## 3 Proposed Scheme: FRBP
### Real-Time Broadcast Tree Construction  
The real-time broadcast tree is composed of three major components: root (source node), intermediate nodes and leaf nodes. To satisfy the \((m,k)\)-firm real-time constraint, the tree construction scheme employs transmission speed estimation, which is the main idea of SPEED [5]. In other words, intermediate nodes in a tree are elected among sensor nodes satisfying the transmission speed. If all intermediate nodes are composed by nodes with a faster speed, then leaf nodes can receive data packets within the deadline consequentially. For energy efficiency, the tree construction scheme tries to elect as few intermediate nodes as possible. The more the leaf nodes, the less energy is consumed since leaf nodes, unlike intermediate nodes, only receive packets, but not transmit them to other nodes. The details are described as follows. The source node generates a Real-time Broadcast Tree Construction (RBTC) message and disseminates it throughout the network by flooding [14]. The RBTC message includes source location, required transmission speed, sender location, sender transmission speed, sender's parent location and hop count. The information is used for intermediate nodes' election and recovery mechanism. The required transmission speed is calculated by the source node with the desired time deadline and the distance between the source node and the farthest destination. We assume that the source node is aware of the approximated network location since the application-specific property implies planned deployment. The source node measures the farthest network edge from itself as the farthest destination. The hop count means the number of hop counts from the source node and also the level of the broadcast tree. Each sensor node elects its own parent within the neighbors with the election rules related to the tree construction goals. After a node receives the RBTC message, the node performs the parent election process. As described in Algorithm 1, the node excludes neighbors located farther than itself from the source node from being parent candidates. The node also excludes neighbors that do not satisfy the transmission speed for real-time data dissemination. All remaining neighbors could be parent candidates since they satisfy the real-time condition. The node then elects a parent among the candidates with additional rules for energy efficiency. The node compares the hop counts and holds candidates having the least hop count. Lastly, the farthest candidate from the source node is elected as a parent node. These last two rules could contribute to reducing the number of intermediate nodes. Figure 2 shows an illustration of the process. After the parent election process is completed, child nodes announce child information to their parents. Unexpected sensor nodes become leaf nodes and do not participate in the real-time broadcast. Each node maintains the information of neighbors for recovery mechanism, even though the neighbors are eliminated from being parent candidates. The real-time data packets are disseminated along the real-time broadcast tree. The packets could arrive at all sensor nodes since every intermediate node satisfies the required transmission speed. The real-time broadcast tree could reduce energy consumption in comparison with flooding since leaf nodes do not transmit packets, unlike flooding where all nodes transmit packets.