Fluid flow models with state-dependent service rate

Abstract

Fluid-flow models with Markov-modulated source are widely used to describe queueing systems with bursty arrival traffic. Many systematic analyses assuming constant service rate have appeared in the literature recently In this paper, we will introduce an extended model in which the service rate is a function of queue length. A similar set of system differential equations involving queue length distributions and drift functions are derived from the generalization of the model with constant service rate. Furthermore, we investigate the relationship between the continuity of drift functions and the differentiability of queue length distributions. Applying these results to the system with two-state on-off source, a closed-form expression for the queue length distribution can be obtained. Specifically, we studied the linearly adaptive rate functions as an example to demonstrate the state-dependent service policy. Our results show that the adaptive service rate applied to a traffic shaper can result in smoother departure traffic than the constant service rate