A traffic model is a
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
of real-world
traffic
Traffic comprises pedestrians, vehicles, ridden or herded animals, trains, and other conveyances that use public ways (roads) for travel and transportation.
Traffic laws govern and regulate traffic, while rules of the road include traffic ...
, usually, but not restricted to,
road traffic. Traffic modeling draws heavily on theoretical foundations like
network theory
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defi ...
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, i.e. the throughput of mobile units (e.g.
vehicle
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), wa ...
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. When traffic de ...
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: Traffic flow is assumed to depend on individual mobile units, i.e. cars, which are explicitly modeled
;
Macroscopic traffic flow model A Macroscopic traffic flow model is a mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, mean speed of a traffic stream, etc.. Such models are conventionally arrived at by integrating ...
: Only the
mass action or the
statistical
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
properties of a large number of units is analyzed
Examples
*
Biham–Middleton–Levine traffic model
The Biham–Middleton–Levine traffic model is a self-organizing cellular automaton traffic flow model. It consists of a number of cars represented by points on a lattice with a random starting position, where each car may be one of two types: t ...
*
Traffic generation model
*
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, ranging ...
*
Intelligent driver model
*
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 c ...
*
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 Two-fluid model is a macroscopic traffic flow model to represent traffic in a town/city or metropolitan area, put forward in the 1970s by Ilya Prigogine and Robert Herman.
There is also a two-fluid model which helps explain the behavior of superfl ...
See also
*
Braess's paradox
*
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 an vital role in the design of Mobile Ad Hoc Networks(MANET). Most of the times simulators ...
*
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 c ...
**
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
*
Traffic flow
*
Traffic wave
Traffic waves, 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 spot on t ...
*
Queueing theory
**
Traffic equations In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual nodes to be determined. Mitrani notes "if the ne ...
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. It features articles in the fields of politics, foreign affairs, business and the economy, culture and the arts, technology, and science.
It was founded in 1857 in Boston, ...
, date=December 2000
Traffic flow
Mathematical modeling