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We study a passenger-taxi double-ended queue with impatient passengers andtwo-point matching time in this paper. The system considered in this paper isdifferent from those considered in the existing literature, which fullyconsiders the matching time between passengers and taxis, and the taxi capacityof the system. The objective is to get the equilibrium joining strategy and thesocially optimal strategy under two information levels. For the practicalconsideration of the airport terminal scenario, two different informationlevels are considered. The theoretical results show that the passenger utilityfunction in the partially observable case is monotonic. For the complex form ofsocial welfare function of the partially observable case, we use a splitderivation. The equilibrium strategy and socially optimal strategy of theobservable case are threshold-type. Furthermore, some representative numericalscenarios are used to visualize the theoretical results. The numericalscenarios illustrate the influence of parameters on the equilibrium strategyand socially optimal strategy under two information levels. Finally, theoptimal social welfare for the two information levels with the same parametersare compared.

Equilibrium and Socially optimal of a double-sided queueing system with two-mass point matching time