A discrete time batch arrival $Geo^{X}/G/1$ queue is considered, in which the startup of server is controlled by the sum of service times of all arrivals (called service time backlog). The customers enter the system in batch arrival. When the service time backlog of all arriving customers exceeds a given non-negative integer $D$, the server starts its service and lasts until a busy period ends (this policy is called the $D$ policy). The model can offer some theoretical basis for the practitioners of wireless sensor network. Firstly, in the preparation work, the queue size and service time backlog at the start of a busy period, and the busy and idle periods are discussed. Then, by the classifications of the customers who arrive during the idle and busy periods, and the method of probabilistic analysis, the steady-state queue sizes at a departure time and an arbitrary time $n^{+}$ are studied. As two special cases, the steady-state queue sizes for the $Geo^{X}/G/1$ and $D$-policy $Geo/G/1$ queueing systems are derived. Finally, a kind of wireless sensor node is modelled, and the minimum power consumption is numerically gotten.