# Coordinated Multi-Platooning Planning for Resolving Sudden Congestion on Multi-Lane Freeways
## 2 Background and Related Work  
Vehicle platooning refers to a platoon formed by vehicles at close distance and the same velocity on specific road segments. Several models have been proposed for platoon members to perform the car-following maneuver. For example, [PERSON] et al. [17] proposed an extended Intelligent Driver Model (IDM) to describe the car-following behavior. Instead of only considering the front vehicles' position, relative velocity, and delay time, IDM receives the information from both front and rear vehicles to improve the operating efficiency. On the other hand, [PERSON] et al. [18] proposed a Distributed Model Predictive Control (DMPC) method that considers the trajectory of the preceding vehicle to predict parameters such as vehicle velocity, acceleration, and distance for a limited future time to prevent collisions. [PERSON] et al. [19] extended the Cooperative Adaptive Cruise Control (CACC) modeling framework for vehicle following, which prevents vehicles from making unrealistic lane changes. Furthermore, the authors simulated vehicles with CACC under different traffic penetrations scenarios and found that the throughput increases significantly when the CACC-enabled vehicles are above a certain level. To support smooth control, V2X communication technology plays a vital role in vehicle platooning. The communication distance of V2X needs to be long enough to ensure traffic stability and flexibility, as specified in [20,21]. Secondly, vehicle status messages need to be exchanged efficiently and reliably. For example, [PERSON] et al. [22] proposed the Decentralized Environmental Notification Message (DENM) for delivering the sudden event information to the rear vehicle, which requires a highly reliable transmission. Thirdly, V2X needs to support groupcast, which is highly utilized in platoon communication. Safety messages such as DENM are typically delivered to nearby vehicles repeatedly via broadcast or groupcast. In particular, information of dangerous road \begin{table}
\begin{tabular}{c l l l} \hline \hline
**Symbol** & **Description** & **Symbol** & **Description** \\ \hline \(l\) & The number of lanes & \(p^{M}\) & The set of platoon members, \\  & & & \(p^{M}=\{p_{n,2}^{M},p_{n,3}^{M},\ldots,p_{n,n}^{M}\}\) \\ \(L\) & The vehicle length & \(L_{u}(t)\) & At time \(i\), the number of \(P_{n}\) platoon maximum member is \(l_{u}(t)\) vehicles \\ \(L_{i-1}\) & The length of the preceding vehicle \(i-1\) & \(d_{pgup}\) & The inter-vehicle gap of two platoon members \\ \(e_{i}\) & The relative distance between two vehicles & \(\gamma\) & The distance between the vehicle \(j\) and the preceding vehicle \(j-1\) in the platoon \\ \(T\) & The time gap, which can be measured by the time required for the vehicle \(i\) to react to the possible collision and brake to stop & \\ \(t_{react}\) & The time required for the vehicle \(i\) to react to the possible collision & \\ \(t_{brake}\) & The time required for the vehicle \(i\) to stop & \\ \(t^{i}_{exit}\) & The exit time of the \(i\)th vehicle successfully exits the accident spot & \\ \(t^{i}_{arrival}\) & The arrival time of the the \(i\)th vehicle & \\ \(d_{gep}\) & The safe distance between two vehicles (inter-vehicle distance) & \\ \(x^{bra}\) & The position of the bottleneck & \\ \(x^{uff}\) & The position of the vehicle that gets notified from the bottleneck & \\ \(p\) & The set of platoon, \(P=\{P_{1},P_{2},\ldots,P_{n}\}\) & \\ \(j\) & The index of the vehicle in the platoon & \\ \(x_{j}\) & The position of vehicle \(j\) in the platoon & \\ \(v_{p}\) & The target platoon velocity & \\ \(\Delta d_{nj}\) & The distance for the \(j\)th platoon member to catch up with the preceding platoon member & \\ \(a_{max}\) & The maximum acceleration limit & \(t^{i}_{n,j}\) & The time taken to decelerate to the target platoon \\ \(ad_{max}\) & The maximum deceleration limit & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._conditions (e.g., lane blockage, vehicle collision) is prioritized in order to be exchanged among members in time.