The Control Policy <i>M/M/c/N</i> Interrelated Queue with Manageable Incoming Rates, Reverse Balking and Impatient Customers

This study explores an interconnected M/M/c/N queueing model that incorporates reverse balking, reneging, a control technique, and adjustable arrival rates. In reverse balking, the likelihood of a visitor deciding to join or leave a queue is influenced by the current system size, with a higher probability of joining as the system size grows. Conversely, long wait times can lead to customer impatience, causing them to leave the queue before receiving service (reneging). Service begins with the arrival of the initial customer (TL) and continues until the system is empty. We are developing a multi-server queueing system with adjustable arrival rates that includes reverse balking and considers impatient customers. For this model, we determine the steady-state condition and performance metrics such as average waiting time and average system size.