## 3 System Model  
### Mechanism Description  
Figure 1 shows the architecture of the UWSN considered in this paper. As shown in Figure 1, we consider a homogeneous UWSN consisting of three types of nodes: the base station (BS), SNs, and CHs. Each SN or CH has the same physical characteristics and operating mode. SNs are cheaper and have less energy than CHs, which cannot directly communicate with the BS. CHs have more energy and gather packets sent by SNs and forward them to the BS. SNs can generate two types of packets based on different perceived environmental content: emergency packets and non-emergency packets. The information carried by emergency packets is highly urgent and requires timely transmission to the BS. Non-emergency packets have lower real-time transmission requirements and can tolerate significant queueing delays. Therefore, emergency packets are given higher priority and can preempt non-emergency packets' cluster head forwarding rights. Considering that the packets generated by each SN arrive at each CH without discrimination, we mainly focus on analyzing a single CH system to evaluate the overall performance of this architecture. Figure 2 describes the packet forwarding mechanism in the system. Figure 1: The UWSN architecture we considered in this paper [26]. In Figure 2, considering the high sensitivity of emergency packets to latency and the high throughput requirements of non\(-\)emergency packets, a cache with capacity \(K(K\geq 0)\) is set for only non\(-\)emergency packets. However, suppose many non\(-\)emergency packets are stuck in the system. In that case, it may reduce the forwarding performance and make the waiting packets lose their timeliness. Therefore, an access control mechanism is introduced to determine whether non\(-\)emergency packets can enter the cache. Non\(-\)emergency packets will dynamically change their access probability \(f(\tilde{f}=1-f)\) based on the amount of packets. The more packets there are, the less likely the incoming non\(-\)emergency packets can access the system. The access probability \(f\) is expressed as follows. \[f=1-\frac{N(1-f_{\text{min}})}{K+1} \tag{1}\]  
where \(N\) is the amount of packets, \(f_{min}(0\leq f_{min}\leq 1)\) is the minimum value of \(f\), and \(K\) is the cache size. Due to the fact that the cache can hold up to \(K\) packets and the CH can hold one packet, \(N\) will not exceed \(K+1\). For the sake of simplicity, let \(\alpha\)=\(\frac{K+1}{1-f_{\text{min}}},\alpha\in[K+1,\infty)\) and refer to \(\alpha\) as the adjustment factor of \(f\). Therefore, the access probability \(f\) can be succinctly expressed as follows. \[f=1-\frac{N}{\alpha} \tag{2}\]  
We define the packet forwarding process by the CH as the working state; otherwise, it is defined as the sleep state. When the CH is in sleep state, it can be regarded as a cache space that can only hold one packet rather than forward it. Considering that the transition of the CH from the sleep state to working state requires a significant amount of energy consumption, a wakeup control mechanism controlled by a wakeup threshold \(H(0\leq H\leq K)\) is introduced to reduce the state switching frequency of the CH. The setting of \(H\) cannot exceed the cache size \(K\), so that the system can accumulate \(H\) non\(-\)emergency packets before being awakened, thereby reducing the frequency of state switching. Only  
Figure 2: The packet forwarding mechanism. when the CH is in the working state or the amount of non\(-\)emergency packets in the cache reaches \(H\) will the CH forward the non\(-\)emergency packets in the cache. On the contrary, once emergency packets arrive at the CH, the CH will forward them directly.