## 5 Numerical Experiments
### Impact of IoT-SBL Strategy on Queue Length  
This article investigated the application of IoT-SBL technology, which allows passenger vehicles to access the bus-only lane, thereby increasing traffic capacity for these vehicles and alleviating congestion in general traffic lanes. This section analyzes fluctuations in vehicle queue lengths during a single signal cycle at the Priority Traffic Signal Intersection, offering insights into the effectiveness of the proposed strategy.  
The signal cycle comprises a 60 s red phase and a 40 s green phase. Lost time (e.g., startup delays during phase transitions) is accounted for by assuming that vehicles begin moving at the start of the green phase after a brief transition interval, which is embedded within the fixed cycle duration. The all-red phase, typically used for intersection clearance, is not explicitly modeled here, as the analysis focuses on queuing dynamics during the active red and green phases. Figure 4 illustrates the variation in the number of vehicles in regular lanes throughout the entire signal cycle under different traffic control strategies, particularly at various saturation levels. The outer circle represents the signal cycle in seconds, while the inner circle denotes the average queue length in passenger car units (pcus).  
In Figure 4a, at a saturation level of 0.1, the queue length observed with the IoT-SBL strategy closely mirrors that of the bus-only lane strategy, showing only minor improvements. However, as the saturation level increases, the differences in vehicle queue lengths between the two strategies become more pronounced. Figure 4b depicts a saturation level of 0.5, while Figure 4c,d illustrate saturation levels of 0.9 and 0.97, respectively.  
The outer circles denote the signal cycle duration (seconds) while the inner circles show average queue lengths (pcus). At \(V/C=0.97,~{}L_{t}\) peaks at 28 vehicles (traditional lane) vs. 15 vehicles (IoT-SBL), while \(~{}K_{t}~{}\) reaches 12 vehicles. With each increase in saturation, it is evident that the IoT-SBL strategy significantly reduces queue lengths compared to the bus lane strategy. This analysis highlights the potential of IoT-SBL in optimizing traffic flow and enhancing overall intersection performance, particularly in high-saturation scenarios, ultimately contributing to a more efficient transportation system.  
The impact of the IoT-SBL strategy on reducing vehicle queue lengths across various saturation levels is depicted in Figure 5. At a saturation level of 0.1, the IoT-SBL strategy achieves a queue length reduction of up to 2.91%. Conversely, at a saturation level of 0.97, this reduction can reach an impressive 71.15%. The findings presented in Figures 4 and 5 align with expectations, as the traditional bus lane strategy effectively manages traffic under low saturation conditions, rendering the IoT-SBL strategy less critical. However, as saturation levels increase, the traditional bus lane strategy becomes progressively less effective in handling high traffic volumes, underscoring the advantages of the IoT-SBL strategy in these scenarios. Additionally, it is important to note that the performance of the IoT-SBL strategy is contingent upon its capacity, which is primarily influenced by the prevailing traffic volume.