  Decentralized intersection control techniques have received attention in the
literature as tools that address scalability issues of network intersection
control. Chief among these techniques are backpressure (BP) control algorithms,
which were originally developed of for large wireless networks. In addition to
being light-weight computationally, they come with guarantees of performance at
the network level, specifically network-wide stability. The dynamics in
backpressure control are represented using networks of point queues and this
also applies to all of the applications to traffic control. As such, BP in
traffic fail to capture the spatial distribution of vehicles along the
intersection links and, consequently, spill-back dynamics. This paper derives a
position weighted backpressure (PWBP) control policy for network traffic
applying continuum modeling principles of traffic dynamics and thus capture the
spatial distribution of vehicles along network roads and spill-back dynamics.
PWBP inherits the computational advantages of traditional BP. To prove
stability of PWBP, (i) a Lyapunov functional that captures the spatial
distribution of vehicles is developed; (ii) the capacity region of the network
is formally defined in the context of macroscopic network traffic; and (iii) it
is proved, when exogenous arrival rates are within the capacity region, that
PWBP control is network stabilizing. We conduct comparisons against a
real-world adaptive control implementation for an isolated intersection.
Comparisons are also performed against other BP approaches in addition to
optimized fixed timing control at the network level. These experiments
demonstrate the superiority of PWBP over the other control policies in terms of
capacity region, network-wide delay, congestion propagation speed,
recoverability from heavy congestion (outside of the capacity region), and
response to incidents.
