  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.
