Efficient frontier of route choice for modeling the equilibrium under travel time variability with heterogeneous traveler preferences

Travelers consider the average duration and the reliability of travel time when choosing their route. However, the relative importance of average travel time and reliability not only depends on the purpose of the trip, but also varies from one person to another. Users seek to minimize their travel costs leading to an equilibrium condition in which they choose routes in such a way that they cannot reduce the general cost of their own trip. In this paper, we adopt the concept of the efficient frontier to represent the equilibrium route choice of the heterogeneous users in a network under travel time variability. Then, we use the primary properties of the efficient frontier to propose a mathematical formulation for the route choice problem for a discrete or continuous distribution of sensitivity of users to variations in route travel times. An analytical-based algorithm is designed to assign the heterogeneous demand to the network. Efficiency of the proposed algorithm in solving the route choice problem is also compared in a numerical example with a classic iterative method with a smoothing factor.