A queueing model for an automatic manufacturing system with disasters, breakdowns, and vacations : optimal design and analysis

We study a queueing model with disasters, working breakdowns, balking, reneging, and vacations. This is a novel and realistic queueing model that captures the complex dynamics and behaviors of an automatic manufacturing system (AMS) with various uncertainties and disruptions. The system loses all customers when a disaster occurs and repairs start immediately. New customers get slower service during breakdowns. We use matrix methods to find the system’s steady state along with performance measures like the expected number of customers lost, the expected waiting time, and system reliability. We also optimize the system parameters (system capacity, number of servers, service rates) to minimize the cost function using a combined direct search method and quasi-Newton method. Our results can enhance the AMS’s performance, profit, and customer satisfaction.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).