## 3 Proposed Scheme
### Adaptive Lane Change  
When avoiding an obstacle, a vehicle in a lane other than the outermost lanes has two candidate lanes to which it moves. A vehicle in the closed lane can choose either lane to its immediate left or right. On the other hand, a vehicle in the free lane can choose to change lanes to move away from the obstacle or go straight ahead. In our scheme, the destination lane for these vehicles is selected according to Strategy 1 (avoiding congested lanes) and Strategy 2 (adjusting the balance among lanes). **Strategy 1: Avoiding congested lanes**: As shown in Figure 4a, the ego vehicle, a vehicle that will change lanes, evaluates the number of vehicles between itself and the obstacle in each destination candidate lane. First, it counts the number of vehicles in front of itself in each lane and in its communication range on the basis of the number of unique  
Figure 3: Control rules based on distance between an obstacle and approaching vehicles on a road with three or more lanes. vehicle IDs included in the packets sent from the vehicles. Let \(a\) and \(b\) be indices of the destination candidate lanes and let \(m_{a}\) and \(m_{b}\) be the number of vehicles in each of the lanes, respectively. If either the ratio of \(m_{a}\) or \(m_{b}\) to the sum of \(m_{a}\) and \(m_{b}\) exceeds a predefined threshold \(L\) (e.g., 0.6), the vehicle regards the lane as congested and moves to another lane to balance the traffic of the lanes ahead. In other words, lane \(i\) (\(\in\{a,b\}\)) that satisfies \(m_{i}/(m_{a}+m_{b})>L\) cannot be a candidate destination lane. If neither candidate is selected, the vehicle uses Strategy 2 to determine the destination lane. **Strategy 2: Adjusting the balance among lanes**: As shown in Figure 4b, a vehicle determines a destination lane in such a way that the number of vehicles in each free lane will have the same amount of traffic. First, the vehicle counts the number of vehicles in each lane behind itself and its communication range on the basis of the number of unique vehicle IDs included in the packets sent from the vehicles. Let us assume that the road has \(n\) lanes (\(n\geq 1\)), then the index of each lane is \(i\) (\(\in\{0,\,1,\,\cdots,\,n-1\}\)), the number of counted vehicles in each lane is \(m_{i}\), and \(M=\sum_{i=0}^{n-1}m_{i}\). If the counted vehicles are evenly distributed among the \(n-1\) free lanes, the ideal number of vehicles per free lane is \(M/(n-1)\). To adjust the number of vehicles in each lane to be closer to this ideal number, the probability that a vehicle moves from lane \(i\) to lane \(j\)\(p_{i\to j}\) (\(j\in\{i-1,\,i,\,i+1\}\)) in either direction from each lane is calculated in three steps as follows, where the index of the closed lane is denoted by \(c\). The candidates of a destination lane of a vehicle are limited by its current lane. Vehicles in the rightmost lane cannot move right, vehicles in the leftmost lane cannot move left lane, vehicles in the closed lane cannot go straight ahead, and vehicles always change lanes to the lane farther from the obstacle. Thus,  
\[P_{0\to-1}=0,\,\,\,\,P_{n-1\to n}=0,\,\,\,\,P_{c\to c}=0, \tag{1}\] \[P_{i\to i+1}=0,\,\,\,\,i\in\{0,\,1,\,\cdots,\,\,c-1\},\] (2) \[P_{i\to i-1}=0,\,\,\,\,\,i\in\{c+1,\,c+2,\,\cdots,\,n-1\}. \tag{3}\]  
Next, we calculate the lane change probability to balance the traffic among lanes. The number of vehicles that should move to lane \(j\) is calculated on the basis of the difference between the number of vehicles \(m_{j}\) and the ideal number of vehicles \(M/(n-1)\). In this case, \(P_{j\to j+(j-i)}\times m_{j}\) vehicles in lane \(j\) should move to another lane. Accordingly, the difference between the number of vehicles in lane \(j\) and the ideal number of vehicles in each lane will be \(M/(n-1)-(1.0-P_{j\to j+(j-i)})m_{j}\). Then, we calculate the probability \(P_{i\to j}\) so that the number of vehicles changing lanes from lane \(i\) to lane \(j\) can be \(M/(n-1)-(1.0-P_{j\to j+(j-i)})m_{j}\). Thus,  
Figure 4: Adaptive lane change.