Abstract: Consider an queue with
exponentially distributed multiple and single working vacations where the server
cooks at a slower rate rather than completely stops service during vacation
periods. Using supplementary variable technique, we derive the steady-state
distributions for the number of customers in the system both at the arbitrary
epoch and departure epoch. Further the expected system size and various
probabilities are calculated and the results obtained are illustrated
numerically.
Keywords and phrases: working vacations, supplementary
variable technique.
