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Double orbit finite retrial queues with priority customers and service interruptions

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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.

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