## 5 Experimental Results  
To evaluate our message scheduling method, we applied it to the communication system which has 4 nodes in BMW X7. The duration of communication cycle is the typical value of 5 ms in where the static segment occupies 3 ms and the dynamic segment occupies 2 ms. And other simulation parameters are shown in Table 3. The table shows the configuration of FlexRay network parameters dedicated to construct the data frame. In this study, we designed experiments with two different sets of data (Tables 4 and 5). Table 4 shows the SAE benchmark data. Table 5 shows the signal parameters of BMW's 7 series where signal repetition rate is set to 1, 2, 4 and 8 respectively. Both of Tables 4 and 5 shows in detail about the period of transmitted signals of each ECU, repetition, and data length. The experiment was as follows. (1) Using the SAE benchmark data. Let signals of Table 4 as experimental raw data. Repetition values are set to 1, 2, and 20. The sample signal's length is equal to 8 bits and randomly expanded. The proposed algorithm and BCBFD algorithm which BC and BFD is an abbreviation of Bandwidth Consumption and Best Fit Decreasing respectively [15], are used to the signal set packing, respectively. Compared the upper and lower limits of payload data payload length, as well as bus utilization and the number of slots. Figure 6 shows that how the upper and lower bound of the frame's payload of \(l^{L}\), \(l^{H}\) change when the number of signals increases. As shown in Figure 6, the lower bound of the frame payload length of the two algorithms is fixed and have equal values. It is determined by the maximum value of the length of all signals in the node. It results in the effective length of 8 bits in a single signal payload without considering a signal expanding. Even in the case of continually increased \(l^{H}\), it can be seen that the NFD scheduling algorithm can effectively control the increase of the upper bound of the payload, and save operation time. As shown in Figure 7, the result of the curve of network utilization indicates that the average network utilization rate of scheduling algorithm proposed in this paper has a higher value than the average network utilization rate of BCBFD algorithm. Even though the network utilization of BCBFD algorithm increases with the number of signals, there is a gap that compared with the algorithm in this paper. This shows that the NFD scheduling algorithm has a stronger ability to save network resources. The comparison of the slot number is shown in Figure 8. The number of FIDs in BCBFD algorithm increases linearly with the number of messages, while the number of FIDs in NFD algorithm increases slowly. The conclusion is that the NFD scheduling algorithm is stronger than the BCBFD algorithm in resolving scheduling problems of static segment. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Signal** & **ECU** & **Repetition** & **Size (bit)** & **Signal** & **ECU** & **Repetition** & **Size (bit)** \\ \hline
1 & 1 & 1 & 20 & 26 & & 4 & 20 \\
2 & & & 12 & 27 & & & 16 \\
3 & & & 10 & 28 & & & 8 \\
4 & & 2 & 16 & 29 & & & 8 \\
5 & & & 12 & 30 & 3 & 2 & 16  
BCBFD algorithm and NFD scheduling algorithm execution time ratio is shown in Figure 9. The bound of upper and lower of the length payload segment are precisely calculated, also effectively reduced. The number of iterations of the algorithm is reduced, and the execution efficiency of the algorithm is improved. Figure 8: Comparison of frame ID (_FID_). Figure 6: Bound limits of the frame payload segment. Figure 7: Comparison of network utilization. (2) Using the BMW's 7 series data, to show the benefits of the NFD algorithm, we used the illustrative case, and compared with BCBFD algorithm [15]. The experiment is based on the vehicle bus simulation tools Network Designer and CANoe. FlexRay where the network system is built on. The case uses the data of Table 5. The signal data length is 2-20 bit, the payload length is taken as 20-56 bits, and the repetition rate of BMW 7 Series are 1, 2, 4, and 8.