Solution Example
Let's assume a ring road with 50 vehicles. Then, vehicle 1 will follow vehicle 50. 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 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.
Read more about this topic: Intelligent Driver Model
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