Performance analysis of a fluid queue with random service rate in discrete time

We consider a fluid queue in discrete time with random service rate. Such a queue has been used in several recent studies on wireless networks where the packets can be arbitrarily fragmented. We provide conditions on finiteness of moments of stationary delay, its Laplace-Stieltjes transform and various approximations under heavy traffic. Results are extended to the case where the wireless link can transmit in only a few slots during a frame.