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Resource optimization for MMAP[c]/PH[c]/S catastrophic queueing model with PH retrial times

Author

Listed:
  • Raina Raj

    (Department of Mathematics)

  • Vidyottama Jain

    (Department of Mathematics)

Abstract

A multi-server catastrophic retrial queueing model is developed in this study, which takes into account a controllable preemptive priority scheduling with phase-type distributed retrial times. For clarity purpose, the model operating scenarios that take place before and after the tragedy are termed as the normal environment and the catastrophic environment, respectively. In a normal environment, the inbound calls are divided into handoff calls and new calls. Controllable preemptive priority is assigned to handoff calls over new calls. In the catastrophic environment, when a calamity shuts down the entire system and all the operational channels are failed, a network of backup channels is swiftly deployed to resume services. Now, the inbound calls are classified into handoff call, new call, and emergency call as a result of the emergency scenario in the affected area. Due to the immediate imperative to save lives in such circumstances, emergency calls are also given controllable preemptive priority over new or handoff calls. By establishing that the Markov chain meets the requirements for asymptotically quasi-Toeplitz Markov chains, the chain’s ergodicity critera is established. Furthermore, the non-dominated sorting genetic algorithm-II (NSGA-II) approach has been employed to tackle a multi-objective optimization problem to determine the optimal number of backup channels and threshold values of preemption.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:3:d:10.1007_s12597-023-00731-3
    DOI: 10.1007/s12597-023-00731-3
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    References listed on IDEAS

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    1. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    2. Nitin Kumar & U. C. Gupta, 2020. "Analysis of batch Bernoulli process subject to discrete-time renewal generated binomial catastrophes," Annals of Operations Research, Springer, vol. 287(1), pages 257-283, April.
    3. 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.
    4. 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.
    5. Wei Chang, 1965. "Preemptive Priority Queues," Operations Research, INFORMS, vol. 13(5), pages 820-827, October.
    6. 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.
    7. S. H. Alsamhi & N. S. Rajput, 2016. "Implementation of call admission control technique in HAP for enhanced QoS in wireless network deployment," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(2), pages 141-151, October.
    8. Shin, Yang Woo & Moon, Dug Hee, 2011. "Approximation of M/M/c retrial queue with PH-retrial times," European Journal of Operational Research, Elsevier, vol. 213(1), pages 205-209, August.
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