Influence of Various Traffic Densities on 1/f Noise

Previously, we examined 1/f noise for a simple cellular automata model. For illustrative purposes, we considered a specific case of approaching a city. The case involves a traffic light where one continues on the main road, where additional cars are entering at the light. At this intersection an alternative route begins, which is longer, but where no additional cars are entering. In this paper we add a ‘slow to start’ model. We calculate the Fourier transform of the average velocity for each traffic light cycle. We consider different average ‘slow to start cases’ and obtain different results for different cases. All cases can be written as \(1/f^{\alpha }\). We check by least squares the value of \(\alpha \). We compare qualitatively our results to experiments. When we do not assume cars which are ‘slow to start’, the results differ from the experiment, but when we introduce ‘slow to start’ cars, the results are similar to the experimental values. We consider different densities of cars. There are different characteristics for low densities, mid range and high densities.