Intelligent Driver Model
Encyclopedia
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 with other "intelligent" driver models such as Gipps' Model
, which loose realistic properties in the deterministic limit.
, 
denotes its position at time 
, and 
its velocity. Furthermore, 
gives the length of the vehicle. To simplify notation, we define the net distance 
, where 
refers to the vehicle directly in front of vehicle 
, and the velocity difference, or approaching rate, 
. For a simplified version of the model, the dynamics of vehicle 
are then described by the following two ordinary differential equation
s:
, 
, 
, 
, and 
are model parameters which have the following meaning:
The exponent
is usually set to 4.
can be separated into a free road term and an interaction term:
This leads to a driving behavior that compensates velocity differences while trying not to brake much harder than the comfortable braking deceleration
.
For this example, the following values are given for the equation's parameters.
The two ordinary differential equations are solved using Runge-Kutta methods of orders 1, 3, and 5 with the same time step, to show the effects of computational accuracy in the results.
This comparison shows that the IDM does not show extremely irrealistic properties such as negative velocities or vehicles sharing the same space even for from a low order method such as with the Euler's method (RK1). However, traffic wave
propagation is not as accurately represented as in the higher order methods, RK3 and RK 5. These last two methods show no significant differences, which lead to conclude that a solution for IDM reaches acceptable results from RK3 upwards and no additional computational requirements would be needed. None-the-less, when introducing heterogeneous vehicles and both jam distance parameters, this observation could not suffice.
Traffic flow
Traffic flow, in mathematics and civil engineering, is the study of interactions between vehicles, drivers, and infrastructure , with the aim of understanding and developing an optimal road network with efficient movement of traffic and minimal traffic congestion problems.-History:Attempts to...
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 with other "intelligent" driver models such as Gipps' Model
Gipps' Model
Gipps’ Model is a car-following model named after Peter G. Gipps who developed it in the late-1970s under S.R.C. grants at the at the University of Newcastle-Upon-Tyne and the Transport Studies Group at the University College London. It is based directly on driver behavior and expectancy for...
, which loose realistic properties in the deterministic limit.
Model definition
As a car-following model, the IDM describes the dynamics of the positions and velocities of single vehicles. For vehicle, denotes its position at time , and its velocity. Furthermore, gives the length of the vehicle. To simplify notation, we define the net distance , where refers to the vehicle directly in front of vehicle , and the velocity difference, or approaching rate, . For a simplified version of the model, the dynamics of vehicle are then described by the following two ordinary differential equationOrdinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s:
, , , , and are model parameters which have the following meaning:
- desired velocity
: the velocity the vehicle would drive at in free traffic - minimum spacing
: a minimum net distance that is kept even at a complete stand-still in a traffic jam - desired time headway
: the desired time headway to the vehicle in front - acceleration
- comfortable braking deceleration
The exponent
is usually set to 4.Model characteristics
The acceleration of vehicle can be separated into a free road term and an interaction term:- Free road behavior: On a free road, the distance to the leading vehicle
is large and the vehicle's acceleration is dominated by the free road term, which is approximately equal to 
for low velocities and vanishes as 
approaches 
. Therefore, a single vehicle on a free road will asymptotically approach its desired velocity 
.
- Behavior at high approaching rates: For large velocity differences, the interaction term is governed by
.
This leads to a driving behavior that compensates velocity differences while trying not to brake much harder than the comfortable braking deceleration
.- Behavior at small net distances: For negligible velocity differences and small net distances, the interaction term is approximately equal to
, which resembles a simple repulsive force such that small net distances are quickly enlarged towards an equilibrium net distance.
Solution Example
Let's assume a ring road with 50 vehicles. Then, vehicle 50 will follow vehicle 1. Initial speeds are given and since all vehicles are considered equal, vector ODEs are further simplified to:For this example, the following values are given for the equation's parameters.
| Description | Value |
|---|---|
| Desired velocity | 30 m/s |
| Safe time headway | 1.5 s |
| Maximum acceleration | 1.00 m/s2 |
| Desired deceleraton | 3.00 m/s2 |
| Acceleration exponent | 4 |
| Jam distance | 2 m |
| Vehicle length | 5 m |
The two ordinary differential equations are solved using Runge-Kutta methods of orders 1, 3, and 5 with the same time step, to show the effects of computational accuracy in the results.
This comparison shows that the IDM does not show extremely irrealistic properties such as negative velocities or vehicles sharing the same space even for from a low order method such as with the Euler's method (RK1). However, traffic wave
Traffic wave
Traffic waves, also called stop waves or traffic shocks, are travelling disturbances in the distribution of cars on a highway. Traffic waves usually travel backwards in relation to the motion of the cars themselves, or "upstream". The waves can also travel downstream, however, more commonly become...
propagation is not as accurately represented as in the higher order methods, RK3 and RK 5. These last two methods show no significant differences, which lead to conclude that a solution for IDM reaches acceptable results from RK3 upwards and no additional computational requirements would be needed. None-the-less, when introducing heterogeneous vehicles and both jam distance parameters, this observation could not suffice.