Wireless sensor network (WSN) consists of several small sensor nodes with limited energy and low cost. these sensors are distributed in a wide area to sense, measure, observe, track or monitor physical environmental phenomenon, such as temperature, pressure, wind, humidity, etc. WSN has more restrictions in resources such as memory and energy supply, therefore, the main challenge in designing these nodes is to maximize energy efficiency through optimal resources management. One effective approach is utilizing the Duty cycling technique where the node goes through different power levels. The node is periodically placed into low-power mode (sleep mode) and active mode of the main radio; however, the nodes still suffer of energy exhaustion due to overhearing and idle listening problems in addition to challenges associated with nodes clocks synchronization. Recent power management techniques tried to add an auxiliary radio called Wake-up receiver (WuRx), which can be active at all times and consume less power compared to the main radio. In this paper, we propose a discrete event model for the WuRx sensor node that depicts the various operation modes associated with the energy computation of each mode. Furthermore, the effectiveness of the WuRx in reducing the energy consumption and increasing the throughput is verified by simulating a WSN and comparing the energy consumption with other common energy saving techniques.