IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v269y2015icp674-690.html
   My bibliography  Save this article

Priority retrial queueing model operating in random environment with varying number and reservation of servers

Author

Listed:
  • Dudin, Alexander
  • Kim, Chesoong
  • Dudin, Sergey
  • Dudina, Olga

Abstract

We consider a multi-server queueing system with two types of customers operating in the Markovian random environment. Under the fixed state of the random environment, the arrival flow is described by the marked Markovian arrival process. Type 1 customers have preemptive priority over type 2 customers. Type 1 customer is lost only if, at its arrival moment, all servers are busy by type 1 customers. The service times of both types of customers have an exponential distribution with the rate depending on the type of a customer. Type 2 customer is accepted for service if the number of busy servers at its arrival epoch does not exceed a fixed threshold. Otherwise, the arriving customer makes a randomized choice to leave the system permanently (to balk) or to join so called orbit and try to obtain service later. The inter-retrial times have an exponential distribution. Customers in orbit can be impatient and may leave the system after an exponentially distributed amount of time. Due to preemptive priority of type 1 customers, service of type 2 customer can be interrupted. In this case, the interrupted customer makes a randomized choice to leave the system permanently or go into orbit. When the random environment changes its state, immediately the following parameters of the system change their value: the total number of servers, the number of servers available for type 2 customers, the matrices defining the arrival process, the rates of service of customers, the rate of retrials, the impatience intensity, the probability of balking the system at the arrival moment or the moment of termination of service of type 2 customer. Behavior of the system is described by the level dependent multi-dimensional Markov chain that belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allows us to derive the ergodicity condition for this Markov chain and compute its stationary distribution. The main performance measures of the system are expressed via the stationary state probabilities. Numerical illustrations are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:674-690
    DOI: 10.1016/j.amc.2015.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315010607
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.005?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. Marcel F. Neuts & David M. Lucantoni, 1979. "A Markovian Queue with N Servers Subject to Breakdowns and Repairs," Management Science, INFORMS, vol. 25(9), pages 849-861, September.
    2. 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.
    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. 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.
    2. Ashis Kumar Chakraborty & Ritwika Chattopadhyay & Inder Kaur & Sayaran Mittra, 2022. "Optimization of the number of maintenance crew in a manufacturing unit," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 1-19, March.
    3. Kim, Chesoong & Klimenok, V.I. & Dudin, A.N., 2017. "Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 154-172.
    4. V. Vinitha & N. Anbazhagan & S. Amutha & K. Jeganathan & Bhanu Shrestha & Hyoung-Kyu Song & Gyanendra Prasad Joshi & Hyeonjoon Moon, 2022. "Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers," Mathematics, MDPI, vol. 10(13), pages 1-18, 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. 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.
    2. K. R. Rejitha & K. P. Jose, 2018. "A stochastic inventory system with two modes of service and retrial of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 134-149, March.
    3. 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.
    4. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    5. 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.
    6. Liu, Gia-Shie, 2011. "Dynamic group instantaneous replacement policies for unreliable Markovian service systems," International Journal of Production Economics, Elsevier, vol. 130(2), pages 203-217, April.
    7. Gia-Shie Liu, 2019. "A Group Replacement Decision Support System Based on Internet of Things," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    8. Nadav Lavi & Hanoch Levy, 2020. "Admit or preserve? Addressing server failures in cloud computing task management," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 279-325, April.
    9. 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.
    10. Kim, Chesoong & Klimenok, V.I. & Dudin, A.N., 2017. "Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 154-172.
    11. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    12. 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.
    13. Lam, Yeh & Zhang, Yuan Lin & Liu, Qun, 2006. "A geometric process model for M/M/1 queueing system with a repairable service station," European Journal of Operational Research, Elsevier, vol. 168(1), pages 100-121, January.
    14. 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.
    15. Dijk, N.M. van & Trapman, F.J.J., 1989. "Exact solutions for central service systems with breakdowns," Serie Research Memoranda 0028, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    16. 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.
    17. 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.
    18. Dmitry Efrosinin, 2013. "Queueing model of a hybrid channel with faster link subject to partial and complete failures," Annals of Operations Research, Springer, vol. 202(1), pages 75-102, January.
    19. Efrosinin, Dmitry & Sztrik, Janos, 2018. "An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 271(3), pages 934-952.
    20. Wartenhorst, Pieter, 1995. "N parallel queueing systems with server breakdown and repair," European Journal of Operational Research, Elsevier, vol. 82(2), pages 302-322, April.

    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:269:y:2015:i:c:p:674-690. 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.