Longitudinal Traffic model: The IDM

In this simulation, we used the Intelligent-Driver Model (IDM) to simulate the longitudinal dynamics, i.e., accelerations and braking decelerations of the drivers.

The IDM is a "car-following model", i.e., the traffic state at a given time is characterized by the positions, velocities, and the lane index of all vehicles. The decision of any driver to accelerate or to brake depends only on his own velocity, and on the "front vehicle" immediately ahead of him. Lane-changing decisions, however, depend on all neighboring vehicles. Specifically, the acceleration dv/dt of a given driver depends on his velocity v, on the distance s to the front vehicle, and on the velocity difference Delta v (positive when approaching),

IDM acceleration equation

where

relation for desired distance

The acceleration is divided into a "desired" acceleration a [1-(^v/_v₀)^delta] on a free road, and braking decelerations induced by the front vehicle. The acceleration on a free road decreases from the initial acceleration a to zero when approaching the "desired velocity" v0.

The braking term is based on a comparison between the "desired dynamical distance" s^*, and the actual gap s to the preceding vehicle. If the actual gap is approximatively equal to s^*, then the breaking deceleration essentially compensates the free acceleration part, so the resulting acceleration is nearly zero. This means, s^* corresponds to the gap when following other vehicles in steadily flowing traffic. In addition, s^* increases dynamically when approaching slower vehicles and decreases when the front vehicle is faster. As a consequence, the imposed deceleration increases with

decreasing distance to the front vehicle (one wants to maintain a certain "safety distance")
increasing own velocity (the safety distance increases)
increasing velocity difference to the front vehicle (when approaching the front vehicle at a too high rate, a dangerous situation may occur).

Model Parameters

The IDM has intuitive parameters:

desired velocity when driving on a free road, v0
desired safety time headway when following other vehicles, T
acceleration in everyday traffic, a
"comfortable" braking deceleration in everyday traffic, b
minimum bumper-to-bumper distance to the front vehicle, s0
acceleration exponent, delta.

In general, every "driver-vehicle unit" can have its individual parameter set, e.g.,

trucks are characterized by low values of v0, a, and b,
careful drivers drive at a high safety time headway T,
aggressive ("pushy") drivers are characterized by a low T in connection with high values of v0, a, and b.

Often two different types are sufficient to show the main phenomena. The standard parameters used in the simulations are the following:

Parameter	Value Car	Value Truck	Remarks
Desired velocity v₀	120 km/h	80 km/h	For city traffic, one would adapt the desired velocity while the other parameters essentially can be left unchanged.
Time headway T	1.5 s	1.7 s	Recommendation in German driving schools: 1.8 s; realistic values vary between 2 s and 0.8 s and even below.
Minimum gap s₀	2.0 m	2.0 m	Kept at complete standstill, also in queues that are caused by red traffic lights.
Acceleration a	0.3 m/s²	0.3 m/s²	Very low values to enhance the formation of stop-and go traffic. Realistic values are 1-2 m/s²
Deceleration b	3.0 m/s²	2.0 m/s²	Very high values to enhance the formation of stop-and go traffic. Realistic values are 1-2 m/s²

For more details, see the scientific reference for the IDM, or the Wikipedia article.

Martin Treiber

Last modified: Thu May 26 12:12:25 CEST 2011