Queueing models play a significant role in analysing the performance of power management systems in various electronic devices and communication systems. This paper adopts a multiple vacation queueing model with a threshold policy to analyse the power-saving mechanisms of the wireless sensor network(WSN) using the Dynamic Power Management technique. The proposed system consists of a busy state(transmit state), wake-up state, shutdown state and inactive state. In this model, the server switches to a shutdown state for a random duration of time after serving all the events(data packets) in the busy state. Events that arrive during the shutdown period cannot be served until the system size reaches the predetermined threshold value of k and further it requires start-up time and a change of state to resume service. At the end of the shutdown period, if the system size is less than k, then the server begins the inactive period; otherwise, the server switches to the wake-up state. For this system, an explicit expression for the transient and steady-state solution is computed in a closed-form. Furthermore, performance indices such as mean, variance, probability that the server is in various stages of power management modes and mean power consumption are computed. Finally, graphical illustrations are made to understand the effect of the parameters on the performance of the system.