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

ABSTRACT

We study a passenger-taxi double-ended queue with negative passengers and two-point matching time. The system considered in this paper is different from those studied in the existing literature, which fully explores 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 investigated. 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 is compared.

KEYWORDS:

• $N$-policy
• negative passengers
• equilibrium strategies
• two-point matching time

Acknowledgments

We are grateful to the anonymous reviewers and editors for their constructive comments and feedback that help us improve the presentation and quality of this manuscript. This work was supported in partial by The Research start-up funds of Guilin University of Electronic Technology (No. UF21047Y), the Guangxi Young Teachers Basic Ability Improvement Project (No. 2022KY0191), and the Natural Sciences and Engineering Research Council of Canada (No. 315660).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada [No. 315660]; Guangxi Young Teachers Basic Ability Improvement Project [No. 2022KY0191]; The Research start-up funds of Guilin University of Electronic Technology [No. UF21047Y].