## 4 Modeling of AV-Mixed Traffic Information Services
### Modeling of Services  
In this sub-section, traffic information services are modeled via the notation proposed in Section 3.2, including the operations' name for each service and the input parameters/output for each operation. As presented in Table 3, the primitive information service provides seven types of AV-mixed traffic information. The input parameters for each operation consist of time/location conditions. Time condition (\(\{fromTime,toTime\}\)) refers to a time range, and location condition (\(\{minimumLongtitude,maximumLongtitude,minimumLatitude,maximumLatitude\}\)) refers to a location range. The output of each operation is the list of \(TrInfo^{Type}\) (\(\langle TrInfo^{Type}\rangle\)). Figure 4: Process of Service Derivation. \begin{table}
\begin{tabular}{c c} \hline
**Name** & Primitive Information Service \\ \hline
**Description** & A service consisting of operations that provide predefined \\  & types of AV-mixed Traffic Information \\ \hline
**Operation** & **Input** & **Output** \\ \hline getTrafficFlow() & \(<TrInfo^{Flow}>\) \\ \hline getTrafficIncident() & \(<TrInfo^{Incident}>\) \\ \hline getTrafficFacility() & \([\{fromTime,toTime\},\) \\  & \(\{minimumLongitude,\) \\  & \(maximumLongitude,\) \\  & \(minimumLatitude,\) \\  & \(maximumLatitude\}]\) \\ \hline getTrafficSignal() & \(<TrInfo^{Signal}>\) \\ \hline getAutonomousVehicle() & \(<TrInfo^{AutVehicle}>\) \\ \hline \end{tabular}
\end{table} 
Table 3: Specification of Primitive Information Service. Table 4 presents the descriptive information service. It has four operations that are filtered and removed based on professional opinions, as shown in Figure 4. These operations provide the descriptive statistics (minimum, q1, median, q3, maximum, standard deviation, mean) of information type. The input parameters of each operation consist of time/location conditions. \(\delta\) is a function that calculates the descriptive statistics of values in the elements of \(C\) in \(TrInfo^{Type}\). The output of each operation is the list of descriptive statistics. Table 5 presents the diagnostic information service. It has two operations that are filtered based on professional opinions, as shown in Figure 4. These operations provide the results of diagnostic analysis (e.g., regression and correlation analysis). The input parameters of the first operation consist of one any \(TrInfo^{Type}\) (\(TrInfo^{Any}\)), which is the dependent variable, any multiple \(TrInfo^{Type}\) (\(\langle TrInfo^{Any}\rangle\)), which are the independent variables, and time/location conditions. \(\zeta\) is a function that derives the multiple important \(TrInfo^{Type}\) that influence an event (e.g., traffic accidents) and the importance values. The output of this operation is the list of important factors and their importance values (\(<\{importantFactor,\ importanceValue\}>\)). The input parameters of the second operation consist of any two \(TrInfo^{Type}\) (\(\{TrInfo^{Any}\), \(TrInfo^{Any}\}\)) and time/location conditions. \(\eta\) is a function that calculates the Pearson correlation coefficient between two \(TrInfo^{Type}\). The output of this operation is the list of the Pearson correlation coefficients (\(\{correlationValue\}\)). \begin{table}
\begin{tabular}{c c} \hline Name & \multicolumn{2}{c}{Descriptive Information Service} \\ \hline \multicolumn{2}{c}{A service providing descriptive statistics} \\
**Description** & \(\#\delta:\ link\ or\ lane\ \rightarrow\) \\  & \( descriptive\ statistics\ of\ value(s)\ in\ elements of\ C\ in\ TrInfo^{Type}\) \\ \hline
**Operation** & **Input** & **Output** \\ \hline getTrafficFlowStatistics() & \(\{\{fromTime,toTime\}\), \\ \hline getTrafficIncidentStatistics() & \(\{\{minimumLongitude,\}\) \\  & \( maximumlongitude,\) \\ \hline getAutonomousVehicleStatistics() & \( minimumLatitude,\) \\ \hline getTrafficFlowIndexStatistics() & \( maximumLatitude\}]\) \\ \hline \end{tabular}
\end{table} 
Table 4: Specification of Descriptive Information Service.