Economic analysis of M/M/c/N queue with retention of impatient customers

This paper investigates a finite capacity multi-server Markovian queuing model with customer impatience in which the probability of retaining the impatient customers is incorporated. This concept of retaining the 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 reneging (customer impatience). The steady-state solution of the model has been obtained and different measures of effectiveness have been computed. It has been found that the expected number of customers in the system increases as the probability of retaining the impatient customers (say, q) increases. The economic aspects of the model have also been discussed. It has been observed that the total expected profit of the system increases steadily with the increase in the probability of retaining the impatient customers. Such analysis may help decision makers decide about the formulation of different customer retention strategies by knowing costs and profits associated with them.