IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v90y2018i1d10.1007_s11134-018-9582-1.html
   My bibliography  Save this article

The state-dependent M / G / 1 queue with orbit

Author

Listed:
  • Opher Baron

    (University of Toronto)

  • Antonis Economou

    (National and Kapodistrian University of Athens)

  • Athanasia Manou

    (Koç University)

Abstract

We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.

Suggested Citation

  • Opher Baron & Antonis Economou & Athanasia Manou, 2018. "The state-dependent M / G / 1 queue with orbit," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 89-123, October.
    • Handle: RePEc:spr:queues:v:90:y:2018:i:1:d:10.1007_s11134-018-9582-1
    DOI: 10.1007/s11134-018-9582-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-018-9582-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-018-9582-1?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. Binyamin Oz & Ivo Adan & Moshe Haviv, 2017. "A rate balance principle and its application to queueing models," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 95-111, October.
    2. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    3. Athanasia Manou & Antonis Economou & Fikri Karaesmen, 2014. "Strategic Customers in a Transportation Station: When Is It Optimal to Wait?," Operations Research, INFORMS, vol. 62(4), pages 910-925, August.
    4. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    5. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    6. Moeko Yajima & Tuan Phung-Duc, 2017. "Batch arrival single-server queue with variable service speed and setup time," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 241-260, August.
    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. Anatoly Nazarov & Ekaterina Fedorova & Olga Lizyura & Radmir Salimzyanov, 2023. "Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate," Mathematics, MDPI, vol. 11(14), pages 1-10, July.

    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. Opher Baron & Antonis Economou & Athanasia Manou, 2022. "Increasing social welfare with delays: Strategic customers in the M/G/1 orbit queue," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2907-2924, July.
    2. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    3. Sohner, Volkmar & Schneeweiss, Christoph, 1995. "Hierarchically integrated lot size optimization," European Journal of Operational Research, Elsevier, vol. 86(1), pages 73-90, October.
    4. Pradhan, Salil & Damodaran, Purushothaman & Srihari, Krishnaswami, 2008. "Predicting performance measures for Markovian type of manufacturing systems with product failures," European Journal of Operational Research, Elsevier, vol. 184(2), pages 725-744, January.
    5. Kumar Satyam & Ananth Krishnamurthy, 2013. "Performance analysis of CONWIP systems with batch size constraints," Annals of Operations Research, Springer, vol. 209(1), pages 85-114, October.
    6. Kris Lieckens & Nico Vandaele, 2016. "Differential evolution to solve the lot size problem in stochastic supply chain management systems," Annals of Operations Research, Springer, vol. 242(2), pages 239-263, July.
    7. Yang, Feng, 2010. "Neural network metamodeling for cycle time-throughput profiles in manufacturing," European Journal of Operational Research, Elsevier, vol. 205(1), pages 172-185, August.
    8. 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.
    9. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    10. Kavusturucu, Ayse & Gupta, Surendra M., 1999. "Manufacturing systems with machine vacations, arbitrary topology and finite buffers," International Journal of Production Economics, Elsevier, vol. 58(1), pages 1-15, January.
    11. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    12. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2022. "Delay analysis of a discrete-time single-server queue with an occasional extra server," Annals of Operations Research, Springer, vol. 310(2), pages 551-575, March.
    13. Olga Bountali & Antonis Economou, 2019. "Equilibrium threshold joining strategies in partially observable batch service queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 231-253, June.
    14. 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).
    15. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    16. 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).
    17. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    18. 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).
    19. Sunkyo Kim, 2011. "Modeling Cross Correlation in Three-Moment Four-Parameter Decomposition Approximation of Queueing Networks," Operations Research, INFORMS, vol. 59(2), pages 480-497, April.
    20. Czerny, Achim I. & Guo, Pengfei & Hassin, Refael, 2022. "Shall firms withhold exact waiting time information from their customers? A transport example," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 128-142.

    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:spr:queues:v:90:y:2018:i:1:d:10.1007_s11134-018-9582-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.