Last time we have looked at how four different parking strategies work when inflow of drivers is homogeneous. We have done similarly to what was done in [1, 2], though our angle was a bit different.

This time we have modified the approach further. Namely, now we allow you to randomize the inflow of drivers and explore how do the performance of these strategies change in nonhomogeneous society.

A quick video about stop-and-go waves and how they arise and how to prevent them. Spoiler: the solution is not that original.

Traffic problems are ones we all face every day and we can explore using Physics of Risk tools such as agent-based models. Here we will take a look at a couple simple parking strategies from [1, 2].

In the last post we have provided you with interactive app, which allows you to compare Euler method and Runge-Kutta 4th order method. Now we share a video by Good Vibrations, which discusses the exact derivation of the Runge-Kutta methods.

Apps in the last two posts (see here and here) differ in another important regard: the first app plots analytical solution of one ODE, while the second plots numerical solution of another ODE. Numerical solution is chosen, because it is impossible to obtain analytical solution.

Here, in this post, we will numerically solve ODE:

\begin{equation} \frac{d}{d t} x = - \left( x + a \right)^2 . \label{eq:rk4-ode} \end{equation}

It is simple enough to have analytical solution and thus we can compare two different numerical solution methods: Euler method and Runge-Kutta 4th order method.