## 4 Performance Evaluation
Moreover, due to fewer detours on the way to the destination, _Proposed_ was more efficient in terms of distance, thereby leading to shorter travel times. _Compare_ designed its reward by considering only driving time as a single objective, while \(ds+ad\) designed its reward by considering travel time as a linear function through which to address multiple objectives. Hence, although both methods aim to minimize travel time, they showed a difference of about 8-10% due to the different reward designs. On the other hand, \(ds+nv\) considers only travel speed and vehicle density, thus resulting in many detours to the destination due to the lack of consideration for driving distance. Consequently, it exhibited the worst performance in terms of travel distance, thereby leading to a lower travel time performance compared to other methods. Figure 8 shows the average waiting times for AVs in City1 and City2. A low average waiting time implies that the traffic flows smoothly and that the AVs drive without waiting. It can be observed that _Proposed_ had a shorter waiting time than the other methods. Therefore, _Proposed_ indicated a better distribution of traffic flow than the other methods. As mentioned previously, as the MPR increases, the driving distance and driving time of the AVs decrease, and the driving speed of the AVs thus increases. In other words, the higher the ratio of AVs adapted to the dynamic environment, the smoother the traffic flow, and the lower the waiting time of the AVs. In addition, the reduction in the waiting time for the AVs indicated that the traffic congestion was low and had a good distribution, thereby \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Compare** & **Proposed** & **ds + ad** & **ds + ds + nv** \\ \hline City1 & 7.29 \(\pm\) 0.13 & 7.55 \(\pm\) 0.11 & 7.31 \(\pm\) 0.14 & 7.18 \(\pm\) 0.13 \\ \hline City2 & 8.44 \(\pm\) 0.19 & 8.89 \(\pm\) 0.22 & 8.66 \(\pm\) 0.25 & 8.3 \(\pm\) 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average driving speed in City1 and City2 (unit: m/s). implying that the density of AVs was minimized. Therefore, City1, with its higher vehicle density, exhibited approximately 13-15% longer waiting times than City2. Figure 9a,b show the average driving time for AVs to reach their destinations under different vehicle arrival rates in City1 and City2. Figure 10a,b show the average waiting time for AVs under different vehicle arrival rates in City1 and City2. The figures indicate that the average driving and waiting times when the vehicle arrival rates (where the MPR value was 50%) were 0.3, 0.5, 0.7, and 0.9. As the vehicle arrival rate increased, the number of vehicles on the road also increased. This led to higher traffic density on the roads, thus resulting in increased traffic congestion. Consequently, the driving and waiting times for the AVs in City1 and City2 increased. _Proposed_, which minimizes detour routes to the destination, exhibited the best performance in terms of average driving and waiting times. This was because _Proposed_ ensures smooth traffic flow regardless of the vehicle arrival rate. _Compare_ and _ds + ad_, which have relatively few detours, then followed, and _ds + nv_ was found to deliver the worst performance due to recommending many detours. Figure 8: The average waiting times in City1 and City2. Figure 7: The average driving time for different MPRs: (**a**) in City1 and (**b**) in City2. Figure 9: The average driving time for different vehicle arrival rates: (**a**) in City1 and (**b**) in City2. Thus, _Proposed_ yielded the best performance in any environment when the MPR was low or high, as well as when the vehicles were high or low in density. In addition, the performance of _Proposed_ was more pronounced in a more dynamic traffic environment. If the driving distance was simply defined as a reward function without considering the destination, the shortest distance between actions was selected. This generated detours to the destination, which increased both driving time and distance.