IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp308-328.html
   My bibliography  Save this article

On a batch matching system with impatient servers and boundedly rational customers

Author

Listed:
  • Chai, Xudong
  • Liu, Liwei
  • Chang, Baoxian
  • Jiang, Tao
  • Wang, Zhen

Abstract

In this paper we consider a batch matching system with impatient servers and boundedly rational customers, which is essentially a double-ended batch service system. Each server is responsible for a batch of customers and serves them instantaneously. Especially, we assume that the servers have the characteristic of ”impatience”, which will lead to incomplete batch processing of each service. To derive the stationary distribution of system states, we combine two methods (called probability generating function method and G-matrix method), and some main performance measures are captured. In addition, we assume the customers are boundedly rational, that is, they are unable to estimate their sojourn times and utilities accurately. To deal, a logit model is employed to model this characteristic of the customers, and by which, we obtain the customers’ equilibrium joining fraction which is compared with the equilibrium joining probability of fully rational customers afterwards. Depending on whether the service is visible or invisible, we conduct some numerical analyses to show main parameters’ impact on equilibrium fraction, along with some intuitive explanations. Finally, to make the system viable economically, a function of service provider’s utility is developed and several numerical plots are presented to study the impact of several main parameters on the utility. Through the PSO (Particle Swarm Optimization) algorithm, we numerically obtain the maximum utility point within a certain range of multiple parameters.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:308-328
    DOI: 10.1016/j.amc.2019.02.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031930102X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2019.02.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Uri Yechiali, 1971. "On Optimal Balking Rules and Toll Charges in the GI / M /1 Queuing Process," Operations Research, INFORMS, vol. 19(2), pages 349-370, April.
    2. 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.
    3. James M. Dobbie, 1961. "Letter to the Editor---A Doubled-Ended Queuing Problem of Kendall," Operations Research, INFORMS, vol. 9(5), pages 755-757, October.
    4. Antonio Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2012. "A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 937-954, December.
    5. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    6. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    7. B. Kashyap, 1967. "Further results for the double ended queue," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 11(1), pages 168-186, December.
    8. Tingliang Huang & Gad Allon & Achal Bassamboo, 2013. "Bounded Rationality in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 263-279, May.
    9. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    10. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    11. Tao Jiang & Liwei Liu & Yuanyuan Zhu, 2018. "Analysis of a Batch Service Polling System in a Multi-phase Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 699-718, June.
    12. Xuanming Su, 2008. "Bounded Rationality in Newsvendor Models," Manufacturing & Service Operations Management, INFORMS, vol. 10(4), pages 566-589, May.
    13. 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.
    14. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Garmani, Hamid & Ait Omar, Driss & El Amrani, Mohamed & Baslam, Mohamed & Jourhmane, Mostafa, 2020. "Analysis of a dynamics duopoly game with two content providers," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. 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).
    3. Bu, Qihui & Sun, Yun & Chai, Xudong & Liu, Liwei, 2020. "Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    4. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    4. Tingliang Huang & Gad Allon & Achal Bassamboo, 2013. "Bounded Rationality in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 263-279, May.
    5. 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.
    6. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    7. Eliran Sherzer & Yoav Kerner, 2018. "Customers’ abandonment strategy in an M / G / 1 queue," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 65-87, October.
    8. 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).
    9. Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
    10. Zaiming Liu & Can Cao & Shan Gao, 2019. "Equilibrium Joining Strategies in the Geo / Geo K /1 Queueing System," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    11. 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.
    12. Jordan Tong & Daniel Feiler, 2017. "A Behavioral Model of Forecasting: Naive Statistics on Mental Samples," Management Science, INFORMS, vol. 63(11), pages 3609-3627, November.
    13. 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).
    14. Shiliang Cui & Senthil Veeraraghavan, 2016. "Blind Queues: The Impact of Consumer Beliefs on Revenues and Congestion," Management Science, INFORMS, vol. 62(12), pages 3656-3672, December.
    15. Jinting Wang & Ke Sun, 2022. "Optimal pricing and capacity sizing for online service systems with free trials," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 57-86, March.
    16. Fajardo, Val Andrei & Drekic, Steve, 2015. "Controlling the workload of M/G/1 queues via the q-policy," European Journal of Operational Research, Elsevier, vol. 243(2), pages 607-617.
    17. Mirko Kremer & Francis de Véricourt, 2022. "Mismanaging diagnostic accuracy under congestion," ESMT Research Working Papers ESMT-22-01, ESMT European School of Management and Technology.
    18. Mirko Kremer & Laurens Debo, 2016. "Inferring Quality from Wait Time," Management Science, INFORMS, vol. 62(10), pages 3023-3038, October.
    19. W. Rogiest & K. Laevens & J. Walraevens & H. Bruneel, 2015. "Random-order-of-service for heterogeneous customers: waiting time analysis," Annals of Operations Research, Springer, vol. 226(1), pages 527-550, March.
    20. Li, Feng & Du, Timon C. & Wei, Ying, 2020. "Enhancing supply chain decisions with consumers’ behavioral factors: An illustration of decoy effect," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:308-328. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.