Optimization of an M/M/1/N feedback queue with retention of reneged customers

Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.