Impatient Customers in an M/M/c queue with Single and Multiple Synchronous Working Vacations

In this paper, an M/M/c queuing model with synchronous working vacation and impatient customers is considered. The model is analyzed for two vacation policies i.e. multiple working vacation (MWV) policy and single working vacation (SWV) policy. The servers serve the customers at a slower rate than the normal busy period during a working vacation and this becomes the cause of customer's impatience. The M/M/c queue with two such policies is described and using the PGF method, we obtain various system performance measures in terms of two indicators. We have derived some results relating to the limiting behavior of some performance measures. At the end of each model, we have presented some numerical examples to demonstrate the effects of system parameters on some performance measures. Finally, a comparison between the two models is carried out.