Microscopic traffic flow model explained
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.
Car-following models
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
. It is assumed that the input stimuli of the drivers are restricted to their own velocity
, the net distance (bumper-to-bumper distance)
s\alpha=x\alpha-1-x\alpha-\ell\alpha-1
to the leading vehicle
(where
denotes the vehicle length), and the velocity
of the leading vehicle. The
equation of motion of each vehicle is characterized by an acceleration function that depends on those input stimuli:
\ddot{x}\alpha(t)=
\alpha(t)=F(v\alpha(t),s\alpha(t),v\alpha-1(t),s\alpha-1(t))
In general, the driving behavior of a single driver-vehicle unit
might not merely depend on the immediate leader
but on the
vehicles in front. The equation of motion in this more generalized form reads:
\alpha(t)=f(x\alpha(t),v\alpha(t),x\alpha-1(t),v\alpha-1(t),\ldots,
(t),
(t))
Examples of car-following models
Cellular automaton models
Cellular automaton (CA) models use integer variables to describe the dynamical properties of the system. The road is divided into sections of a certain length
and the time is
discretized to steps of
. Each road section can either be occupied by a vehicle or empty and the dynamics are given by updated rules of the form:
(the simulation time
is measured in units of
and the vehicle positions
in units of
).
The time scale is typically given by the reaction time of a human driver,
. With
fixed, the length of the road sections determines the granularity of the model. At a complete standstill, the average road length occupied by one vehicle is approximately 7.5 meters. Setting
to this value leads to a model where one vehicle always occupies exactly one section of the road and a velocity of 5 corresponds to
, which is then set to be the maximum velocity a driver wants to drive at. However, in such a model, the smallest possible acceleration would be
\Deltax/(\Deltat)2=7.5m/s2
which is unrealistic. Therefore, many modern CA models use a finer spatial discretization, for example
, leading to a smallest possible acceleration of
.
Although cellular automaton models lack the accuracy of the time-continuous car-following models, they still have the ability to reproduce a wide range of traffic phenomena. Due to the simplicity of the models, they are numerically very efficient and can be used to simulate large road networks in real-time or even faster.
Examples of cellular automaton models
See also
Notes and References
- 10.1016/0191-2615(81)90037-0. 0191-2615. 15. 2. 105–111. Gipps. P. G.. A behavioural car-following model for computer simulation. Transportation Research Part B: Methodological. 2022-02-17. 1981.
- 10.1103/physreve.62.1805. 1063-651X. 62. 2 Pt A. 1805–1824. Treiber. null. Hennecke. null. Helbing. null. Congested traffic states in empirical observations and microscopic simulations. Physical Review E. August 2000. 11088643. cond-mat/0002177. 2000PhRvE..62.1805T. 1100293.
- 10.1109/IV48863.2021.9575314 . 2021 IEEE Intelligent Vehicles Symposium (IV) . 496–501 . Isha . Most. Kaniz Fatema . Shawon . Md. Nazirul Hasan . Shamim . Md. . Shakib . Md. Nazmus . Hashem . M.M.A. . Kamal . M.A.S. . A DNN Based Driving Scheme for Anticipatory Car Following Using Road-Speed Profile . 2021 IEEE Intelligent Vehicles Symposium (IV) . July 2021.
