## 3 Research Method
When a data set exhibits a standard normal distribution, the probability of a data point deviating from the mean can be calculated. In this study, the collected data were standardized for a standard normal distribution; the average \(\overline{x}\) was 0, and the standard deviation \(S\) was 1. The \(Z\)-scores of all data points were calculated; \(Z\) = 0 indicated that the data point was equal to the mean, \(Z\) = 1 indicated that the data point was one standard deviation from the mean, and so forth. The equation of standard deviation is shown in (1) and the data points were converted into \(Z\)-scores using the following Equation (2):  
\[\sigma=\sqrt{\frac{1}{N}{\sum_{i=1}^{N}{(x_{i}-\overline{x})}^{2}}} \tag{1}\]  
\[Z=\frac{x_{i}-\overline{x}}{\sigma} \tag{2}\]  
In a normal distribution curve table, the probability of a data point's \(Z\)-score being \(\leq\)3 is 95.7%, and the probability of it being \(>\)3 is 4.3%. Therefore, in this study, data points with a \(Z\)-score of \(>\)3 were considered outliers and did not account for more than 4.3% of the total data. The average and standard deviation of the travel times between a pair of departure and arrival locations were calculated, with the data points that were three or more standard deviations away from the average being excluded. The average of the remaining data was then calculated and used as the average travel time between the pair of departure and arrival locations. The data are stored in the MS SQL database using T-SQL for computing which can ignore the process of importing data and reduce the time. A Pseudocode is shown in Figure 3.  
Following the aforementioned procedures, we could obtain the average travel time between two points for which historical travel data were available. However, not all pairs of locations had direct travels between them, and for some locations, the number of direct travels was low. For these locations, the average calculation was not conducted because sample size reflects the quality of the result, with a larger sample indicating a higher level of representativeness of the obtained result. A small sample would possibly fail to reflect the actual travel time under regular travel conditions. To ensure the quality of our results, travel history with an inadequate sample size was excluded. Before proceeding with this study, the original electronic maps used by the fleet estimated the travel time between two locations by planning the shortest route and the static predicted travel time, without considering the traffic conditions in different periods or peak and off-peak travel hours. Since the travel time is obtained from the electronic map planning route, the data source is the determined road length and speed limit, which should be highly representative in theory. However, additional verification was required if this study's estimated results differed considerably from the estimations by the electronic maps. A reference ratio is the percent ratio of the sample size to the difference between the estimated and electronic map data. The number of samples has a positive relationship with the reference rate, while the difference between the predicted results and the electronic map's estimations has a negative relationship with the reference rate. First, the predicted travel time is obtained from the model and the ratio of the difference between the travel time of the original map and the travel time of the original map. Then, the reference rate is obtained by (number of samples/time difference) \(\times\) 100%. The lower reference rates will be excluded and not used, to confirm that the quality of the statistical results is sufficient to replace the prediction results of the original map. For example, if there is a group of data with a sample size of 17, the average travel time obtained by this study model is 3270, and the travel time predicted by the map is 2796, the time difference is \((3270-2796)/2796=16.9\), and the reference rate is 17/16.9, which is about 100%. The equation of reference rate is shown in (3).