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Equilibrium Strategies and Optimal Control for a Double-Ended Queue

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  • Ying Shi

    (The School of Information, Zhejiang University of Finance and Economics, Hangzhou, P. R. China)

  • Zhaotong Lian

    (Faculty of Business Administration, University of Macau, Macau SAR, P. R. China)

Abstract

In this paper, we study a passenger–taxi matching queue system. The system is modeled as a birth-and-death process. Since the system is so complex, we mainly focus on numerical analysis. A centralized system and a decentralized one are considered. In the centralized system, the government sets thresholds for both passengers and taxis to maximize the social welfare. We analyze the performance measures of this model, discuss the range of two thresholds that ensures positive social welfare, and numerically give the upper bound of threshold. In the decentralized system, passengers and taxis determine whether to join the system or balk based on their individual utility functions. Further, we consider the government’s tax and subsidy to the taxi drivers. Numerical results show that the social welfare function in the centralized system is concave with respect to the thresholds and the government central planning benefits the society. In the decentralized system, no matter what the passenger and taxi arrival rates are, the social welfare is concave with respect to the taxi fare. Moreover, we analyze the effect of the arrival rates and the benefits of the tax and subsidy.

Suggested Citation

  • Ying Shi & Zhaotong Lian, 2016. "Equilibrium Strategies and Optimal Control for a Double-Ended Queue," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-18, June.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:03:n:s0217595916500226
    DOI: 10.1142/S0217595916500226
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    Cited by:

    1. Yang, Qiaoli & Qiao, Zheng & Yang, Bo & Shi, Zhongke, 2021. "Modeling and uncovering the passenger–taxi dynamic queues at taxi station with multiple boarding points using a Markovian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Qiao‐Chu He & Tiantian Nie & Yun Yang & Zuo‐Jun Shen, 2021. "Beyond Repositioning: Crowd‐Sourcing and Geo‐Fencing for Shared‐Mobility Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3448-3466, October.
    3. Hung Q. Nguyen & Tuan Phung-Duc, 2022. "Strategic customer behavior and optimal policies in a passenger–taxi double-ended queueing system with multiple access points and nonzero matching times," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 481-508, December.
    4. Yang, Qiaoli & Yang, Bo & Qiao, Zheng & Tang, Min-an & Gao, Fengyang, 2021. "Impact of possible random factors on queue behaviors of passengers and taxis at taxi stand of transport hubs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

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