Detection of optimal working vacation service rate for retrial priority G-queue with immediate Bernoulli feedback

The idea behind the proposed queueing model is its adequacy in daily existent workplaces like hospitals, banks, and multinational companies where the service quality of computer networks and telecommunication systems are to be improved. The study consists of an $M^X/G/1$ retrial G-queue with preemptive priority arrivals where the service provider takes a working vacation and the vacation may get interrupted. The novelty of the proposed model lies as it anticipates state-dependent arrivals wherein unsatisfied clients may come up with immediate Bernoulli feedback. Also, the concept of preemptive priority is included which can be seen in various service systems of day-to-day life. The supplementary variable technique (SVT) is used to unfold the model and obtain the system performance indices and reliability measures. In continuation, the Grey Wolf Optimization (GWO) algorithm is used to obtain the optimal working vacation service rate and retrial rate under two scalar optimization problems where the system works under minimal cost and minimal awaiting time respectively. Lastly, the Pareto optimal solution of a bi-objective problem is also presented.