Modeling urban taxi services with multiple user classes and vehicle modes

Abstract

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. 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. The multi-class multi-mode formulation allows the modeling of both mileage-based and congestion-based taxi fare charging mechanisms in a unified framework, and can more realistically model most urban taxi services, which are charged on the basis of both time and distance. The introduction of multiple taxi modes can also be used to model the differentiation between luxury taxis and normal taxis by their respective service areas and customer waiting times. 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 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. The SLNE can be solved by a Newtonian algorithm with a line search. The CNEM is formulated as a special case of the general travel demand model so that it is possible to incorporate the taxi model into an existing package as an add-on module, in which the algorithm for the CNEM is built in practice. Most of the parameters are observable, given that such a calibrated transport planning model exists. A numerical example is used to demonstrate the effectiveness of the proposed methodology. © 2008 Elsevier Ltd. All rights reserved.