Microscopic Model

Figure: In IDM, we simulate motion of each individual vehicle. Since this model is based on traditional car-following model, the relationship with the leading vehicle plays an important role in this model.

Intelligent Driver Model (IDM)

IDM is one of the most widely used microscopic models to simulate the motion of an individual vehicle in a traffic flow. In this model, each vehicle's state is described with position and speed at the given time step.


Vehicle = {position, speed}


Also, there are six additional variables to describe the trait of the vehicle.


  1. Minimum desired distance to leading vehicle,

  2. Desired time to move forward with current speed,

  3. Upper bound of the acceleration,

  4. Comfortable braking deceleration,

  5. Target speed it wants to maintain,

  6. Length of this vehicle


Then, assuming there is no lane change, and that each vehicle just follows its leading vehicle, IDM computes the acceleration term at the current time step using the relationship with the leading vehicle. That is, it first computes the position and speed delta to the leading vehicle, and then uses these terms and all the additional variables to compute optimal space between the vehicle and the leading vehicle. Then, the acceleration term is computed based on this optimal space.

Since all of the operations used here are differentiable, we do not have to worry about its differentiability. However, we could observe negative speed when we purely used this model, we clamped the negative speed to zero, and thus gradient becomes zero there. Please see our paper for more details.