. We also study a system with an adaptive service rate; and its queue length distribution and delay distribution are discussed, followed by some comparisons with those of a constant service rate from the simulation results