In this research, we propose a unified framework for (1) analyzing dynamical and stationary patterns subject to different control strategies; and (2) designing control strategies based on understanding of traffic patterns. We will describe the evolution of traffic dynamics in a signalized network by the Link Transmission Model (Yperman et al., 2006; Yperman, 2007), which, together with Newell's simplified kinematic wave model (Newell, 1993), is another formulation of the network kinematic wave theory based on the LWR model. In (Jin, 2014), two continuous formulations of LTM were derived from the Hopf-Lax formula for the Hamilton- Jacobi equation of the LWR model. Then we will (1) analytically derive macroscopic fundamental diagrams (MFD) for stationary traffic patterns with different network topologies, road conditions, driving behaviors, and signal settings; (2) quantify congestion mitigation effects of different signal settings, including cycle lengths, green splits,  and offsets, as well as speed limits and road lengths; (3) formulate an optimization problem to find optimal road, speed limit, and signal control parameters under certain demand levels, and (4) develop a set of simple decision-support tools for arterial network improvement.

The objective of this research is to evaluate the impacts of connected and autonomous vehicles (CAVs) on the performance of signalized networks at the aggregate level. CAVs are expected to improve alleviate traffic congestion, but their impacts are usually evaluated at the microscopic level, for example, through the design of optimal vehicle trajectories or optimal operation of individual intersections. In this proposal, we aim to develop a new performance evaluation framework through network fundamental diagrams (NFD), which capture the relationship between the average flow-rate and density at the network level. In particular, we will study how individual advisory speed limits of connected vehicles and different start-up and clearance behaviors of autonomous vehicles can increase the network capacity and reduce the start-up and clearance lost times. This research will take advantage of a microscopic simulation platform based on Newell's car-following model that incorporates different bounded acceleration (start-up) and aggressiveness (clearance). Connected vehicles' individual advisory speed limits are determined by a feedback control strategy which incorporates traffic signal information and loop detector data. Different start-up and clearance behaviors of autonomous vehicles are implemented by changing their acceleration bounds and aggressiveness when traffic lights turn yellow. Under each combination of technologies, we determine the NFD in time-independent stationary states with periodic vehicle trajectories. A goal is to determine whether their impacts are additive or alternative.