## 4 Results
### Vulnerability Results  
Since the results of this paper focus on evaluating our framework within the context of the Modbus protocol, increased interest was placed on the critical transitions of the device processing and timeouts when receiving valid and invalid attack packets, as shown in Figure 11. Of particular interest was the ability of the DUT to filter incorrect packets and maintain the responses to valid packets. At the beginning of each test, the configuration of  
Figure 10: Network simulation of device.  
Figure 9: Intelligent electronic device configuration.  
the specific test is saved, allowing for replication of any discovered vulnerabilities. This also allows a user to re-run and capture any traffic sent on the network.  
During our testing, the device was only abnormally affected when correct Modbus headers were sent, as outlined in Figure 4. However, another interesting issue arose when the device did not respond to valid packet headers, an exception was returned for the attack traffic, as shown in Figure 12. This response is unexpected, as the transaction identifier and unit identifier were incorrect for the device's Modbus configuration. To mitigate the impact of packets that degrade link reliability, it is essential to implement practical strategies that can enhance the resilience of communication systems in real-world deployments. One such strategy is the use of redundancy, where multiple copies of critical packets are transmitted to ensure device operation in applications that are not time-sensitive. Additionally, adopting a defense-in-depth approach, which involves layering multiple security and reliability measures, can help further safeguard the network and ensure malicious packets are not transmitted to an endpoint. This could include error detection and correction protocols, traffic prioritization, and congestion management. Furthermore, utilizing adaptive communication strategies, such as dynamically adjusting the packet size or transmission rate based on network conditions, can ensure better performance under fluctuating conditions.  
From the results collected in Table 1, we can see that these invalid responses were only obtained when 10 packets or more per second were injected into the connection, and these responses were only generated when a valid Modbus application header was present with a valid protocol identifier. This illustrates the ability to detect incorrect or incomplete protocol implementations.  
Figure 11: Modbus device states.  
Figure 12: Incorrect device response.  
The results presented in this section demonstrate the effectiveness and feasibility of the proposed framework in detecting errors that arise from device implementations of protocol specifications. This capability is of paramount importance for ensuring the seamless interoperability of devices within distributed networks. By employing formal modeling techniques, the framework is able to pinpoint critical transitions within the device implementations that could potentially lead to vulnerabilities. Additionally, the physical testbed plays a key role in generating reproducible test scenarios that simulate real-world conditions, allowing for the validation of a device's operation under varying network loads. The insights and results obtained from these tests can then be directly translated into high-fidelity network simulations, providing a comprehensive understanding of device performance and potential issues in realistic network environments.