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

TL;DR

This paper analyzes a passenger-taxi double-ended queue with two-point matching time, deriving equilibrium and socially optimal strategies under different information levels, and illustrating how parameters influence these strategies through numerical examples.

Contribution

It introduces a novel analysis of a queueing system considering matching time and taxi capacity, with strategies characterized under partial and full information scenarios.

Findings

Equilibrium and socially optimal strategies are threshold-type.

Passenger utility function is monotonic in the partially observable case.

Numerical results show parameter effects on strategies and social welfare.

Abstract

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.