Abstract
This paper studies an M/M/1 queue with single, multiple working vacations and customers’ variant impatient behavior. During working vacations, the arriving customers are served with slower service rate than the service rate of non-vacation period. An arriving customer, during working vacation, finds the system empty and gets his service immediately, does not become impatient. The only customers who are waiting for service, during working vacation, become impatient. The transient system size probabilities of this model are derived explicitly in the closed form using continued fraction. The time-dependent mean and variance are also computed. Numerical examples are provided to visualize the analytical results.
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