Cost optimisation of a discrete-time retrial queue with Bernoulli feedback and starting failure

In this paper, we explore the performance characteristics of a discrete-time Geo/G/1 retrial queue with Bernoulli feedback where the server is subjected to starting failure. On the arrival of a customer, the server may either resume its service successfully with probability υ or may not resume its service successfully with probability ῡ = 1 − υ due to some faults which in turn force the server to repair and the customer may join the orbit. The service time, retrial time and repair time are general distributed. The purpose of this paper is two-fold. Firstly, we use generating function method and supplementary variable technique to derive expressions for system size, orbit size and other performance measures. Secondly, for a cost-effective system, we have found the optimal values of some critical system parameters such that the total system cost is minimised using particle swarm optimisation (PSO) technique. Finally, sensitivity analysis is also provided.