# A Reliability Scheduling Algorithm for the Static Segment of FlexRay on Vehicle Networks +
## 3 Experimental Results
### Performance Evaluation  
In order to evaluate the performance of the proposed algorithm, we compared the execution time and slot utilization with existing algorithms [9; 10; 11]. This comparatively analyzes the related work to achieve the desired reliability target needed to determine the running time and slot usage. The slot utilization is related to the bandwidth utilization of FlexRay, as in Equation (10):  
\[\text{Slot Utilization }=\frac{used\ slots}{all\ slots}=\sum_{1}^{n}\frac{RT_{i}+1}{ T_{i}}\times\frac{L_{FC}}{N_{slot}}\ \leq\ 1 \tag{10}\]  
These methods [9; 10; 11] show the execution time and slot utilization in experimental results; however, they did not discuss the relationship between performance (running time) and resource utilization (slot usage) when the number of messages is increased. Now that we have proposed a cost function, we can use it to analyze the performance and efficiency of previous works, as in Equations (11)-(13):  
\[cost=K_{1}\times f(\Delta time)+K_{2}\times f(slot) \tag{11}\]  
\[f(\Delta time)=\text{slope}(t_{i},t_{i-1})/\Delta\text{number of message }\times 100\%,i=2,\ldots,n \tag{12}\]  
\[f(slot)=\text{slot utilization}/\text{number of messages} \tag{13}\]  
where \(K_{1}\) and \(K_{2}\) are the weight factors in the cost function, and they are the same and equal to 1 to balance the performance and resource utilization. \(f(\Delta time)\) is used to evaluate the rates of change (slopes) between the running time and the increased number of messages. Note that the \(cost\) value will be invalid in two cases: \(f(\Delta time)\) is negative when \(t_{i}\) is smaller than \(t_{i-1}\), and the other is the lowest number of messages is the baseline for the slope function. \(f(slot)\) indicates the resource utilization of a single message in each experiment. First, the experimental data will be separated into three parts according to the different parameter configurations of existing methods. The message parameters are generated by random and each setting has 100 examples. The FlexRay bus parameters are fixed in Setting 1 and Setting 3, and are not fixed in Setting 2, as shown in Table 2. In addition, these results are also compared directly by \(cost\) value. The comparison and analysis of the proposed FRSA and existing methods in each setting are as follows. \(\bullet\) Comparison 1, [PERSON]'s method [9]  
In [9], there are 16 test cases with fixed parameters in FlexRay in the experiment. In particular, the probability of failure (\(PF_{i}\)) is not related to the size of messages and the bit error rate, but is varied between 1% and 50%, respectively. The major focus of [PERSON]'s method is to save the bandwidth utilization rate. They defined an evaluation function to calculate the greatest contribution value, and then generated a new package of message re-transmission. This means that each message which is retransmitted makes a significant improvement in reliability and further improves slot usage. As the main aim of [PERSON]'s method, we can observe that work [9] has better performance in saving slot utilization than the proposed FRSA when the number of signals under 16, as Table 3 shows. However, along with an increase of the number of messages in test cases, the computational complexity of the evaluation function always causes a greater time cost than the proposed FRSA, as shown in Figure 4. When the performance evaluation is according to cost function, the fluctuating range of \(f(\Delta time)\) of [PERSON]'s method is more extreme than the proposed method. In addition, the average \(cost\) of the proposed method is better than [PERSON]'s method.