Parallel queueing networks with Markov-modulated service speeds in heavy traffic

We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions