Optimizing Textile Manufacturing with an MX/G/1 Queueing Model: Two Heterogeneous Services, Bernoulli Vacations, and Disaster–Repair Interventions

This study investigates an MX/G/1 queueing system tailored to the textile manufacturing industry, incorporating two heterogeneous service types, Bernoulli vacation schedules, and the effects of disasters and repairs. The system handles bulk fabric arrivals following a Poisson process, where customers can opt for either standard finishing or advanced finishing services. Disasters such as equipment malfunctions cause system interruptions, necessitating stochastic repair periods, while Bernoulli vacation schedules allow the machines to take probabilistic vacations based on operational conditions. By employing the supplementary variable technique, the probability generating function (PGF) for the number of customers in the system is obtained. Key performance metrics are derived alongside rate arguments to analyze system behavior comprehensively. Numerical techniques are utilized to explore and illustrate the influence of model parameters, providing practical insights for optimizing resource allocation, enhancing production efficiency, and maintaining system reliability in textile manufacturing operations.