IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i15p1797-d604014.html
   My bibliography  Save this article

MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback

Author

Listed:
  • Divya Velayudhan Nair

    (Department of Mathematics, NSS College, Cherthala 688556, India)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, India)

  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku AZ 1148, Azerbaijan)

  • Sevinj Aliyeva

    (Applied Mathematics and Cybernetics, Baku State University, Baku AZ 1148, Azerbaijan)

Abstract

In this paper, we consider two single server queueing systems to which customers of two distinct priorities ( P 1 and P 2 ) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P 1 customer to feedback is θ on completion of his service. The feedback ( P 1 ) customers, as well as P 2 customers, join the low priority queue. Low priority ( P 2 ) customers are taken for service from the head of the line whenever the P 1 queue is found to be empty at the service completion epoch. We assume a finite waiting space for P 1 customers and infinite waiting space for P 2 customers. Two models are discussed in this paper. In model I, we assume that the service of P 2 customers is according to a non-preemptive service discipline and in model II, the P 2 customers service follow a preemptive policy. No feedback is permitted to customers in the P 2 line. In the steady state these two models are compared through numerical experiments which reveal their respective performance characteristics.

Suggested Citation

  • Divya Velayudhan Nair & Achyutha Krishnamoorthy & Agassi Melikov & Sevinj Aliyeva, 2021. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1797-:d:604014
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/15/1797/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/15/1797/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Alan Cobham, 1954. "Priority Assignment in Waiting Line Problems," Operations Research, INFORMS, vol. 2(1), pages 70-76, February.
    3. Chia-Jung Chang & Jau-Chuan Ke & Fu-Min Chang, 2018. "Unreliable retrial queue with loss and feedback under threshold-based policy," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 30(1), pages 1-20.
    4. Mohan L. Chaudhry & James J. Kim & Abhijit D. Banik, 2019. "Analytically Simple and Computationally Efficient Results for the GI X / Geo / c Queues," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-18, September.
    5. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.
    6. N. K. Jaiswal, 1961. "Preemptive Resume Priority Queue," Operations Research, INFORMS, vol. 9(5), pages 732-742, October.
    7. V. Jailaxmi & R. Arumuganathan & A. Rathinasamy, 2017. "Performance analysis of an M x /G/1 feedback retrial queue with non-persistent customers and multiple vacations with N-policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 29(2), pages 149-169.
    Full references (including those not matched with items on IDEAS)

    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. Jori Selen & Brian Fralix, 2017. "Time-dependent analysis of an M / M / c preemptive priority system with two priority classes," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 379-415, December.
    2. 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.
    3. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 5-28.
    4. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    5. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    6. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.
    7. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2021. "Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
    8. 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.
    9. 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.
    10. Atencia, I., 2017. "A Geo/G/1 retrial queueing system with priority services," European Journal of Operational Research, Elsevier, vol. 256(1), pages 178-186.
    11. G. Ayyappan & S. Karpagam, 2018. "An M [ X ] / G ( a , b )/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service," Mathematics, MDPI, vol. 6(6), pages 1-18, June.
    12. Guodong Pang & Andrey Sarantsev & Yana Belopolskaya & Yuri Suhov, 2020. "Stationary distributions and convergence for M/M/1 queues in interactive random environment," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 357-392, April.
    13. Agassi Melikov & Sevinj Aliyeva & Janos Sztrik, 2021. "Retrial Queues with Unreliable Servers and Delayed Feedback," Mathematics, MDPI, vol. 9(19), pages 1-23, September.
    14. 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.
    15. Atencia-Mc.Killop, Ivan & Galán-García, José L. & Aguilera-Venegas, Gabriel & Rodríguez-Cielos, Pedro & Galán-García, MÁngeles, 2018. "A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 245-253.
    16. 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.
    17. Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    18. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    19. 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.
    20. Maria E. Mayorga & Emmett J. Lodree & Justin Wolczynski, 2017. "The optimal assignment of spontaneous volunteers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(9), pages 1106-1116, September.

    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:gam:jmathe:v:9:y:2021:i:15:p:1797-:d:604014. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.