  We study a passenger-taxi double-ended queue with impatient passengers and
two-point matching time in this paper. The system considered in this paper is
different from those considered in the existing literature, which fully
considers the matching time between passengers and taxis, and the taxi capacity
of the system. The objective is to get the equilibrium joining strategy and the
socially optimal strategy under two information levels. For the practical
consideration of the airport terminal scenario, two different information
levels are considered. The theoretical results show that the passenger utility
function in the partially observable case is monotonic. For the complex form of
social welfare function of the partially observable case, we use a split
derivation. The equilibrium strategy and socially optimal strategy of the
observable case are threshold-type. Furthermore, some representative numerical
scenarios are used to visualize the theoretical results. The numerical
scenarios illustrate the influence of parameters on the equilibrium strategy
and socially optimal strategy under two information levels. Finally, the
optimal social welfare for the two information levels with the same parameters
are compared.
