Variant impatient customers in an M/M/1 queue with balking re-service and Bernoulli multiple vacations

The impatient behavior of customers' plays a vital role in the growth of the economy of a country. Customers leaving the queue, before getting served due to impatience, lead to heavy loss in trading centers. So, it is very important to study and analyze the impatient behavior of customers in various queueing models. A mathematical analysis of one such model is presented in this present research work. This paper analyzes the transient behavior of an M/M/1 queue with Bernoulli multiple vacations, balking, re-service and variant impatient customers. As soon as the server becomes free, he resumes Bernoulli multiple vacations. That is, the server commences either multiple vacations or multiple working vacations. During vacations and working vacations, the customers possess balking behavior. During working vacations, as the service speed is low, the customers waiting in the queue become impatient due to the huge waiting time. But, the customer who gets the service in slow service rate does not become impatient. After the completion of service, the customers may demand re-service during the busy periods. The transient system size probabilities, mean and variance are derived. Further, numerical simulations are provided to analyze the influence of various parameters of the system.