A multiperiod dynamic model of taxi services with endogenous service intensity

This paper presents a spatially aggregated multiperiod taxi service model with endogenous service intensity. The whole day service period is divided into a number of subperiods; during each subperiod, taxi supply and customer demand characteristics are assumed to be uniform. Customer demand is period-specific and described as a function of waiting time and taxi fare. Taxi operating cost for each work shift consists of two components: one component a function of total service time and the other component period-dependent. Each taxi driver can work for one or more shifts each day and freely chooses the starting and ending time of each shift. Equilibrium of taxi services is obtained when taxi drivers cannot increase their individual profits by changing their individual working schedules. A novel clock network representation is proposed to characterize the multiperiod taxi service equilibrium problem. The problem of interest is formulated as a network equilibrium model with path-specific costs and arc-capacity constraints, which can be solved using conventional nonlinear network flow optimization methods. The proposed model can ascertain at equilibrium the service intensity and utilization rate of taxis and the level of service quality throughout the day. The information obtained is useful for the prediction of the effects of alternative government regulations on the equilibrium of demand and supply in the urban taxi industry.