  In traffic signal control, flow-based (optimizing the overall flow) and
pressure-based methods (equalizing and alleviating congestion) are commonly
used but often considered separately. This study introduces a unified framework
using Lyapunov control theory, defining specific Lyapunov functions
respectively for these methods. We have found interesting results. For example,
the well-recognized back-pressure method is equal to differential queue lengths
weighted by intersection lane saturation flows. We further improve it by adding
basic traffic flow theory. Rather than ensuring that the control system be
stable, the system should be also capable of adaptive to various performance
metrics. Building on insights from Lyapunov theory, this study designs a reward
function for the Reinforcement Learning (RL)-based network signal control,
whose agent is trained with Double Deep Q-Network (DDQN) for effective control
over complex traffic networks. The proposed algorithm is compared with several
traditional and RL-based methods under pure passenger car flow and heterogenous
traffic flow including freight, respectively. The numerical tests demonstrate
that the proposed method outperforms the alternative control methods across
different traffic scenarios, covering corridor and general network situations
each with varying traffic demands, in terms of the average network vehicle
waiting time per vehicle.
