Modeling the bilateral micro-searching behavior for urban taxi services using the absorbing Markov chain approach

This paper develops a mathematical model that is based on the absorbing Markov chain approach to describe taxi movements, taking into account the stochastic searching processes of taxis in a network. The local searching behavior of taxis is specified by a logit form, and the O-D demand of passengers is estimated as a logit model with a choice of taxi meeting point. The relationship between customer and taxi waiting times is modeled by a double-ended queuing system. The problem is solved with a set of non-linear equations, and some interesting results are presented. The research provides a novel and potentially useful formulation for describing the urban taxi services in a network.