In this paper, a M[X]/G (a, b)/1 queueing system with modified M‐vacation policy and variant arrival rate is considered. After a service completion, if the number of waiting customers is less than a, then the server avails of multiple vacations till the queue length reaches a or consecutively avail of M number of vacations, whichever occurs first. After completing the Mth vacation, if the queue length is still less than a then the server remains in the system till it reaches a. The server starts the service only if the queue length ξ≥a, with a batch of min (ξ,b) customers, where b≥a. It is considered that the arrival rate is dependent on the state of the server. The steady state queue size distribution at an arbitrary time is obtained. The expected queue length, waiting time, length of busy and idle periods are derived. Numerical illustration is also presented.
