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Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

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BOUCHENTOUF A. A., GUENDOUZI A., HOUALEF M., MAJID S.
Operations Research and Decisions
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2022
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vol. 32
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issue 2
16-33
EN
In this paper, we analyze an M/M/1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . . , K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system.
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A queueing model for an automatic manufacturing system with disasters, breakdowns, and vacations : optimal design and analysis

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Yatim N. R., Bouchentouf A. A., Laxmi P. V.
Operations Research and Decisions
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2024
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vol. 34
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issue 4
231-250
EN
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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