Numerical Solutions to the Logit Lane Assignment Model

The Logit lane assignment model is a macroscopic model for multi-lane flow. This model assumes that drivers evaluate the utility of available lanes, and that each driver chooses the lane with highest utility. The utility of a lane increases with the speed of traffic, and is stochastic with Gumbel random component. Since the speed of traffic on a lane, and hence the attractively of a lane, decreases with the number of cars using the lane, a (dynamic) equilibrium forms. This equilibrium results in the lane choice of drivers and the assignment of traffic between lanes. Formally it is a Logit model. The traffic flow is assumed multi-class, and FIFO on each lane, but not all lanes are available to all driver classes. The paper will address the homogeneous case, far from on-and off-ramps or intersections, where all lanes are accessible to all users. It will be shown that in the homogeneous case the total density follows a LWR model even though all lane speeds are different. The model can be expressed as a system of conservation laws with a smooth flux function, but analytical solutions are generally not available with very few exceptions. Thus numerical methods are required in order to use the model for applications. The paper will explore numerical methods in the case of a regular section.