Matrix-geometric analysis of heterogeneous server queueing systems with multiple working vacations: Comparison with ANFIS

Year 2025, Volume: 54 Issue: 5, 1954 - 1975, 29.10.2025

Indumathi P Karthikeyan K

https://doi.org/10.15672/hujms.1637390

Abstract

This study investigates a Markovian queueing system in which server 2 operates under multiple working vacations and is subject to service-time breakdowns. Server 1 remains continuously available and provides service at a normal rate (\(\omega_1\)). Both servers adjust their service rates to manage an infinite queue of customers. The intermittent availability of server 2, which provides service at rate \(\omega_2\) during regular working periods, affects the overall performance of the system. Customers join the system with probability \(\beta\) when at least one server is available; otherwise, they leave with probability \(\overline{\beta}\). After receiving service, customers leave the system with probability \(\eta\) or return to the queue for another service attempt with probability \(1 - \eta\). The matrix-geometric method is employed to perform steady-state analysis and derive stability conditions. A cost analysis is also performed to optimize system expenditure and improve resource utilization. The computational results demonstrate the impact of various system parameters on performance metrics. Additionally, a soft computing-based Adaptive Neuro-Fuzzy Inference System is used to validate the analytical findings.

Keywords

ANFIS , balking , cost analysis , feedback , heterogeneous servers , matrix geometric method , stability condition , working vacation

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