Nopassing Multiserver Queue with Additional Heterogeneous Servers and Inter-dependent Rates

In many congestion problems, the customers may not like to join a long queue and may balk. To reduce the balking behavior of the customers, the provision of additional servers can be made in such situations. In the present paper, we investigate a Markovian queueing model with balking, interdependent rates and additional servers under no passing constraint. Due to nopassing restriction, the customers are allowed to depart from the system in the same chronological order in which they entered the system. Based on the service requirements, the customers are classified in two classes; the type ’A’ of the customers has zero service time whereas the service times of type ’B’ customers follow exponential distribution. By using recursive approach, we obtain the queue size distribution at equilibrium. Various performance indices such as the mean waiting time and the difference between the expected waiting time for both types of customers have been established. By setting appropriate parameters, some special cases of existing models have been discussed. In order to demonstrate the computational tractability of the performance indices derived analytically, numerical experiment has been performed.