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The Double-Ended Queue with Bulk Service and Limited Waiting Space

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  • B. R. K. Kashyap

    (University of Jodhpur, Jodhpur, India)

Abstract

The double-ended queue involving taxis and customers at a taxi-stand has been considered under the assumption that there is limited waiting space both for customers and for taxis, and that the taxis “serve” the customers in bulk. The arrivals of customers and taxis are taken as general and Poisson respectively. Two separate probability generating functions have been defined for the cases when (i) taxis are waiting and (ii) when customers are waiting and their Laplace transforms (L.T.'s) as well as that of the probability for empty state have been obtained by using the supplementary variable technique. Cases of Erlangian and Poisson arrivals of customers and of single-seated taxis are considered as particular cases.

Suggested Citation

  • B. R. K. Kashyap, 1966. "The Double-Ended Queue with Bulk Service and Limited Waiting Space," Operations Research, INFORMS, vol. 14(5), pages 822-834, October.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:5:p:822-834
    DOI: 10.1287/opre.14.5.822
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    Cited by:

    1. Xu, Zhengtian & Yin, Yafeng & Zha, Liteng, 2017. "Optimal parking provision for ride-sourcing services," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 559-578.
    2. Fabien Leurent, 2019. "Microeconomics of a taxi service in a ring-shaped city," Working Papers hal-02047269, HAL.
    3. 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).
    4. Antonio Di Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2018. "A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation," Mathematics, MDPI, vol. 6(5), pages 1-23, May.
    5. Lu Wang & Vidyadhar Kulkarni, 2020. "Fluid and diffusion models for a system of taxis and customers with delayed matching," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 101-131, October.
    6. Mohammadreza Nazari & Alexander L. Stolyar, 2019. "Reward maximization in general dynamic matching systems," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 143-170, February.
    7. Shi, Ying & Lian, Zhaotong, 2016. "Optimization and strategic behavior in a passenger–taxi service system," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1024-1032.
    8. Philipp Afèche & Adam Diamant & Joseph Milner, 2014. "Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks," Operations Research, INFORMS, vol. 62(5), pages 1179-1201, October.
    9. Burak Büke & Hanyi Chen, 2017. "Fluid and diffusion approximations of probabilistic matching systems," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 1-33, June.
    10. Chai, Xudong & Liu, Liwei & Chang, Baoxian & Jiang, Tao & Wang, Zhen, 2019. "On a batch matching system with impatient servers and boundedly rational customers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 308-328.
    11. Chai, Xudong & Jiang, Tao & Chang, Baoxian & Liu, Liwei, 2021. "On a multiple priorities matching system with heterogeneous delay sensitive individuals," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    12. 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.
    13. Geni Gupur, 2022. "On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-16, April.
    14. Xin Liu, 2019. "Diffusion approximations for double-ended queues with reneging in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 49-87, February.
    15. Guodong Pang & Alexander L. Stolyar, 2016. "A service system with on-demand agent invitations," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 259-283, April.
    16. 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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