Economic analysis of an M / M / c / N queuing model with balking, reneging and retention of reneged customers

In this paper, we study a finite capacity, multi-server Markovian queuing model with balking and reneging in which the probability of retaining the reneged customers is incorporated. This concept of retaining the reneged (impatient) customers has a great significance in revenue generating queuing systems. The queuing model developed in this paper is a new advancement in the fundamental queuing models dealing with balking and reneging. The transient and steady-state solutions of the model are obtained and different measures of effectiveness are derived. It is found that the average number of customers in the system increases as the probability of retaining the reneged customers (say, q) increases. Economic analysis of the model is also performed to study the effect of the probability of retaining the reneged customers on total expected profit of the system. Some important queuing models are obtained as particular cases of this model.