## 5 Simulation Results and Discussion
### Impact of the Zone Sizes  
Finally, let us investigate the impact of the zone sizes of the proposed scheme. Figure 11 shows simulation results when the sizes of the avoidance zone, preliminary avoidance zone, and gap adjustment zone are varied in Scenario 30. Our proposed method focuses on the vehicles moving in the wide range behind the obstacle. Wide range control may have a negative side effect on the following traffic. For example, deceleration for changing lanes may affect the behavior of vehicles to adapt to road structures, such as ramps and intersections. Therefore, a shorter zone is preferable as long as safe, smooth, and fair obstacle avoidance can be assured.  
**Avoidance zone**: If the avoidance zone is too small, vehicles in the closed lane cannot change lanes. Therefore, the size of the avoidance zone (\(d_{\text{avoid}}\)) should be sufficient for vehicles in the closed lane to accomplish a lane change. Simulation results show that traffic throughput, fairness, and comfort level deteriorate when \(d_{\text{avoid}}<250\,\text{m}\). On the other hand, all metrics are stable when \(d_{\text{avoid}}\geq 250\,\text{m}\). Consequently, we can conclude that a suitable size of the avoidance zone is \(250\,\text{m}\) or more.  
**Preliminary avoidance zone**: If a vehicle in the closed lane and a vehicle in a free lane begin attempting to change lanes at the same point in time, the vehicle in the closed lane may be able to change lanes faster than the vehicle in the free lane. In this case, the vehicle density in the free lane temporarily increases, and vehicles in the free lane will be forced to decelerate. Therefore, the size of the preliminary avoidance zone (\(d_{\text{prelim}}\)) should be sufficient to shift the lane-change timings for vehicles in the closed lane and the lane change timing for vehicles in the free lane. Simulation results show that traffic throughput improves when \(d_{\text{prelim}}\geq 30\,\text{m}\). However, the fairness and comfort level deteriorate when \(d_{\text{prelim}}>100\,\text{m}\). This result can be explained as follows. If the size of the preliminary avoidance zone is too large, there is too much of a time lag between the lane change of the vehicle in the free lane and the lane change of the vehicle in the closed lane, and the following vehicle accelerates to shorten the long inter-vehicular gap made by the lane changes of the vehicles in the free lane. As a result, when the vehicle in the closed lane starts to change lanes, there will be insufficient space for it to change lanes smoothly, and the vehicles need to decelerate. Thus, the fairness of the traffic throughput and comfort level deteriorate with frequent deceleration in the lane next to the closed one. Consequently, we can conclude that a suitable size of the preliminary avoidance zone is 30-100 m.  
**Gap adjustment zone**: In the gap adjustment zone, vehicles do not decelerate rapidly to double the time headway within a short time because of the minimum acceleration \(a_{\text{comfort}}\). If the gap adjustment zone is too short, vehicles cannot double the time headway. Therefore, the size of the gap adjustment zone (\(d_{\text{decel}}\)) should be sufficient to double the time headway without reducing ride comfort. Simulation results show that traffic throughput and fairness deteriorate when \(d_{\text{decel}}<200\,\text{m}\). In addition, traffic throughput deteriorate when \(d_{\text{decel}}>600\,\text{m}\). This is because as the gap adjustment zone becomes larger, the travel time of vehicles at low speed becomes longer. Consequently, we can conclude that a suitable size of the gap adjustment zone is 200-600 m.