Abstract
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.
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