This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using probability generating function (PGF) technique, we obtain the steady-state solution of the system. In addition, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using quadratic fit search method (QFSM). Finally, numerical examples are provided in order to visualize the analytical results.

On page 04, after equation (3.2), we should have (λ + β(µ 1 + µ 2)) P 2 = (β(µ 1 + µ 2) + ηδ) P 3 + λP 1 , n = 2. (0.1) 2. Instead of equation (3.3), we should have λ n−1 + β(µ 1 + µ 2) + (n − 2)ηδ P n = (β(µ 1 + µ 2) + (n − 1)ηδ) P n+1 + λ n−2 P n−1 , 3 ≤ n ≤ N − 1.