IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v25y2017i1d10.1007_s11750-016-0428-x.html
   My bibliography  Save this article

Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience

Author

Listed:
  • R. Sudhesh

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • P. Savitha

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • S. Dharmaraja

    (Indian Institute of Technology Delhi)

Abstract

A two-heterogeneous servers queue with system disaster, server failure and repair is considered. In addition, the customers become impatient when the system is down. The customers arrive according to a Poisson process and service time follows exponential distribution. Each customer requires exactly one server for its service and the customers select the servers on fastest server first basis. Explicit expressions are derived for the time-dependent system size probabilities in terms of the modified Bessel function, by employing the generating function along with continued fraction and the identity of the confluent hypergeometric function. Further, the steady-state probabilities of the number of customers in the system are deduced and finally some important performance measures are obtained.

Suggested Citation

  • R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0428-x
    DOI: 10.1007/s11750-016-0428-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-016-0428-x
    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/s11750-016-0428-x?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. R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    2. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    3. Ke, Jau-Chuan & Liu, Tzu-Hsin & Wu, Chia-Huang, 2015. "An optimum approach of profit analysis on the machine repair system with heterogeneous repairmen," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 40-51.
    4. Mor Armony & Amy R. Ward, 2010. "Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems," Operations Research, INFORMS, vol. 58(3), pages 624-637, June.
    5. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
    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. 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.
    2. Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, December.
    3. Raina Raj & Vidyottama Jain, 2024. "Resource optimization for MMAP[c]/PH[c]/S catastrophic queueing model with PH retrial times," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1192-1223, September.

    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. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    2. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    3. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    4. 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.
    5. Jiang Tao, 2018. "Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters," Journal of Systems Science and Information, De Gruyter, vol. 6(4), pages 349-365, August.
    6. Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, December.
    7. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    8. Xu Jia & Liu Liwei & Zhu Taozeng, 2018. "Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 69-84, February.
    9. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik & Andreas Plank, 2020. "Approximations in Performance Analysis of a Controllable Queueing System with Heterogeneous Servers," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    10. Dongyuan Zhan & Gideon Weiss, 2018. "Many-server scaling of the N-system under FCFS–ALIS," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 27-71, February.
    11. Atkinson, Mariam K. & Saghafian, Soroush, 2019. "Who Should See the Patient? On Discretionary Patient-Provider Assignments in Hospitals," Working Paper Series rwp19-037, Harvard University, John F. Kennedy School of Government.
    12. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    13. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    14. J. G. Dai & Pengyi Shi, 2019. "Inpatient Overflow: An Approximate Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 894-911, October.
    15. Mor Armony & Guillaume Roels & Hummy Song, 2021. "Pooling Queues with Strategic Servers: The Effects of Customer Ownership," Operations Research, INFORMS, vol. 69(1), pages 13-29, January.
    16. R. Sudhesh & A. Azhagappan, 2018. "RETRACTED ARTICLE: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 787-806, November.
    17. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
    18. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    19. Laura A. McLay & Maria E. Mayorga, 2013. "A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 205-220, May.
    20. Dinard van der Laan, 2015. "Assigning Multiple Job Types to Parallel Specialized Servers," Tinbergen Institute Discussion Papers 15-102/III, Tinbergen Institute.

    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:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0428-x. 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.