Queueing is a common phenomenon in various stages of manufacturing systems and some other organisations. Queueing usually reduces the time required by managers and manufacturers to complete a desired task. The queueing mathematical theory is a viable tool for analysing a waiting line model. This research presents the implementation of robots at the packaging stage of a virtual manufacturing scenario in which mathematical models were used to describe each stage of the manufacturing process. Some suitable parameters and operating conditions were assumed, and the Newton-Raphson iteration formula was implemented for numerical analysis of the models. Simulation was carried out to achieve optimal values that could yield efficient productivity. The optimisation process gave an outcome that adequately showed how queueing can be managed in the packaging stage in an advanced manufacturing environment.