# Coordinated Multi-Platooning Planning for Resolving Sudden Congestion on Multi-Lane Freeways
## 3 System Model and Problem Description  
We consider the scenario where an accident occurs at position \(x^{btt}\) on the road segment \(X\) of a freeway with \(k\) lanes. There is a set of \(S\) vehicles at the front of the accident segment before the accident is cleared, denoted by \(S=\{1,2,\ldots,|S|\}\). The notation \(\alpha\) denotes the number of lanes blocked due to the accident. In Figure 1, a truck accident blocks one of the four lanes on the freeway. As a result, \(k-\alpha\) lanes remain available for the vehicles to pass through. The maximum allowed vehicle velocity on this road segment is \(v_{max}\). In our proposed approach, we assumed that every vehicle is equipped with an On-Board Unit (OBU) to support data sharing. The OBUs support vehicle-to-vehicle communications, which are specified in 3 GPP standards [13]. The control protocols for vehicles in a platoon can be found in [14]. Further, each vehicle is also expected to be equipped with an Advanced Driver Assistance System (ADAS) to run the consensus plan negotiation procedure, which is generated by our traffic coordination scheme. Additionally, we assumed that all vehicles will voluntarily adopt our proposed algorithm when they pass the congestion \(x^{ntf}\) spot. Generally, this work aims to (i) manage \(S\) vehicles to exit the road segment \(X\) in the shortest time, (ii) maintain the maximum number of incoming vehicles that can drive through \(X\) at their maximum velocity, and (iii) prevent further congestion and accidents due to the shockwave phenomenon. The first two goals can be indirectly solved by sorting the vehicles by order and then maximizing the velocity of the vehicles on the segment. The objective is to minimize the delay of vehicles from chaotic movements. We proposed a decentralized algorithm to manage the maneuvers of vehicles in \(S\) in the congestion area (e.g., from 3.5 km behind the accident spot). The proposed decentralized traffic planning is based on a heuristic algorithm. Specifically, the platoon forming starts from the vehicles in a small area near the congestion/accident spot and then occurs repetitively to the ones in the further areas. Each small area can be defined as in the V2V communication range. This heuristic approach is based on the motivation that arranging vehicles into platoons could accelerate traffic flow. Generally, platoon-based planning can reduce the time taken to exit the congestion spot for all vehicles. In this way, every vehicle will benefit from such well-organized movement planning to pass the accident point. As a result, the final goal to reach the objective of the optimization problem can be partially gained. The waiting time of the vehicles can be minimized by solving the optimization problem as follows:  
\[ \begin{split}\min_{S,v_{max},k,\alpha}&\frac{\sum _{i=1}^{|S|}(t_{exit}^{i}-t_{arrival}^{i})}{|S|}\\ \text{s.t.}& 0<\alpha<k,\\ & 0\leq v_{i}(t)\leq v_{max},\forall i\in S\\ & x_{i-1}-d_{gap}\geq x_{i},i\in S-\{1\}\end{split}  \tag{1}\]  
where  
* \(x_{i}\), \(v_{i}\) are the position and velocity of the \(i\)th vehicle to exit the congestion area (\(i\in S\)). * \(t_{exit}^{i}\) is the exit time of the \(i\)th vehicle successfully exiting the accident spot; \(t_{arrival}^{i}\) is the arrival time of the the \(i\)th vehicle; \(d_{gap}\) is the safe distance between two vehicles (inter-vehicle distance). Equation (1) means the goal of minimizing the congestion by cutting down the mean time taken of all of the vehicles to exit the accident spot. To achieve the goal, we must release the vehicles as fast as possible. Indeed, the problem of finding the fastest and fairest path for each vehicle to drive through the congestion area is a complicated issue. First, it will be unfair if the design always schedules the vehicles on the accident-free lanes to leave while making the vehicles on the blocked lanes wait indefinitely. For example, as illustrated in Figure 1, the vehicles in Lane 0 do not need to wait until all of the vehicles in Lanes 1, 2, and 3 have exited to change lanes.