Balking and Reneging Multiple Working Vacations Queue with Heterogeneous Servers

This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures.