Analysis of an M/M/c queue with heterogeneous servers, balking and reneging

Abstract

This paper analyses a heterogeneous multi-server queuing system with balking and reneging. In this system, when all the c servers are busy, an arriving customer decides either to join the queue with probability p or balk with probability 1 - p. The customers waiting in the queue become impatient due to the long wait for service. Therefore, each individual waiting customer activates an independent impatience timer such that the customer's service starts before his timer expires, he gets the service and leaves the system after the completion of service. Otherwise, he abandons the system and never returns. The time-dependent system size probabilities are derived explicitly using generating function. Further the time-dependent mean, variance, busy period distribution and steady-state probabilities are obtained. Finally, some numerical illustrations are presented.