Modeling Urban Taxi Services with Multiple User Classes and Vehicle Modes

This paper extends the model of urban taxi services in congested networks to the case of multiple user classes, multiple taxi modes, and customer hierarchical modal choice. This paper consider both taxis and normal traffic in the network. There are several classes of customers with different values of time and money, and several modes of taxi services with distinct combinations of service area restrictions and fare levels. To model the taxi traffic, it is assumed that a customer, having taken a taxi (similar to normal traffic), will try to minimize the individual travel cost from origin to destination; and a vacant taxi, having set down a customer, will try to minimize the individual expected search cost that is required to meet the next customer. Both mileage-based and congestion-based taxi fare charging mechanisms are considered in a unified framework. We propose a simultaneous mathematical formulation of two equilibrium sub-problems for the model. One sub-problem is a combined network equilibrium model (CNEM) that describes the hierarchical logit mode choice model of occupied taxis and normal traffic, together with the vacant taxi distributions in the network. The other sub-problem is a set of linear and nonlinear equations (SLNE), which ensures the satisfaction of the relation between taxi and customer waiting times, the relation between customer demand and taxi supply for each taxi mode, and the taxi service time constraints. The CNEM can be formulated as a variational inequality program that is solvable by means of a Block Gauss-Seidel decomposition approach coupled with the method of successive averages, whereas the SLNE can be solved by a Newtonian algorithm with a line search. A numerical example is used to demonstrate the effectiveness of the proposed methodology.