System Time Minimization in Route Guidance with Elastic Market Penetration

Route planning and guidance (RPG) services are intended to provide benefits to their users, in the form of either convenience or, more importantly, travel time savings. The reduction in system travel time, if achieved, is a “side effect.” How should the transportation management agency then respond to these services? Under what circumstances should the agency encourage or discourage their implementation? A model to answer these questions is developed. Two ingredients are important in the model discussed. First, the market penetration of RPG is modeled in an elastic manner. Analogous to a supply-demand equilibrium, market penetration is determined endogenously in an equilibrium between the benefits and cost of acquiring the services. It is argued that the cost of RPG services could be used as a way to alter the elastic market penetration, and hence modify and, it is hoped, lower the total system congestion. Thus, a bilevel program to capture the situation is formulated. The lower-level program models the multiclass (equipped and unequipped) equilibrium problem with elastic market penetration. The upper-level program then minimizes the system travel time by using the cost of RPG services as a control variable. Numerical results of a small network are provided to illustrate the behavior of this model.