  The control of a network of signalized intersections is considered. Previous
work demonstrates that the so-called back-pressure control provides stability
guarantees, assuming infinite queues capacities. In this paper, we highlight
the failing of current back-pressure control under finite capacities by
identifying sources of non work-conservation and congestion propagation. We
propose the use of a normalized pressure which guarantees work conservation and
mitigates congestion propagation, while ensuring fairness at low traffic
densities, and recovering original back-pressure as capacities grow to
infinity. This capacity-aware back-pressure control allows to improve
performance as congestion increases, as indicated by simulation results, and
keeps the key benefits of back-pressure: ability to be distributed over
intersections and O(1) complexity.
