## 2 Related Work
### Broadcast Routing Protocols  
To achieve broadcast, flooding [14] is a simple approach in that it provides fast broadcast even though it does not consider real-time requirements. The source node broadcasts a data packet, and then, the neighbors located within one hop from the source node receive the packet. Each neighbor rebroadcasts the packet to its own neighbors, but does not broadcast the same packet received before. This process is repeated until all sensor nodes receive the packet. Flooding is simple and fast since fast nodes are naturally selected to forward the packets. At each hop, a node receiving and processing the packet first can forward it immediately. However, frequent flooding can be a huge burden on the networks since it consumes many network resources. In flooding, all sensor nodes have to transmit the packet once and receive many duplicated packets from their all neighbors. Therefore, without any consideration for real-time service, this broadcast storm problem may lead to the increase of delay, collision and congestion, which adversely affect real-time performance. As for energy-efficient broadcast, existing geographic broadcast protocols [15; 16; 17] try to minimize the number of forwarding nodes. Since the problem of minimizing the number of forwarding nodes is known to be NP-hard [18], they solve the problem by heuristic-based or topology-based plans. Sprinkler [15] reduces the number of forwarding nodes with the topology-based plan. It embeds a virtual grid structure over the network to separate sensor nodes in a suitable range for one-hop broadcast. Only one sensor node per cell becomes a forwarding node, and others only receive the packets. Moreover, construction of a virtual grid does not incur the transmitting and receiving costs since it is constructed by only the computation of each node. However, detouring paths of Sprinkler are a critical problem for real-time communication. In addition, [PERSON] and [PERSON] [16] decrease the number of forwarding nodes by a probability-based algorithm, one of the heuristic-based strategies. They made the observation that if the node has more siblings, there is a higher likelihood that its child nodes receive a packet, even if it does not forward the packet instantly. In this way, the more siblings a node has, the more its forwarding likelihood may be diminished. Meanwhile, if a node has numerous child nodes, it needs to forward the packet with a higher likelihood. Therefore, forwarding likelihood corresponds to the quantity of child nodes and conversely relative to the quantity of sibling nodes. [PERSON] et al. [17] propose the tree-based broadcast protocol, one of the topology-based plans. They construct a spanning tree out of all nodes in the network rooted at the source of the broadcast. The broadcast tree eventually becomes a Breadth-First Search (BFS) tree  
Figure 1: State transition diagram example of (2,3)-firm [6] where M and m represent deadline meet and miss, respectively. where each node maintains the shortest path to the root. This protocol also reduces the number of forwarding nodes. However, it is less effective than others since the first goal is the shortest path. As mentioned above, these broadcast protocols focus on energy efficiency, not the real-time requirement. In other words, they do not consider the node's delay for electing forwarding nodes, so this can lead to real-time performance being unsatisfied. In addition to the mentioned approach, there are some research works to improve the broadcast routing protocol by introducing the opportunistic flooding algorithm in WSN. First, [PERSON] et al. [19] proposed opportunistic flooding in low-duty-cycle networks with unreliable wireless links and predetermined working schedules. Here, a new forwarder selection method is presented to resolve simultaneous forwarding operations through the hidden terminal problem and a link-quality-based backoff method. [PERSON] et al.