Linear Dependence of User Equilibrium Routes in the Transportation Network

User equilibrium (UE) models are widely used in network flow assignment in transportation engineering. For a given UE solution, the link flow pattern is unique, although the flows of entire routes may have many solutions. On the basis of linear substitution relationships detected between the equilibrated travel routes, this study proposes a new, efficient approach to find a maximum set of independent UE routes, referred to as “the set of basic routes.” The basic route set is associated with a basis of the linear space of route flow solutions, which plays an important role in the sensitivity analysis of the UE models. The linear relationships are observed within a specific structure composed of a set of grouped alternative segments (GAS). Certain properties of the GAS structure are derived. A simple process for generating the basic routes is provided by using the features of the GAS. Numerical results on several networks demonstrate that using the GAS structure to find the set of independent UE routes can be efficient.