M/M/m Queue with Balking, Reneging and Additional Servers

In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer’s balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and their service- times follow exponential distribution. The number of servers in long run depends on the queue-length. We obtain equilibrium queue size distribution. The expression for expected number of customers in the system in the long run has been obtained. Some other performance measures have also been provided. In order to match our results with earlier work, special cases are discussed. The numerical results are presented to verify the validity of the proposed analytical method.