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

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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.

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Funding

The first author, Raina Raj is supported by a senior research fellowship (SRF) Grant No.- 09/1131(0024)/2018-EMR-I from Council of Scientific and Industrial Research (CSIR), India.

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  1. Raina Raj and Vidyottama Jain have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Central University of Rajasthan, Rajasthan, India

    Raina Raj & Vidyottama Jain

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  1. Raina Raj
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  2. Vidyottama Jain
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Contributions

All the authors have equally contributed to the work. RR and VJ formulated the model. RR completed the mathematical analysis. VJ verified the results and modified the manuscript. RR and VJ reviewd the manuscript.

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Correspondence to Vidyottama Jain.

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Raj, R., Jain, V. Resource optimization for MMAP[c]/PH[c]/S catastrophic queueing model with PH retrial times. OPSEARCH (2024). https://doi.org/10.1007/s12597-023-00731-3

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