Robust Control of Arrivals into a Queuing Network

Queuing networks have been widely-used to model congestion in transportation systems. Due to their interconnected nature, delays in a queuing network can propagate as customers traverse through the network; similarly, downstream resources can be underutilized due to poor control policies. This paper considers the regulation of arrivals into a queuing network in order to maintain a desired level of occupancy (queue length) in the system. The dynamics of the queuing network is represented by a fluid-flow model, which is then used to develop a robust controller for tracking the desired queue length. The controller is based on a sliding mode control approach, with predictor-based feedback to account for propagation delays. For a single queue, we determine sufficient conditions for tracking the queue length, and bounds on the tracking error. We also present an analysis of the tracking performance for queues in tandem. We demonstrate our approach for the example of airport surface congestion control. The proposed robust control framework is based on a queuing network model of the airport, and is used to tactically manage aircraft departures in order to reduce congestion on the airport tarmac.