Metaheuristic Cost Optimization of <i>M^X/G₁,G₂/</i> 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

Abstract

We presented a MX /G1, G2 /1 queueing system with a Bernoulli schedule that includes service disruption, working breakdown, balking, catastrophe and extended server vacations. All customers that arrive are served by a single server, with service time determined by general distribution. As soon as the system fails, the server keeps serving the current client at a reduced rate while repairs are made. It is believed that the vacation schedule is broad. Random disruptions to the server occur, with an exponential distribution in the length of the disruption. We assume that besides a Poisson stream of positive arrivals, there is a Poisson stream of negative arrivals, which we refer to as catastrophes. Using the supplementary variable technique, the Laplace transforms of the time-dependent probability of the system state are derived. We can infer steady-state outcomes from this. The average waiting time and queue size were also obtained. An additional topic of discussion is Adaptive Neuro-Fuzzy Inference system (ANFIS). Furthermore, this work uses Particle Swarm Optimisation (PSO), Artificial Bee Colonies (ABC), and Genetic Algorithms (GA) to swiftly find the system’s optimal cost. Additionally, we examined the convergence of several graph-optimisation strategies.