Modeling urban taxi services in congested road networks with elastic demand

This paper extends the simple network model of urban taxi services proposed by Yang and Wong (Yang, H., Wong, S.C., 1998. Transportation Research B 32, 235-246). The extensions include incorporation of congestion effects, customer demand elasticity, reformulation of the model and development of a new solution algorithm. Instead of the previous characterization of pure taxi movements in a network by a system of nonlinear equations, a two-level model formulation is proposed for taxi movements in congested road networks. The bi-level problem is a combined network equilibrium model that describes simultaneous movements of vacant and occupied taxis as well as normal traffic in a user-optimal manner for given total customer generation from each origin and total customer attraction to each destination. The upper-level problem is a set of linear and nonlinear equations ensuring that the relation between taxi and customer-waiting times and the relation between customer demand and taxi supply are satisfied. The lower-level problem can be solved by the conventional multi-class combined trip distribution and assignment algorithm, whereas the upper-level problem is solved by a Newtonian algorithm with line search. A numerical example is presented to illustrate the proposed model and algorithm and demonstrate the characteristics of the taxi services in congested road networks.