Performance analysis of the queue with gated servicing and adaptive vacations

A queueing model of the B M A P / G / 1 type with gated servicing and vacations depending on the state of the system is analysed. The queue stationary distributions at the instants of gate switching on and at arbitrary time as well as of a customer waiting time are computed. This model may prove useful for tuning the parameters of the adaptive polling mechanism applicable in the broadband wireless Wi-Fi and WiMax networks.