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<p>This paper analyzes a single-server retrial queue with batch arrivals, event-driven impatience, and active server breakdowns, incorporating reservation time and a Bernoulli vacation policy. Arriving batches finding the server unavailable collectively enter the retrial orbit or leave the system. The server may fail during service, requiring immediate repair; upon failure, customers may remain or move to a service orbit, inducing a reservation period. This model has practical applications in domains such as computer networks and cloud computing. Using the supplementary variable method, we derive steady-state probability distributions, stability conditions, and key performance measures of the system, including the average number of customers in the orbit and system, and the expected busy and idle periods of the server. Furthermore, we analyze the system’s reliability and formulate the cost function of our model. A numerical analysis is conducted, including sensitivity study, cost function optimization with both L-BFGS-B algorithm and Particle Swarm Optimization (PSO), where both methods reach the same numerical optimum within the adopted stopping tolerances. Additionally, three one-input Adaptive Neuro-Fuzzy Inference System (ANFIS) surrogate models are developed for the mean orbit size over selected stable ranges. The ANFIS outputs closely match the corresponding analytical curves for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>, showing that lightweight data-driven surrogates can be useful when repeated evaluation of selected one-parameter scenarios is required.</p>

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Analysis and performance evaluation of a bulk arrival retrial queue with impatient customers, server breakdowns, and bernoulli vacation policy

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Ratiba Moulai,
  • Mohamed Boualem,
  • Isma Benrais

摘要

This paper analyzes a single-server retrial queue with batch arrivals, event-driven impatience, and active server breakdowns, incorporating reservation time and a Bernoulli vacation policy. Arriving batches finding the server unavailable collectively enter the retrial orbit or leave the system. The server may fail during service, requiring immediate repair; upon failure, customers may remain or move to a service orbit, inducing a reservation period. This model has practical applications in domains such as computer networks and cloud computing. Using the supplementary variable method, we derive steady-state probability distributions, stability conditions, and key performance measures of the system, including the average number of customers in the orbit and system, and the expected busy and idle periods of the server. Furthermore, we analyze the system’s reliability and formulate the cost function of our model. A numerical analysis is conducted, including sensitivity study, cost function optimization with both L-BFGS-B algorithm and Particle Swarm Optimization (PSO), where both methods reach the same numerical optimum within the adopted stopping tolerances. Additionally, three one-input Adaptive Neuro-Fuzzy Inference System (ANFIS) surrogate models are developed for the mean orbit size over selected stable ranges. The ANFIS outputs closely match the corresponding analytical curves for \(\lambda \) λ , \(\beta _1\) β 1 , and \(\omega \) ω , showing that lightweight data-driven surrogates can be useful when repeated evaluation of selected one-parameter scenarios is required.