## 1 Introduction  
In harsh industrial fields, workers can be exposed to unexpected accidents. Damage can be reduced or avoided if the proper measures are taken in time. This requires a context-aware monitoring and control system in which a sink or server collects context data from sensor devices (nodes) installed in the target work field, judges the situation based on the analysis of the collected data, and warns the workers of any accident by sending a warning message to the nodes around the accident site. The slotted sense multiple access (SSMA) protocol deals with the problem of reliable data collection from sensor nodes in wireless sensor networks (WSNs) [1]. On the contrary, a sink or a server needs to send a message or command for warning to some nodes or actuators in the target field. In this case, the warning message has to be delivered in a reliable manner under a reasonable delay bound. However, it is difficult to achieve this due to time-varying link conditions caused by node mobility, and internal and external interferences (internal interference indicates an interference caused by different data transmissions in the same network, while external interference is caused by data transmissions in other wireless networks using the same frequency band) [2], and various obstructions such as steel materials, concrete blocks, etc. The energy management of a node is another critical issue due to the difficulty in replacing a battery. Thus, this paper aims at designing a protocol for a reliable and energy-efficient delivery of a command message in dynamic WSNs. Various protocols for the transmission of a command message have been proposed so far and can be divided into three categories: flooding [3; 4], selective rebroadcasting [5; 6; 7; 8; 9; 10; 11], and tree-based rebroadcasting [12; 13; 14]. The first category is a brute-force flooding approach in which a node rebroadcasts a received message after a random delay if it receives the message for the first time. It can achieve high reliability in message delivery; however, it causes high-energy consumption due to poor energy management, as well as the redundancy of transmitting and receiving or overhearing an identical broadcast message multiple times. The Glossy protocol [4] tried to reduce the flooding period with the use of capture effect, by which a node can demodulate a message successfully if it receives multiple identical messages within the time difference of 0.5 \(\upmu\)s or smaller. Thus, every node rebroadcasts a received message with no delay. It can save energy; however, if all nodes have to rebroadcast a message, and the nodes that fail to demodulate a message have to remain active until it receives the message successfully from other nodes. Meanwhile, many approaches are based on selective rebroadcasting. In Reference [5], they adjust a rebroadcast probability dynamically such that the more broadcast messages a node has received, the lower the probability of rebroadcasting it gets. In the dynamic probabilistic flooding algorithm based on neighbor information (DPFNI) protocol [6], a node also adjusts its rebroadcast probability such that the more siblings it has, the lower probability it gets, and the more children it has, the higher probability it gets. The rebroadcast probability is dynamically adjusted according to the change history of neighbor relationships after the specified times of flooding. Another approach builds a connected dominating set (CDS) such that flooding is completed if every node in a CDS rebroadcasts a message once [7]. In Reference [8], the protocol relies on slot scheduling to avoid collision, as well as the construction of a CDS. Finding the optimal CDS is known to be NP-complete [15]. Thus, in paper Reference [9], instead of finding a CDS, they try to assign a broadcast slot number incrementally to a node according to the distance from the node to a sink, and adjust the broadcast slot numbers for multiple nodes of the same distance to remove the possibility of collision.