Queues with service rate controlled by a delayed feedback

We consider a single queue with a Markov modulated Poisson arrival process. Its service rate is controlled by a scheduler. The scheduler receives the workload information from the queue after a delay. This queue models the buffer on an earth station in a satellite network where the scheduler resides in the satellite. We obtain the conditions for stability, rates of convergence to the stationary distribution and the finiteness of the stationary moments. Next we extend these results to the system where the scheduler schedules the service rate among several competing queues based on delayed information about the workloads in the different queues.