# A Reliability Scheduling Algorithm for the Static Segment of FlexRay on Vehicle Networks +
## 3 Experimental Results
### Performance Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Message Parameter Configuration in Static Segments**} \\ \hline
**Parameter** & **Setting 1** & **Setting 2** & **Setting 3** \\ \hline Period (\(T_{l}\)) & 5 ms\(\sim\)-20 ms & 1 ms\(\sim\)-25 ms & 2 ms\(\sim\)-40 ms \\ Deadline (\(D_{i}\)) & same as \(T_{i}\) & same as \(T_{i}\) & same as \(T_{i}\) \\ Size of message (\(S_{i}\)) & 64 bits & 32 bits–72 bits & 32 bits \\ Bit Error Rate (BER) & - & \(10^{-3}\) & - \\ Probability of failure (\(PF_{i}\)) & 1\%-50\% & \(1\ -\ (1\ -\ BER)^{S_{i}}\) & 1\%-50\% \\ \hline \multicolumn{4}{c}{**The Parameter Configuration of FlexRay Buses**} \\ \hline FlexRay cycle (\(L_{FC}\)) & 5 ms & 5 ms & 5 ms \\ Length of static segment (\(L_{ST}\)) & 3 ms & 3 ms & 3 ms \\ Length of slot in SS (\(L_{slot}\)) & 20 us & 8.3 us-50 us & 8.57 us \\ The number of slot in static segment (\(N_{slot}\)) & 150 & 60\(\sim\)360 & 350 \\ \hline \multicolumn{4}{c}{**The Parameter Configuration of Systems**} \\ \hline Range of messages & 5–20 & 1\(\sim\)60 & 5–20 \\ System reliability goal (\(SR\)) & 99\% & 99\% & 99\% \\ Testing time (\(\tau\)) & 3,600,000 ms & 3,600,000 ms & 3,600,000 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameter settings of related work. Figure 4: Comparison of running time with [PERSON]’s method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of Messages**} & \multicolumn{2}{c}{**Proposed Method**} & \multicolumn{2}{c}{**[PERSON]’s Method [9]**} \\ \cline{2-5}  & **Running Time** & **Slot Utilization** & **Running Time** & **Slot Utilization** \\ \hline
5 & 7.79 & 16.54 & 48 & 12 \\
6 & 7.17 & 26.84 & 51 & 20 \\
7 & 7.79 & 30.84 & 54 & 26 \\
8 & 8.39 & 36.24 & 59 & 28 \\
9 & 8.93 & 40.25 & 62 & 36 \\
10 & 9.51 & 45.97 & 67 & 40 \\
11 & 10.26 & 49.75 & 66 & 46 \\
12 & 10.72 & 54.12 & 70 & 50 \\
13 & 11.44 & 59.92 & 78 & 56 \\
14 & 12.0\(\bullet\) Comparison 2, [PERSON]'s method [11]  
On the other hand, [PERSON] et al. proposed a frame-packing algorithm based on transmission reliability (FPBTR) [11]. This algorithm is implemented by considering both reliable transmission and maximized bandwidth utilization. The comparison of the running time and slot utilization of the proposed FRSA algorithm and [PERSON]'s method are shown in Table 4. According to the FPBTR method, the number of slots in the static segment (\(N_{slot}\)) is dependent on the range of messages; they do not optimize static slot allocations. The proposed FRSA excluded messages which do not need to re-transmitted to further improve slot utilization. It can be found that the proposed FRSA has better performance in slot utilization than [PERSON]'s method when the same parameters are utilized. Moreover, the FPBTR method has been focused on optimizing the frame packing of \(L_{slot}\) and \(N_{slot}\) which creates a greater time cost to meet the demands of the given reliability than the proposed FRSA, as shown in Figure 5.  
\(\bullet\) Comparison 3, [PERSON]'s method [10]  
[PERSON] et al. [10] proposed a method to sort each message in descending order by its reliability value. After sorting, the new single message reliability goal is according to the reliability of the previous message. When the reliability goal does not satisfy reliability constraints, [PERSON]'s method computes the average of the reliability value of messages; if the reliability of messages is smaller than the average value, then these messages should be corrected. The comparison of the slot utilization of the proposed FRSA algorithm and [PERSON]'s method is shown in Table 5. [PERSON]'s method has better performance in slot utilization in each test case; however, with the iterative method, it is difficult to estimate the execution time. Obviously, the \(f(\Delta time)\) of [PERSON]'s method increased sharply when the number of messages is 8.