Aryabhatta Journal of Mathematics & informatics

The Present communication explores the cost effectiveness of M/M/1/N Queue system with impatient nature of customers. The most dominant difference between queue with impatient customers & ordinary queue is the impatient acts (balking & reneging) in queue. Some arriving customers looking large queue in the system do not like to stand in queue, balk with some probability from the system and others stand in the queue for a while but leave or renege without getting service. Assuming Reneging rate exponentially distributed, the steady state probability equations have been developed with the help of Markov process technique and Matrix form solution has been derived. A central challenge in designing & managing any service operation in a queue system is to achieve a cost balance between operational efficiency & service quality. The objective of this paper is to develop a mathematical model in order to find the optimal service rate and the equilibrium point between the degree of waiting time and the total expected cost.