## 3 Proposed ASVMR Protocol
### Adaptive Pipe Radius Scheme  
In practice, it is typical to select a sufficiently large routing pipe radius to increase the number of candidates forwarding nodes and improve the PDR. However, a larger radius also enables more sensor nodes with comparable waiting times to forward the same data packet, leading to redundant transmissions and energy waste. To enhance energy efficiency, it is necessary to impose additional restrictions on the data packet transmissions during the routing process.  
However, if the data packet transmissions are suppressed excessively, it will result in a reduction in the PDR. The PDR is a measure of transmission reliability. In a sparse network, where it is essential to increase the PDR, the pipeline imposes fewer restrictions on the participating sensor nodes. Conversely, in a dense network, to minimize unnecessary energy consumption, the pipeline imposes limitations on the sensor nodes involved in routing. Therefore, to enhance the energy efficiency and maintain high transmission reliability, we propose an adaptive pipe radius scheme.  
Figure 4: Neighbor selection, forwarding, and waiting time calculation.  
First, the routing pipe radius is initialized as the maximum value \(R\). To balance transmission reliability and energy consumption, a PDR threshold is utilized, which can be tailored to suit the specific requirements of the practical application scenario in the UASN.  
Second, the source attaches the number of generated data packets to the transmitted data packet during the data packet transmission phase. After the data packet is received, the sink node determines the PDR by dividing the quantity of data packets successfully delivered by the overall count of generated data packets.  
If the PDR exceeds the threshold, the routing pipe radius will be reduced during the subsequent transmission to improve energy efficiency. If the PDR falls below the threshold, the sink node initiates a broadcast message to expand the routing pipe radius, and the source will attach the new routing pipe radius to the transmitted data packet. This will result in an increase in the pipe radius of eligible forwarders during the next transmission round, which will improve the delivery ratio.  
The proposed adaptive pipe radius scheme is illustrated in Algorithm 1.  
```
\(R\) is the communication range of nodes. \(P_{\text{gen}}\) is the cumulative count of data packets generated. \(P_{\text{rec}}\) denotes the number of data packets that have been successfully received. \(PDR\) is the current PDR. \(PDR_{\text{th}}\) is the predefined threshold of PDR.
1: Initialize the routing pipe radius to \(R\)
2:while the packet transmission phase is ongoing do
3: Commerce a fresh iteration of data packet transmission
4: Attach \(P_{\text{gen}}\) to the transmitted data packet at the source
5: Calculate the PDR at the sink node using \(PDR=\frac{P_{\text{gen}}}{P_{\text{gen}}}\)
6:if\(PDR>PDR_{\text{th}}\)then
7: Decrease the routing pipe radius during the next transmission round
8:else
9: Increase the routing pipe radius during the next transmission round
10:endif
11:endwhile
```  
**Algorithm 1**Adaptive Pipe Radius Scheme