The path-specific traffic equilibrium problem with generalized cost functions

The traffic equilibrium problem (TEP) is an essential module in transportation planning. This paper studies an extended TEP version, i.e the path-specific traffic equilibrium problem (PS-TEP), which has many applications in the real world. Due to inherent path interactions, the PS-TEP cannot be formulated as an optimization model but can be formulated as a variational inequality model. The corresponding user equilibrium conditions are characterized by the equal and minimum generalized path cost, which in turn can be expressed as a function of actual path costs and path-specific disutility. To interpret the PS-TEP as an extension of the TEP, an augmented network representation that includes a basic network (incurred actual path costs) and an additional virtual network (incurred path-specific disutility) is proposed. A path-based solution algorithm, called the gradient projection method, is modified for demonstration. Four path-specific cost schemes of the path-specific disutility are used for elaboration using the same framework. The numerical examples show that the user equilibrium conditions are fully satisfied. Future research should address the corresponding efficient solution algorithms.