Robust scheduling and congestion control for flexible queueing networks

We consider a general flexible queueing network in which each queue can be processed by several servers, which in turn can serve multiple queues. Important special cases of this model include open multiclass queueing networks [11] and flexible parallel server systems [16]. A scheduling policy decides how server capacities are allocated over time. It is robust if it does not depend on network parameters such as arrival and service rates. In this paper, we propose a robust and throughput-optimal scheduling policy for general flexible queueing networks when service rates depend only on the queues. The policy balances all the flows in the network, by minimizing an objective function using stochastic gradient projection over time. We also propose a joint robust scheduling and congestion control policy to maximize the utility of the network. Finally, we provide simulation results to show the performance of the algorithms.