Advanced Transportation Systems & Dynamic Traffic Assignment: User Equilibrium Kinetics, Cell Transmission Modeling, and Traffic Flow Hydrodynamics
Advanced Transportation Systems and Dynamic Traffic Assignment (DTA) evaluate time-varying spatial and temporal network traffic flows across urban transportation networks. Unlike static traffic assignment models that assume time-invariant demand and instantaneous path travel times, dynamic traffic assignment incorporates real-time congestion kinetics, queue propagation, bottleneck bottlenecking, and time-dependent route choice behaviors of drivers. According to Wardrop's First Principle of Dynamic User Equilibrium (DUE) , for each origin-destination (O-D) pair at departing time interval $t$, the dynamic travel cost $C_p(t)$ on all utilized paths $p \in P_k$ is equal and minimal, while no non-utilized path has a lower travel cost: $$C_p(t) \begin{cases} = \pi_k(t) & \text{if } f_p(t) > 0 \\ \ge \pi_k(t) & \text{if } f_p(t) = 0 \end{cases}$$ Where $f_p(t)$ is the time-dependent path flow rate and $\pi_k(t)$ is the minimum dynamic travel cost between O-D pair $k$ for...