IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v253y2015icp324-344.html
   My bibliography  Save this article

Double orbit finite retrial queues with priority customers and service interruptions

Author

Listed:
  • Jain, Madhu
  • Bhagat, Amita
  • Shekhar, Chandra

Abstract

The present study deals with the double orbit finite capacity retrial queues with unreliable server. The system facilitates the arrival of two types of customers known as priority and non priority customers and can hold a maximum of L priority customers and K non-priority customers as per its capacity. The priority customers are served prior to the non-priority customers. Moreover, the server is unreliable which may breakdown while servicing either priority or non-priority customer. The failed server is sent for repair following threshold recovery policy to become as good as earlier. Both transient as well as steady state analysis of the model has been done using by matrix method. Various performance measures including queue length, reliability metrics, long run probabilities, etc. have been obtained using various state probabilities. The application of the model to cellular radio network has been discussed. The cost function has been constructed and optimized using meta heuristic approach. The sensitivity analysis of various performance indices has been performed as an illustration.

Suggested Citation

  • Jain, Madhu & Bhagat, Amita & Shekhar, Chandra, 2015. "Double orbit finite retrial queues with priority customers and service interruptions," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 324-344.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:324-344
    DOI: 10.1016/j.amc.2014.12.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314017202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.12.066?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. Madhu Jain & G.C. Sharma & Richa Sharma, 2012. "Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(2), pages 152-174.
    2. Leonenko, G.M., 2009. "A new formula for the transient solution of the Erlang queueing model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 400-406, February.
    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. 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.
    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. 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.
    2. Ahuja, Anjali & Jain, Anamika & Jain, Madhu, 2022. "Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 464-490.
    3. Dudin, Alexander & Kim, Chesoong & Dudin, Sergey & Dudina, Olga, 2015. "Priority retrial queueing model operating in random environment with varying number and reservation of servers," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 674-690.
    4. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

    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. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    2. 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.
    3. 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.
    4. Se Won Lee & Bara Kim & Jeongsim Kim, 2022. "Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication," Annals of Operations Research, Springer, vol. 310(2), pages 505-518, March.
    5. Dong-Yuh Yang & Po-Kai Chang, 2015. "A parametric programming solution to the -policy queue with fuzzy parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 590-598, March.
    6. Wee Meng Yeo & Xue-Ming Yuan & Joyce Mei Wan Low, 2017. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement," Annals of Operations Research, Springer, vol. 248(1), pages 553-578, January.
    7. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    8. 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.
    9. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.
    10. Lamia Lakaour & Djamil Aïssani & Karima Adel-Aissanou & Kamel Barkaoui, 2019. "M/M/1 Retrial Queue with Collisions and Transmission Errors," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1395-1406, December.
    11. 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.
    12. Baek, Jung Woo & Moon, Seung Ki & Lee, Ho Woo, 2014. "A time-dependent busy period queue length formula for the M/Ek/1 queue," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 98-104.
    13. 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.
    14. Bara Kim & Jeongsim Kim, 2016. "Analysis of the $$M^X/G/1$$ M X / G / 1 retrial queue," Annals of Operations Research, Springer, vol. 247(1), pages 193-210, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Konstantin Avrachenkov & Evsey Morozov, 2014. "Stability analysis of GI/GI/c/K retrial queue with constant retrial rate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 273-291, June.
    20. Rami Atar & Anat Lev-Ari, 2018. "Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 225-255, December.

    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:253:y:2015:i:c:p:324-344. 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.