On an unreliable-server retrial queue with customer feedback and impatience

Analysis of an unreliable-server retrial queue with customer's feedback and impatience is presented. Truncated classical and constant retrial policies are taken into account. This system is analyzed as a process of quasi-birth-and-death (QBD). The quasi-progression algorithm is applied to compute the rate matrix of QBD model. A recursive solver algorithm for computing the stationary probabilities is also developed. To make the investigated system viable economically, a cost function is developed to decide the optimum values of servers, mean service rate and mean repair rate. Quasi-Newton method, pattern search method and Nelder-Mead simplex direct search method are employed to implement the optimization tasks. Under optimum operating conditions, numerical results are provided for a comparison of retrial policies. We also give a potential application to illustrate the system's applicability.