Impatient customers in an M/M/1 queue with single and multiple working vacations

We consider an M/M/1 queue with impatient customers and two different types of working vacations. The working vacation policy is the one in which the server serves at a lower rate during a vacation period rather than completely stop serving. The customer’s impatience is due to its arrival during a working vacation period, in which the customer service rate is lower than the normal busy period. We analyze the queue for two different working vacation termination policies, a multiple working vacation policy and a single working vacation policy. Closed-form solutions and various performance measures like, the mean queue lengths and the mean waiting times are derived. The stochastic decomposition properties are verified for both multiple and single working vacation cases. A comparison of both the models is carried out to capture their performances with the change in system parameters.