Cost optimality of an erratic Geo^X/G/1 retrial queue under J-vacation scheme using nature inspired algorithms

In this article, we have explored a Geo^X/G/1 model with Bernoulli feedback wherein the clients that enter and find the system to be busy, halt for a while prior to attempting again to enter the system. The server is erratic and can take utmost J-vacations regularly unless one client appears in the virtual track (orbit) again on returning from vacation. Also, the server is sent for repair on an urgent basis as soon as it breaks down. Using the probability generating function technique, the system size distribution of the server during busy, breakdown, vacation state and orbit size along with some performance measures have been derived. These derived quotients are then visualised and validated with the help of tables and graphs. Further, the cost analysis of the model is carried out and the optimal cost for the system is obtained. We have used direct search method, particle swarm optimisation (PSO), artificial bee colony (ABC) and cuckoo search (CS) techniques for the comparative study and presented the graphs for the convergence of these techniques.