Cell Transmission Model (CTM) is a popular numerical method proposed by Carlos Daganzo[1] to solve the kinematic wave equation.
[5] CTM predicts macroscopic traffic behavior on a given corridor by evaluating the flow and density at finite number of intermediate points at different time steps.
The flow across the cells is determined based on μ(k) and λ(k), two monotonic functions that uniquely define the fundamental diagram as shown in Figure 1.
However, CTM replicates discontinuities and shock that take a span of few cells of space but moves at correct speed predicted by the Kinematic wave equation.
For example, in TRANSYT-14 (Note not to be confused with TRANSYT-7F releases), the user is allowed to choose traffic models including CTM, Platoon Dispersion...etc.
when the highway is discritized with variable cell lengths, then one should introduce forward lag for the sending function to preserve the good properties of LCTM.
Newell [10] proposed an exact method to solve the kinematic wave equation based on cumulative curves only at either ends of the corridor, without evaluating any intermediate points.