In mission-critical applications, such as battlefield investigation, fire detection in woodland, and gas monitoring in coal mines, wireless sensor networks are deployed in a wide range of areas, with a large number of sensor nodes detecting and reporting some information of urgencies to the end-users. As there may be no communication infrastructure, users are usually equipped with communicating devices to communicate with sensor nodes. When a decisive event (e.g., gas leak or fire) occurs in the monitoring area and is detected by a sensor node, an alarm needs to be broadcast to the other nodes as soon as possible. Sensor nodes can warn users nearby to escape or take some response to the event. In this paper we aim to design two resolute traffic paths for the transmission of alarm message, and level-by-level offset based wake-up pattern according to the paths, respectively. When a crucial event occurs, an alarm is rapidly transmitted along one of the traffic paths to a center node, and then it is immediately broadcast by the center node along another path without conflict