Discrete Models of Traffic Flow (5-2)

Alternative Models 2

Two Indefiniteness and Two Alternative Models

We can think of two types of indefiniteness.

The first one concerns with what we have already mentioned, the ordering of updates among various cars. In the standard model, a car 's velocity os updated with the preceeding car freezed in the current position. There could be another limit of treating the preceeding car as if it already finished the motion. We might view these two as representing two different types of driving habits in different culture with diffrent mentality. This leads to a model with mixed ordering update that interpolate between these two extremes. This is the model by Abe, Cheon and Seba, which we shall treat in later section.

The second type of indefiniteness concerns the order of three rules to decide the velocity of a car. Since there are two types of decelerations, and the ordering in the standard model is rather arbitrary, another ordering might worth looking at. This possibility is considered in the model of Nishimura, Cheon and Seba.

Here, we first look into the model of Nishimura et al.. Readers will find that this seemingly trifling reordering does cause a change in the dynamics and even results in a new phase structure.

It must be added in rush that the attempt of modifying the rules of standard model is not started here by us. On the contrary, the whole business of discrete modelling of traffic flow has revolved around the standard model. Attemps to make the model more realistic by including finer modifications have reached the point of equipting the traffic authorities at several countries with very realistic traffic simulators which are ultimately derived from the standard model. There are also studies of such objects as aunt trail based on a modifid version of the standard model.

We are not attempting to add one more ellaboration to the already large pile of variants of the standard model. The main shortcommings of the standard model in comparison with the real traffic is in the two-phase structure it predicts. Is there any simple way to understand the dynamics behind the three-phase structure of real-life traffic in transparent manner, without introducing miliard of fine tuning to the standard model. That is the question we pose to ourselves in our attempts.