IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v236y2014i1p177-189.html
   My bibliography  Save this article

A tollbooth tandem queue with heterogeneous servers

Author

Listed:
  • He, Qi-Ming
  • Chao, Xiuli

Abstract

We study a tandem queueing system with K servers and no waiting space in between. A customer needs service from one server but can leave the system only if all down-stream servers are unoccupied. Such a system is often observed in toll collection during rush hours in transportation networks, and we call it a tollbooth tandem queue. We apply matrix-analytic methods to study this queueing system, and obtain explicit results for various performance measures. Using these results, we can efficiently compute the mean and variance of the queue lengths, waiting time, sojourn time, and departure delays. Numerical examples are presented to gain insights into the performance and design of the tollbooth tandem queue. In particular, it reveals that the intuitive result of arranging servers in decreasing order of service speed (i.e., arrange faster servers at downstream stations) is not always optimal for minimizing the mean queue length or mean waiting time.

Suggested Citation

  • He, Qi-Ming & Chao, Xiuli, 2014. "A tollbooth tandem queue with heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 236(1), pages 177-189.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:177-189
    DOI: 10.1016/j.ejor.2014.01.049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714000885
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.01.049?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. Benjamin Melamed, 1986. "Note---A Note on the Reversibility and Duality of Some Tandem Blocking Queueing Systems," Management Science, INFORMS, vol. 32(12), pages 1648-1650, December.
    2. Gu, Weihua & Cassidy, Michael J. & Li, Yuwei, 2012. "On the capacity of highway checkpoints: Models for unconventional configurations," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1308-1321.
    3. Papadopoulos, H. T. & O'Kelly, M. E. J., 1993. "Exact analysis of production lines with no intermediate buffers," European Journal of Operational Research, Elsevier, vol. 65(1), pages 118-137, February.
    4. Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
    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. Olivier Nataf & Lieven Moor & Rosanne Vanpée, 2018. "Was Regulation (EC) No 1060/2009 on Credit Rating Agencies effective?," Journal of Banking Regulation, Palgrave Macmillan, vol. 19(4), pages 299-316, November.
    2. Baoxian Chang & Tao Jiang & Qingqing Ye & Xudong Chai & Liwei Liu, 2020. "Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1145-1167, September.
    3. Baoxian Chang & Qingqing Ye & Jun Lv & Tao Jiang, 2019. "Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 479-501, October.

    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. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    2. Tao Jiang, 2018. "Analysis of a Tollbooth Tandem Queue with Two-Class Customers and Two Heterogeneous Dedicated Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-21, December.
    3. Gu, Weihua & Cassidy, Michael J., 2013. "Maximizing bus discharge flows from multi-berth stops by regulating exit maneuvers," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 254-264.
    4. Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    5. Hu, Sangen & Shen, Minyu & Gu, Weihua, 2023. "Impacts of bus overtaking policies on the capacity of bus stops," Transportation Research Part A: Policy and Practice, Elsevier, vol. 173(C).
    6. Xiuli Chao & Michael Pinedo, 1992. "On reversibility of tandem queues with blocking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 957-974, December.
    7. Shen, Minyu & Gu, Weihua & Hu, Sangen & Cheng, Han, 2019. "Capacity approximations for near- and far-side bus stops in dedicated bus lanes," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 94-120.
    8. Weihua Gu & Michael J. Cassidy & Yuwei Li, 2015. "Models of Bus Queueing at Curbside Stops," Transportation Science, INFORMS, vol. 49(2), pages 204-212, May.
    9. Ilker Topcu, Y. & Ulengin, Fusun & Kabak, Özgür & Ekici, Sule Onsel & Unver, Berna, 2020. "A decision support methodology for increasing the efficiency of the largest border crossing between Europe and Turkey," Research in Transportation Economics, Elsevier, vol. 80(C).
    10. P. Patrick Wang, 2000. "Workload distribution of discrete‐time parallel queues with two servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 440-454, August.
    11. Qi‐Ming He & Jingui Xie & Xiaobo Zhao, 2012. "Priority queue with customer upgrades," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 362-375, August.
    12. Baoxian Chang & Qingqing Ye & Jun Lv & Tao Jiang, 2019. "Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 479-501, October.

    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:ejores:v:236:y:2014:i:1:p:177-189. 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: http://www.elsevier.com/locate/eor .

    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.