# Service-Oriented Cooperation Policies for Intelligent Ground Vehicles Approaching Intersections
## 3 Fundamental Traffic Models and Cooperation Procedure
### Fundamental Traffic Environment Objects  
\(\ell\) and \(\ell_{c}\) are separately defined as a piecewise lane and the current lane on which one vehicle is traveling. An intersection I is a critical traffic area connecting several crossed lanes. In our previous work, \(j^{th}\) intersection I\({}_{j}\) is presented as a tuple: \(<id=j,\zeta_{\ell}^{\texttt{I}_{j}},\{<\ell_{jk},\varpi_{jk},\epsilon_{k1}, \epsilon_{k2}>|\ell_{jk}\in\zeta_{\ell}^{\texttt{I}_{j}},k\in\{1,2,\ldots,| \zeta_{\ell}^{\texttt{I}_{j}}|\}\}>\), as detailed in Table 1.  
To improve the traffic efficiency, one intersection is always divided into a group of no-overlapping rectangular parts, and each inseparable part can be only allocated to one vehicle each time. In our work, each such part is presented as a Static Critical Section(S-CS): \(\gamma\), as shown in Figure 2a. Furthermore, the \(m^{th}\) critical section \(\gamma_{m}\) is expressed via a tuple \(:<id=m,\vec{c},l,w,\zeta_{\ell}^{m},\tau>\), as detailed in Table 1. Of course, one intersection can be mapped to a unique critical section as shown in Figure 2b, simplifying  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Para** & **Definition** & **Para** & **Definition** \\ \hline \multicolumn{4}{c}{Intersection, Critical Section, and Special Positions for one Intersection} \\ \hline I\_id_ & identification number. & \(\mathbb{L}_{\zeta_{\ell}^{\texttt{I}}}^{\texttt{I}}\) & set of connected lanes. \\ I\_\(\Delta\varpi_{jk}\) & direction of \(\ell_{jk}\); & \(\mathbb{L}_{\texttt{c}k_{1}},\mathbb{L}_{\texttt{c}k_{2}}\) & coordinates of two connecting points between I\({}_{j}\) and \(\ell_{jk}\). \\ \(\gamma\)_id_ & identification number. & \(\gamma.\vec{c}\) & coordinate vector of all vertices. \\ \(\gamma\)\(\zeta_{\ell}^{k}\) & set of connected lanes. & \(\gamma\)-\(s\) & status of section: available or forbidden. \\ \(\gamma\)\(\cdot\)I & length of \(\gamma\). & \(\gamma.w\) & width of \(\gamma\). \\ \(\gamma\)\(\cdot\)\(\tau\) & token of \(\gamma\). & \(P_{v}\) & vehicular current position. \\ \(P_{a}\) & position where vehicles beginning & \(P_{r}\) & position where vehicles submit \\  & to adjust the velocity. & & reservation messages. \\  & position where vehicles start to & & position vehicles can’t travel across \\ \(P_{\gamma_{m},b}\) & decelerate if it can’t obtain \(\gamma_{m},\tau\). & \(P_{\gamma_{m},\tau}\) is not authorized. \\ \hline \multicolumn{4}{c}{Model of Heterogenous Vehicles} \\ \hline \(v.id\) & identification number. & \(v.\vec{c}\) & purpose of vehicle or vehicular mission. \\ \(v.p\) & vehicular priority, corresponding & & classic vehicle-specific physical \\  & to its QoS. & & and kinematic parameters. \\ \(v.\ell\) & current lane. & \(v.\gamma\) & current occupied section or _null_. \\ \(v.s\) & current state. & \(v.a\) & current action. \\ \(v.\vec{\gamma}\) & vector of required S-CSs. & \(v.\vec{\tau}\) & vector of required tokens. \\ \hline \multicolumn{4}{c}{Vehicular Action Model} \\ \hline \(\alpha.id\) & identification number. & \(\alpha.\zeta_{s}\) & \(\{s_{0},\ldots,s_{k-1}\}s_{i}\) is \((i+1)^{th}\) status of \\  & action transition matrix: & & this action. \\  & \(M_{s}=[\epsilon_{ij}]_{k\times k}\) & \(\alpha.M_{c}\) & condition matrix for action transiting: \\ \hline \hline \end{tabular}
\end{table}
Table 1: Definitions and Parameters of Traffic Object.  
the traffic management while also decreasing the efficiency. Thus, one intersection \(\mathbb{I}\) can be presented as a relationship set \(\zeta_{\gamma}^{\mathbb{I}}\).  
In Figure 2b, there are also a set of particular positions, \(P_{a}\), \(P_{r}\), and \(P_{\gamma b}\), which are the foundation of the reservation-based cooperation. Correspondingly, there are also several distance notations, \(d_{a}\), \(d_{r}\), and \(d_{b}\), employed in our models. All these aforementioned notations are explained in Table 1.