Discrete Models of Traffic Flow (5-1)

Alternative Models 1

Static and Dynamic Extensions with Site Dependent Parameters

Despite its very simple form, the standard model of Nagel and Schrekenberg is capable of capturing many characteristics of single-lane traffic flow in surprizingly well. In real-life, there are not a single road but many wih crossings. The city road tends to be multi-lane. Every road has its own peculiarity with narrow segments and curves. there are traffic lights everywhere. It is natural to try to incorporate these various features into the standard model with suitable extension and modifications.

It is important that we distinguish two different categories of extensions, "static" and "dynamic", for the standard model.

In the static extension, we consider the locational change of traffic parameters in order to describe narrow segments, curved segments, inclinatons and construction sites. The parameters U and R become quantities that could change from one segment of a road to another. The treatment of traffic lights could be put into this category, we stretch the word "static" to include predictable time-periodic change of parameters.

In the dynamic extension, we consider such situations as two-way traffic that might be treated as segment and time dependent deceleration rate R, but its variation itself comes from the change of desity and flux of the opposite road. We can also consider the crossing at which there are inflow and outflow between the two roads. Rather than the modificaion of the parameter value, a new set of rules that treats such dynamical exchange of cars have to be introduced. Multiple-lane traffic also could be classified into this category.

Temporal Order within Single Time Step

Even apart from above mentioned extensions, there are some indefiniteness in the construction of discretized model of traffic flow that comes precisely from the temporal dicretization procedure itself. Since the time between two time steps represents small but finite passage of time in which plural events could take place in succession. There arize the problem of assigning the order of these events within a single time step.

For example, in the standard model, when the velocity of a car is decided from its distance from the preceeding car, should the location of this preceeding car be calculated from at the start of the time step, or at the end of the ime step, which is equialent to the start of the next time step? There is no ra priori eason to favor one over the other.

We can rather take advantage of this indefinitness, and consider it as different variants of discretized model that correspond to different physical situations.