Queueing systems with random service rate

We consider a queue with the arrival process, the service time process and the service rate process as regenerative processes.We provide conditions for its stability, rates of convergence, finiteness of moments and functional limit theorems. This queue can model a queue serving ABR and UBR traffic in an ATMswitch; amultiple access channel with TDMA orCDMAprotocol and fading; a queue holding best effort or controlled and guaranteed traffic in a router in the integrated service architecture (ISA) of IP-based Internet and a scheduler in the router of a differentiated service architecture. In the process we also provide results for a queue with a leaky bucket controlled bandwidth scheduler. This result is of independent interest.We extend these results to feed-forward networks of queues. We also obtain the results when the arrival rate to the queue can be feedback controlled based on the congestion information in the queue (as in ABR service in the ATM networks or in the real time applications controlled by RTCP protocol in the Internet)