A sensitivity-based solution algorithm for the network model of urban taxi services

The objective of this study is to develop an efficient solution algorithm for a network model for urban taxi services with elastic demand in a congested road network. This model can serve as a tool to evaluate the level of taxi service in terms of taxi utilization, waiting times of taxis and passengers, taxi demands, cost and revenue generation of taxis, with respect to the regulatory measures such as taxi fleet and fare control. The study proposes a new sensitivity-based solution algorithm in which the computation of the Jacobian matrix in a set of linear and nonlinear equations (SLNE) will take into account the characteristics of the combined network equilibrium model (CNEM). Sensitivity analysis is used to calculate the derivatives of the variables and constraint multipliers in the CNEM with respect to the perturbation parameters in the SLNE. Described is the formulation of the taxi model with elastic demand in a congested road network. The new sensitivity-based solution algorithm is proposed and a wide range of computational experiments are conducted to illustrate the computational efficiency of the proposed sensitivity-based algorithm over the original newtonian one.