IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v21y2021i4d10.1007_s12351-019-00519-8.html
   My bibliography  Save this article

Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)

Author

Listed:
  • Madhu Jain

    (Indian Institute of Technology Roorkee)

  • Sandeep Kaur

    (Guru Nanak Dev University)

  • Parminder Singh

    (Guru Nanak Dev University)

Abstract

In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present an overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:4:d:10.1007_s12351-019-00519-8
    DOI: 10.1007/s12351-019-00519-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-019-00519-8
    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/s12351-019-00519-8?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. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    2. S. W. Fuhrmann, 1984. "Technical Note—A Note on the M / G /1 Queue with Server Vacations," Operations Research, INFORMS, vol. 32(6), pages 1368-1373, December.
    3. M. Jain & Shweta Upadhyaya, 2012. "Optimal repairable M X /G/1 queue with Bernoulli feedback and setup," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(6), pages 679-702.
    4. Shan Gao & Jinting Wang & Wei Wayne Li, 2014. "An M/G/1 Retrial Queue With General Retrial Times, Working Vacations And Vacation Interruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-25.
    5. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    6. Gautam Choudhury & Mitali Deka, 2016. "A batch arrival unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 24(1), pages 33-72.
    7. Charan Jeet Singh & Madhu Jain & Binay Kumar, 2014. "Analysis of M X / G / 1 queueing model with balking and vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 19(2), pages 154-173.
    8. Offer Kella, 1989. "The threshold policy in the M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 111-123, February.
    9. M. J. Fischer, 1977. "An Approximation to Queueing Systems with Interruptions," Management Science, INFORMS, vol. 24(3), pages 338-344, November.
    10. 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.
    11. Gautam Choudhury & Mitali Deka, 2015. "A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 318-347.
    12. Madhu Jain & G.C. Sharma & Varsha Rani, 2016. "Maximum entropy approach for an unreliable M X /G/1 queueing system with Bernoulli vacation, restricted admission and delayed phase repair under N-policy," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 23(4), pages 407-442.
    13. M. Senthil Kumar & R. Arumuganathan, 2010. "An M X /G/1 retrial queue with two-phase service subject to active server breakdowns and two types of repair," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 8(3), pages 261-291.
    14. Jau-Chuan Ke & Kai-Bin Huang & Ching-Chang Kuo, 2017. "Reliability-based measures for a batch-arrival queue with an unreliable server and delayed repair under randomised vacations," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 27(4), pages 500-525.
    15. Li, Hui & Yang, Tao, 1995. "A single-server retrial queue with server vacations and a finite number of input sources," European Journal of Operational Research, Elsevier, vol. 85(1), pages 149-160, August.
    16. P. Rajadurai & M. Varalakshmi & M.C. Saravanarajan & V.M. Chandrasekaran, 2015. "Analysis of M [X] /G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(1), pages 19-41.
    17. B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    18. M. Balasubramanian & R. Arumuganathan, 2011. "Steady state analysis of a bulk arrival general bulk service queueing system with modified M-vacation policy and variant arrival rate," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 11(4), pages 383-407.
    19. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    20. Gautam Choudhury & Sangeeta Kalita, 2009. "A two-phase queueing system with repeated attempts and Bernoulli vacation schedule," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(4), pages 392-407.
    21. 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.
    22. Madhu Jain & G.C. Sharma & Richa Sharma, 2013. "Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(2), pages 145-169.
    23. Charan Jeet Singh & Binay Kumar & Sandeep Kaur, 2018. "M X / G /1 state dependent arrival queue with optional service and vacation under randomised policy," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 29(2), pages 252-272.
    24. Madhu Jain & Richa Sharma & G.C. Sharma, 2015. "Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 20(3), pages 369-396.
    25. Charan Jeet Singh & Binay Kumar, 2017. "Bulk queue with Bernoulli vacation and m -optional services under N -policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 30(4), pages 460-483.
    26. Wojciech M. Kempa, 2016. "Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations," Annals of Operations Research, Springer, vol. 239(2), pages 381-400, April.
    27. 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.
    28. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    29. M. Haridass & R. Arumuganathan, 2012. "A batch service queueing system with multiple vacations, setup time and server's choice of admitting reservice," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 14(2), pages 156-186.
    30. Chandi Ram Kalita & Gautam Choudhury, 2019. "Analysis of an unreliable MX/G1G2/1/repeated service queue with delayed repair under randomized vacation policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(21), pages 5336-5369, November.
    31. R. Arumuganathan & K. S. Ramaswami, 2005. "Analysis Of A Bulk Queue With Fast And Slow Service Rates And Multiple Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 239-260.
    32. Gautam Choudhury & Mitali Deka, 2015. "An M/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 7(4), pages 309-337.
    33. Charan Jeet Singh & Sandeep Kaur & Madhu Jain, 2019. "Analysis of bulk queue with additional optional service, vacation and unreliable server," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 14(4), pages 517-540.
    34. S. Jeyakumar & R. Arumuganathan, 2008. "Steady state analysis of a M x /G/1 queue with two service modes and multiple vacations," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 3(6), pages 692-710.
    35. Kailash C. Madan, 1999. "An M/G/1 queue with optional deterministic server vacations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 83-95.
    36. 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.
    37. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, April.
    38. Shweta Upadhyaya, 2015. "Admission control of bulk retrial feedback queue with K-optional vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 215-239.
    39. S. Subba Rao, 1965. "Queuing Models with Balking, Reneging, and Interruptions," Operations Research, INFORMS, vol. 13(4), pages 596-608, August.
    40. Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    41. Qihui Bu & Liwei Liu, 2019. "An M/G/1 clearing queueing system with setup time and multiple vacations for an unreliable server," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(11), pages 2810-2826, June.
    42. Binay Kumar, 2018. "Unreliable bulk queueing model with optional services, Bernoulli vacation schedule and balking," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 12(3), pages 293-316.
    43. Amita Bhagat & Madhu Jain, 2013. "Unreliable M x /G/1 retrial queue with multi-optional services and impatient customers," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 17(2), pages 248-273.
    44. Awi Federgruen & Linda Green, 1986. "Queueing Systems with Service Interruptions," Operations Research, INFORMS, vol. 34(5), pages 752-768, October.
    45. Jau-Chuan Ke & Dong-Yuh Yang, 2016. "Analysis of a batch arrival queue with vacation policy and exceptional service," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3637-3657, June.
    46. S. Subba Rao, 1967. "Queuing with balking and reneging in M|G|1 systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 12(1), pages 173-188, December.
    47. M. Varalakshmi & P. Rajadurai & M.C. Saravanarajan & V.M. Chandrasekaran, 2016. "An M/G/1 retrial queueing system with two phases of service, immediate Bernoulli feedbacks, single vacation and starting failures," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(3), pages 302-328.
    48. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    49. I. L. Mitrany & B. Avi-Itzhak, 1968. "A Many-Server Queue with Service Interruptions," Operations Research, INFORMS, vol. 16(3), pages 628-638, June.
    50. Li, Huan & Zhu, Yixin, 1996. "Analysis of M/G/1 queues with delayed vacations and exhaustive service discipline," European Journal of Operational Research, Elsevier, vol. 92(1), pages 125-134, July.
    51. B. Avi-Itzhak & P. Naor, 1963. "Some Queuing Problems with the Service Station Subject to Breakdown," Operations Research, INFORMS, vol. 11(3), pages 303-320, June.
    52. Quan-Lin Li & Yu Ying & Yiqiang Zhao, 2006. "A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs," Annals of Operations Research, Springer, vol. 141(1), pages 233-270, January.
    53. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    54. Hafida Saggou & Tassadit Lachemot & Megdouda Ourbih-Tari, 2017. "Performance measures of M/G/1 retrial queues with recurrent customers, breakdowns, and general delays," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 7998-8015, August.
    55. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
    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. Dariusz Strzęciwilk, 2023. "Timed Petri Nets for Modeling and Performance Evaluation of a Priority Queueing System," Energies, MDPI, vol. 16(23), pages 1-29, November.
    2. Geni Gupur, 2022. "On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-16, April.
    3. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

    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. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    2. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    3. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.
    4. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    5. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.
    6. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    7. 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.
    8. 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.
    9. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    10. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    11. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    12. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    13. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    14. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    15. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    16. Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    17. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    18. B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    19. 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.
    20. 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.

    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:operea:v:21:y:2021:i:4:d:10.1007_s12351-019-00519-8. 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.