Single server batch arrival bernoulli feedback queueing system with waiting server, K-variant vacations and impatient customers

We consider an infinite capacity batch arrival single server Markovian Bernoulli feedback queueing system with waiting server, K-variant vacations, impatient customers and retention of reneged customers. The model is analyzed using probability generating function (PGF) technique. Various queueing system characteristics are derived. Then, by setting the appropriate parameters, some special cases are discussed. Moreover, a cost model for the queueing system is developed. The parameter optimization is numerically illustrated using particle swarm optimization (PSO). Finally, numerical results are provided to explore the impact of system parameters on performance measures and costs of the queueing system.