Lecture

Cell Transmission Model (CTM)

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Description

This lecture introduces the Cell Transmission Model (CTM) as a numerical method to solve the kinematic wave equation in traffic flow modeling. It covers the fundamental diagram of traffic engineering, calibration, demand and supply capacities, spatial and temporal modeling, macroscopic traffic variables, motorway structure, partitioning into cells, flow conservation, inter-cell flow, and an overview of CTM. The CTM is explained in detail, including the flow-density relationship, flow conservation equations, and the fundamental diagram for each cell.

In MOOC

Intro to Traffic Flow Modeling and Intelligent Transport Systems

Travelers in large cities experience significant congestion during their everyday trips. Expanding roads and infrastructure is not a long-lasting remedy to urban congestion. This course will focus on understanding traffic congestion and will explore ways to improve mobility through advanced traffic management schemes. As we all experience, congestion is a highly complex process without a single explanation. An interesting question is: “Can we describe these complex interactions with simple and elegant ways?

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Related concepts (26)

Traffic flow

In mathematics and transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems.

Microscopic traffic flow model

Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics. In contrast, to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units, so the dynamic variables of the models represent microscopic properties like the position and velocity of single vehicles. Also known as time-continuous models, all car-following models have in common that they are defined by ordinary differential equations describing the complete dynamics of the vehicles' positions and velocities .

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

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