A traffic model is a
mathematical model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
of real-world
traffic
Traffic is the movement of vehicles and pedestrians along land routes.
Traffic laws govern and regulate traffic, while rules of the road include traffic laws and informal rules that may have developed over time to facilitate the orderly an ...
, usually, but not restricted to,
road traffic
Traffic is the movement of vehicles and pedestrians along land routes.
Traffic laws govern and regulate traffic, while rules of the road include traffic laws and informal rules that may have developed over time to facilitate the orderly and ...
. Traffic modeling draws heavily on theoretical foundations like
network theory
In mathematics, computer science, and network science, network theory is a part of graph theory. It defines networks as Graph (discrete mathematics), graphs where the vertices or edges possess attributes. Network theory analyses these networks ...
and certain theories from physics like the
kinematic wave
In gravity and pressure driven fluid dynamical and geophysical mass flows such as ocean waves, avalanches, debris flows, mud flows, flash floods, etc., kinematic waves are important mathematical tools to understand the basic features of the associ ...
model. The interesting quantity being modeled and measured is the
traffic flow
In 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 ai ...
, i.e. the throughput of mobile units (e.g.
vehicle
A vehicle () is a machine designed for self-propulsion, usually to transport people, cargo, or both. The term "vehicle" typically refers to land vehicles such as human-powered land vehicle, human-powered vehicles (e.g. bicycles, tricycles, velo ...
s) per time and transportation medium capacity (e.g. road or lane width). Models can teach researchers and engineers how to ensure an optimal flow with a minimum number of
traffic jam
Traffic congestion is a condition in transport that is characterized by slower speeds, longer trip times, and increased vehicular queueing. Traffic congestion on urban road networks has increased substantially since the 1950s, resulting in m ...
s.
Traffic models often are the basis of a
traffic simulation Traffic simulation or the simulation of transportation systems is the computer simulation, mathematical modeling of transportation systems (e.g., freeway junctions, arterial routes, roundabouts, downtown grid systems, etc.) through the application o ...
.
Types
;
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 rep ...
: Traffic flow is assumed to depend on individual mobile units, i.e. cars, which are explicitly modeled
;
Macroscopic traffic flow model: Only the
mass action or the
statistical
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
properties of a large number of units is analyzed
Examples
*
Biham–Middleton–Levine traffic model
*
Traffic generation model
A traffic generation model is a stochastic model of the traffic flows or data sources in a communication network, for example a cellular network or a computer network. A packet generation model is a traffic generation model of the packet flows o ...
*
History of network traffic models
*
Traffic mix
Traffic mix is a traffic model in telecommunication engineering and teletraffic theory.
Definitions
A traffic mix is a modelisation of user behaviour. In telecommunications, user behaviour activities may be described by a number of systems, rang ...
*
Intelligent driver model
In traffic flow modeling, the intelligent driver model (IDM) is a time-continuous car-following model for the simulation of freeway and urban traffic. It was developed by Treiber, Hennecke and Helbing in 2000 to improve upon results provided wit ...
*
Network traffic Network traffic or data traffic is the amount of data moving across a network at a given point of time. Network data in computer networks is mostly encapsulated in network packets, which provide the load in the network. Network traffic is the main ...
*
Three-phase traffic theory
Three-phase traffic theory is a theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways. Kerner describes three pha ...
*
Two-fluid model
See also
*
Braess's paradox
Braess's paradox is the observation that adding one or more roads to a road network can slow down overall road traffic, traffic flow through it. The paradox was first discovered by Arthur Cecil Pigou, Arthur Pigou in 1920, and Stigler's law of ep ...
*
Gridlock
Gridlock is a form of traffic congestion where continuous queues of vehicles block an entire network of intersecting streets, bringing traffic in all directions to a complete standstill. The term originates from a situation possible in a grid ...
*
Mobility model
Mobility models characterize the movements of mobile users with respect to their location, velocity and direction over a period of time. These models play a vital role in the design of Mobile ad hoc network, Mobile Ad Hoc Networks(MANET). Most of ...
*
Network traffic Network traffic or data traffic is the amount of data moving across a network at a given point of time. Network data in computer networks is mostly encapsulated in network packets, which provide the load in the network. Network traffic is the main ...
**
Network traffic simulation Network traffic simulation is a process used in telecommunications engineering to measure the efficiency of a communications network.
Overview
Telecommunications systems are complex real-world systems, containing many different components which in ...
*
Traffic bottleneck
A traffic bottleneck is a localized disruption of vehicular traffic on a street, road, or highway. As opposed to a traffic jam, a bottleneck is a result of a specific physical condition, often the design of the road, badly timed traffic lights, ...
*
Traffic flow
In 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 ai ...
*
Traffic wave
Traffic waves, which are also called stop waves, ghost jams, traffic snakes or traffic shocks, are traveling disturbances in the distribution of cars on a highway. Traffic waves travel backwards relative to the cars themselves. Relative to a fixed ...
*
Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because th ...
**
Traffic equations
References
External links
*http://math.mit.edu/projects/traffic/
*
*{{cite web, url=https://www.theatlantic.com/magazine/archive/2000/12/the-physics-of-gridlock/378457/, title=The Physics of Gridlock, website=
The Atlantic
''The Atlantic'' is an American magazine and multi-platform publisher based in Washington, D.C. It features articles on politics, foreign affairs, business and the economy, culture and the arts, technology, and science.
It was founded in 185 ...
, date=December 2000
Traffic flow
Mathematical modeling