Modelling and analysis of production management system using vacation queueing theoretic approach

• Published in: Applied mathematics and computation 2024-10, Vol.479, p.128856, Article 128856
• Main Authors: Ambika, K., Vijayashree, K.V., Janani, B.
• Format: Article
• Language: English
• Subjects: Confluent Hypergeometric Function; Continued fractions; Production Management; Transient state probabilities; Vacation interruption
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2024.128856

•We explore an M/M/1 working vacation queueing model within the framework of a production management system, taking into account factors such as customer impatience, interruptions in production, and a bernoulli scheduled maintenance period with a waiting server.•We generate concrete analytical outcomes for the probabilities of the system's capacity when the manufacturing unit transitions through various operational states during transitory periods.•The credibility of the derived expressions is then established by simplifying them to well-recognized outcomes found in existing results.•We present the models steady-state probability providing insight using final value theorem of the system.•Numerical illustrations are also provided that further clarify the models’ characteristics and its potential real-world applications. This paper explores a queueing model in a production management context, featuring periods of working vacations and Bernoulli vacation. When there are no pending orders, the manufacturing unit transits into a maintenance phase, also termed as working vacation, during which production continues, albeit at a slower rate. This diminished productivity could result in longer lead times and potential customer dissatisfaction. Depending on the influx of demand, the maintenance phase could be interrupted, propelling the unit back to full operational capacity. Conversely, if no orders are received during the maintenance phase, the unit has the choice of switching to standby mode in anticipation of incoming orders, or initiating an extended break. We utilize mathematical techniques such as continued fractions, Modified Bessel functions, and Laplace transforms to precisely compute the transient state probabilities of this model. To further illustrate the impact of these operational dynamics on production management, we present corroborative numerical examples.