Abstract We consider the problem of minimizing the delay of jobs moving through a directed graph of service nodes. In this problem, each node may have several links and is constrained to serve one link at a time. As jobs move through the network, they can pass through a node only after they have been serviced by that node. The objective is to minimize the delay jobs incur sitting in queues waiting to be serviced. Two distinct approaches to this problem have emerged from respective work in queuing theory and dynamic scheduling: the backpressure algorithm and schedule-driven control. In this paper, we present a hybrid approach of those two methods that incorporates the stability of queuing theory into a schedule-driven control framework. We then demonstrate how this hybrid method outperforms the other two in a real-time traffic signal control problem, where the nodes are traffic lights, the links are roads, and the jobs are vehicles. We show through simulations that, in scenarios with heavy congestion, the hybrid method results in 50% and 15% reductions in delay over schedule-driven control and backpressure respectively. A theoretical analysis also justifies our results.