Modeling taxi services with smartphone-based e-hailing applications

Traditionally, customers always hail empty-cruising taxis on streets, which may offer low levels of comfort and efficiency especially during rush hours or rainy days. Thanks to the advance of smartphone technology, the e-hailing applications, which enable customers to hail taxis through their smartphones, become popular globally. To provide a systematic account of the impact of e-hailing applications' wide adoption on the taxi system, we first propose a spatial equilibrium model that not only balances the supply and demand of taxi services but also captures both the taxi drivers' and customers' possible adoption of the newly-emerging e-hailing applications in a well-regulated taxi market. We then prove the existence of the proposed equilibrium, and further provide an algorithm to solve it. An extensive equilibrium model with elastic taxi-customer demands is also proposed. Lastly, a numerical example is presented to compare the taxi services with and without the e-hailing application and evaluate two types of e-hailing applications.