Concept and Structure of the Cell Transmission Model (CTM)
The Cell Transmission Model (CTM) is a numerical method designed to simulate and analyze traffic flow on road networks. Originally introduced by Carlos Daganzo, CTM serves as a discrete approximation to the kinematic wave equation, which is essential for predicting macroscopic traffic behavior. The model is particularly useful for evaluating the flow and density of traffic at various intermediate points over time, providing insights into traffic patterns and aiding in traffic management.
Structure of the Cell Transmission Model
Discretization of Road Segments
In CTM, a road is discretized into segments known as "cells," each of which can accommodate a specific number of vehicles. The length of a cell typically corresponds to the distance a vehicle can travel in a fixed time step under free-flow conditions. This discretization enables the model to simulate the progression of traffic across multiple cells over successive time intervals.
Flow Dynamics and Cell Interactions
Traffic flow between cells is governed by fundamental traffic flow principles, particularly the relationship between flow, density, and speed. The model operates using a triangular fundamental diagram, which describes the relationships among these variables. Each cell has a sending function, which dictates the maximum number of vehicles that can exit the cell, and a receiving function, determining the number of vehicles that can enter the cell. These functions take into account the density of the vehicles in the downstream cells.
First Order Approximation
CTM is recognized as a first-order discrete Godunov approximation of the kinematic wave equation. This means it approximates the continuous propagation of traffic waves through a discrete approach that is simple yet effective for many practical applications.
Enhancements and Variations
Lagged Cell Transmission Model (LCTM)
Recognizing the limitations of the original CTM, Daganzo introduced the Lagged Cell Transmission Model (LCTM), which offers a more accurate simulation. The LCTM incorporates lagged downstream density, which is taken from p time steps earlier than the current time, into the receiving function. This improved accuracy, especially when a triangular fundamental diagram is utilized.
Second Order Accuracy
When the highway is discretized with variable cell lengths, adjustments in the forward lag of the sending function become necessary to maintain the beneficial properties of the LCTM. The precise selection of backward and forward lags enhances the model's fidelity, achieving second-order accuracy in simulating traffic dynamics.
Software Implementations
CTM and its derivatives are implemented in various traffic management software tools, such as TRANSYT-14 and SIGMIX, which are used to evaluate and optimize traffic signal settings. These tools allow users to select from different traffic models, including CTM, for comprehensive traffic dynamics simulation.