A Multi-Lane Multi-Class Mixing Model for Traffic Flow on Highways

On multi-lane highways we consider long term lane choice for heterogeneous classes of
vehicles and the coupling with the equilibrium speed at which each lane is travelling. The
research is a continuation of earlier work by van Wageningen-Kessels and Wilson. We use
a static model to allow us to predict how drivers choose certain lanes and the speeds at
which they travel. We have two main components in our model: i) modelling the
macroscopic properties of vehicle classes; and ii) modelling drivers' behavioural choices.
For i), both speed-density and speed-spacing are investigated whilst for ii) driver behaviour
is determined by utility functions and the use of logit choice probabilities.
Within our model framework there are a number of possible approaches: the initial approach
is to study a discrete model with M classes and N lanes. We perform investigations into how
different utility functions affect the mixing and the speed of classes in each lane and the
number of solution combinations (corresponding to traffic patterns) that exist. Special regard
has been given to comparing soft and hard max utility functions. In order to investigate
analytical solutions to our model, certain simplifications have been concentrated on: e.g.,
initially, as a starter problem, we have looked at single class, two lane systems and derived
theory that counts the solutions. Further analytic and numerical investigation is required for
larger numbers of vehicle classes and lanes.
As the number of vehicle classes is increased, we obtain finer and finer descriptions of
different behavioural types. In the limit, it seems logical to examine continuous classes
instead of discrete classes, using probability density functions or vehicles' parameters.
Finally, we will introduce spatio-temporal features to our model to capture congestion
patterns that change in time and distance down the highway.