  The control of a network of signalized intersections is considered. Previous
works proposed a feedback control belonging to the family of the so-called
back-pressure controls that ensures provably maximum stability given
pre-specified routing probabilities. However, this optimal back-pressure
controller (BP*) requires routing rates and a measure of the number of vehicles
queuing at a node for each possible routing decision. It is an idealistic
assumption for our application since vehicles (going straight, turning
left/right) are all gathered in the same lane apart from the proximity of the
intersection and cameras can only give estimations of the aggregated queue
length. In this paper, we present a back-pressure traffic signal controller
(BP) that does not require routing rates, it requires only aggregated queue
lengths estimation (without direction information) and loop detectors at the
stop line for each possible direction. A theoretical result on the Lyapunov
drift in heavy load conditions under BP control is provided and tends to
indicate that BP should have good stability properties. Simulations confirm
this and show that BP stabilizes the queuing network in a significant part of
the capacity region.
