  Given the efficiency and equity concerns of a cordon toll, this paper
proposes a few alternative distance-dependent area-based pricing models for a
large-scale dynamic traffic network. We use the Network Fundamental Diagram
(NFD) to monitor the network traffic state over time and consider different
trip lengths in the toll calculation. The first model is a distance toll that
is linearly related to the distance traveled within the cordon. The second
model is an improved joint distance and time toll (JDTT) whereby users are
charged jointly in proportion to the distance traveled and time spent within
the cordon. The third model is a further improved joint distance and delay toll
(JDDT) which replaces the time toll in the JDTT with a delay toll component. To
solve the optimal toll level problem, we develop a simulation-based
optimization (SBO) framework. Specifically, we propose a simultaneous approach
and a sequential approach, respectively, based on the proportional-integral
(PI) feedback controller to iteratively adjust the JDTT and JDDT, and use a
calibrated large-scale simulation-based dynamic traffic assignment (DTA) model
of Melbourne, Australia to evaluate the network performance under different
pricing scenarios. While the framework is developed for static pricing, we show
that it can be easily extended to solve time-dependent pricing by using
multiple PI controllers. Results show that although the distance toll keeps the
network from entering the congested regime of the NFD, it naturally drives
users into the shortest paths within the cordon resulting in an uneven
distribution of congestion. This is reflected by a large clockwise hysteresis
loop in the NFD. In contrast, both the JDTT and JDDT reduce the size of the
hysteresis loop while achieving the same control objective.
