## 3 Modeling of AV-Mixed Traffic Information
### Notation for AV-Mixed Traffic Information  
To express the defined AV-mixed Traffic Information as a logical model, the concept of trajectory, which is a sequence of chronologically ordered points generated by moving objects, is applied. It can contain various types of information, including the location, direction, and speed of moving objects [45]. Therefore, a trajectory can be described as \(\mathit{Tr}=\{\langle p_{1},p_{2},\ldots,p_{n}\rangle|\ p=(mo,t,l,a)\};mo\) is the moving object, \(t\) is the timestamp of the point; \(l\) is the location (longitude, latitude) of the moving object; \(a\) is a list of additional information for moving objects. In the future, information related to moving objects (e.g., AVs and conventional vehicles), immovable objects (e.g., traffic flow detectors and traffic lights), and non-physical objects, such as the traffic control center controlling the moving and immovable objects, will be provided for roads where AVs and conventional vehicles interact. Therefore, in this study, the notation of a trajectory is used and extended in a broad sense to express the AV-mixed Traffic Information types as logical models. Types of the AV-mixed Traffic Information presented in this study are expressed using the following notation.  
**Notation. AV-mixed Traffic Information Type (\(\mathit{TrInfo^{Type}}\))**  
\[\mathit{TrInfo^{Type}}=\{O,T,L,C\}\]  
where,  
\(O:object,\ O=\{objID,\langle objAttr\rangle\}\)  
\(T:time,\ T\subset\{\mathit{crtTime},\mathit{recTime},\mathit{strtTime}, \mathit{endTime}\}\)  
\(\mathit{crtTime}:time\)\(\mathit{time}\)\(\mathit{that}\)\(\mathit{information}\)\(\mathit{was}\)\(\mathit{created}\)  
\(\mathit{recTime}:time\)\(\mathit{that}\)\(\mathit{information}\)\(\mathit{was}\)\(\mathit{recorded}\)  
\(\mathit{strtTime}:time\)\(\mathit{that}\)\(\mathit{event}\)\(\mathit{was}\)\(\mathit{started}\)  
\(\mathit{endTime}:time\)\(\mathit{that}\)\(\mathit{event}\)\(\mathit{was}\)\(\mathit{ended}\)  
\(L:location,\ L\subset\{\mathit{link},\lambda(link),\mathit{node},\mathit{coord}\}\)  
\(\mathit{link}=\{linkID,\langle linkAttr\rangle\}\)  
\(\mathit{\lambda}(link):link\rightarrow\langle lane\rangle,\ lane=\{laneID,\ \mathit{parentLink},\langle laneAttr\rangle\}\)  
\(\mathit{node}=\{nodeID,\langle nodeAttr\rangle\}\)  
\(\mathit{coord}=\{longitude,latitude,\ altitude\}\)  
\(C:\ a\)\(\mathit{set}\)\(\mathit{of}\)\(\mathit{context}\)\(\mathit{attributes}\)\(\mathit{specified}\)\(\mathit{TrInfo^{Type}},\ C=\{\langle contextAttr\rangle\}\)  
\(\mathit{\cdot}\mathit{O}\times T\times L\rightarrow\mathit{contextAttr}\)  
Since the link has one or more lanes, the notation \(<>\) is introduced, which implies the list that can conation multiple values. Note that the element list of \(C\) is determined by the type of AV-mixed Traffic Information (\(\mathit{TrInfo^{Type}}\rightarrow\mathit{C}\)), and the value(s) in each element of \(C\) (\(\mathit{contextAttr}\)) is specified by combining \(O\), \(T\), and \(L\) (\(O\times T\times L\rightarrow\mathit{contextAttr}\)). It is also of note that the value(s) in attributes (\(objAttr\), \(linkAttr\), \(laneAttr\), \(nodeAttr\), \(contextAttr\)) can be any value, data type, length, and dimension.