CSci 435/535: Software Engineering
Longitudinal Traffic model: The IDM
This is copied from Treiber's webpage
Model Equations
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),
where
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
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.
Typical values that we use in the simulation are v0=120 km/h (you would chose,
e.g., 50 km/h for city traffic), T=1.8 s, a=1 m/s^2, b=3 m/s^2, s0=2 m, and
delta=4.
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 drivers ("rubbernecker 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.
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