Non-linear Dynamical Functioning of a Time-Independent Uncertain System with Optimization

This work investigates a bulk arrival retrial queueing model that offers multi-phases of heterogeneous service. Moreover, as soon as the orbit becomes empty, the server goes on a Bernoulli working vacation (BWV), where it works at a lower speed. At certain times, consumers are also permitted to balk and renege. Further, the busy server may experience a failure at any time. Here the supplementary variable approach has been incorporated in order to derive the probability generating function (PGF) of the number of clients in the system as well as in the orbit. The impact of particular parameters on the system’s overall performance has been demonstrated with the aid of a few numerical examples. Finally, this research is accelerated in order to bring about the best possible (optimal) cost for the system by adopting a range of optimization approaches namely particle swarm optimization (PSO), artificial bee colony (ABC), grey wolf optimizer (GWO) and differential evolution (DE).