IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v236y2014i2p561-572.html
   My bibliography  Save this article

Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers

Author

Listed:
  • Gao, Shan
  • Wang, Jinting

Abstract

This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented.

Suggested Citation

  • Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:561-572
    DOI: 10.1016/j.ejor.2014.01.065
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171400112X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.01.065?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. Dudin, A. N. & Krishnamoorthy, A. & Joshua, V. C. & Tsarenkov, G. V., 2004. "Analysis of the BMAP/G/1 retrial system with search of customers from the orbit," European Journal of Operational Research, Elsevier, vol. 157(1), pages 169-179, August.
    2. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    3. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    4. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    5. Xiaoyong Wu & Percy Brill & Myron Hlynka & Jinting Wang, 2005. "An M/G/1 retrial queue with balking and retrials during service," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 30-51.
    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. Shan Gao & Jinting Wang & Tien Van Do, 2016. "A repairable retrial queue under Bernoulli schedule and general retrial policy," Annals of Operations Research, Springer, vol. 247(1), pages 169-192, December.
    2. Legros, Benjamin, 2021. "Routing analyses for call centers with human and automated services," International Journal of Production Economics, Elsevier, vol. 240(C).
    3. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    4. Shweta Upadhyaya, 2020. "Investigating a general service retrial queue with damaging and licensed units: an application in local area networks," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 716-745, September.
    5. Benjamin Legros, 2021. "Routing analyses for call centers with human and automated services," Post-Print hal-03605426, HAL.
    6. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    7. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    8. P. Rajadurai & V. M. Chandrasekaran & M. C. Saravanarajan, 2016. "Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 197-223, March.

    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. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    2. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    3. T. Deepak, 2015. "On a retrial queueing model with single/batch service and search of customers from the orbit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 493-520, July.
    4. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.
    5. Ke, Jau-Chuan & Huang, Hsin-I & Lin, Chuen-Horng, 2007. "On retrial queueing model with fuzzy parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 272-280.
    6. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    7. V. Radhamani & B. Sivakumar & G. Arivarignan, 2022. "A Comparative Study on Replenishment Policies for Perishable Inventory System with Service Facility and Multiple Server Vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 229-265, March.
    8. Chesoong Kim & Valentina Klimenok & Alexander Dudin, 2014. "A G/M/1 retrial queue with constant retrial rate," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 509-529, July.
    9. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    10. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    11. F. Avram & A. Gómez-Corral, 2006. "On bulk-service MAP/PH L,N /1/N G-Queues with repeated attempts," Annals of Operations Research, Springer, vol. 141(1), pages 109-137, January.
    12. Nitin Kumar & F. P. Barbhuiya & U. C. Gupta, 2020. "Unified killing mechanism in a single server queue with renewal input," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 246-259, March.
    13. Bin Liu & Jie Min & Yiqiang Q. Zhao, 2023. "Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 65-105, June.
    14. Junping Li, 2024. "Birth–Death Processes with Two-Type Catastrophes," Mathematics, MDPI, vol. 12(10), pages 1-17, May.
    15. Altay, Nezih & Green III, Walter G., 2006. "OR/MS research in disaster operations management," European Journal of Operational Research, Elsevier, vol. 175(1), pages 475-493, November.
    16. Chi, Hong & Li, Jialian & Shao, Xueyan & Gao, Mingang, 2017. "Timeliness evaluation of emergency resource scheduling," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1022-1032.
    17. Kim, Chesoong & Klimenok, Valentina I. & Orlovsky, Dmitry S., 2008. "The BMAP/PH/N retrial queue with Markovian flow of breakdowns," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1057-1072, September.
    18. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    19. Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
    20. Caunhye, Aakil M. & Nie, Xiaofeng & Pokharel, Shaligram, 2012. "Optimization models in emergency logistics: A literature review," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 4-13.

    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:2:p:561-572. 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.