  In this paper, we first present a centralized traffic control model based on
the emerging dynamic path flows. This new model in essence views the whole
target network as one integral piece in which traffic propagates based on
traffic flow dynamics, vehicle paths, and traffic control. In light of this
centralized traffic control concept, most requirements for the existing traffic
control coordination will be dropped in the optimal traffic control operations,
such as the common cycle length or offsets. Instead, the optimal traffic
control strategy across intersections will be highly adaptive over time to
minimize the total travel time and it can also prevent any short-term traffic
congestions according to the space-time characteristics of vehicle path flows.
A mixed integer linear programming (MILP) formulation is then presented to
model the propagations of path flows given a centralized traffic control
strategy. Secondly, a new approximated Lagrangian decomposition framework is
presented. Solving the proposed MILP model with the traditional Lagrangian
decomposition approach faces the leveraging challenge between the problem
tractability after decomposition and computing complexity. To address this
issue, we propose an approximate Lagrangian decomposition framework in which
the target problem is reformulated into an approximated problem by constructing
its complicating attributes into the objective function instead of in
constraints to reduce the computing complexity. The computing efficiency loss
of the objective function can be mitigated via multiple advanced computing
techniques. With the proposed approximated approach, the upper bound and tight
lower bound can be obtained via two customized dynamic network loading models.
In the end, one demonstrative and one real-world example are illustrated to
show the validness, robustness, and scalability of the new approach.
