  An infinite buffer batch service vacation queue has been studied where
service rate of the batch is dependent on the size of the batch and vacation
rate is dependent on the queue size at vacation initiation epoch. The arrivals
follow the Markovian arrival process (MAP). For service rule, general bulk
service (GBS) rule is considered. The service time and vacation time both are
considered to be generally distributed. Several joint distributions of interest
are obtained using the bivariate vector generating function method and the
supplementary variable technique (SVT). Numerical results are presented to show
the behavior of the system performance to validate the analytical results.
