## 5 Results and Discussion  
The research utilized the Python language and the Traci toolkit to conduct simulation experiments on intersection traffic scenarios, interfacing with the traffic simulator SUMO, creating models for both a conventional signalized intersection and signal-free intersection. In the conventional signalized intersection model, the duration of the green light was set to 62 s, while the yellow light lasted for 3 s. For the simulation of the signal-free intersection, the FIFO strategy, LDR strategy, and our newly devised DRP strategy were employed. Moreover, the study employed the 2010 Toyota Prius CAV model, which encompasses an Internal Combustion Engine (ICE), two electric Motors/Generators (MG1 and MG2), a Planetary Gear Train (PGT), and a battery [25]. To emulate real traffic conditions, vehicle arrivals were assumed to follow a Poisson process, with four different arrival rates established to simulate various traffic demands. By comparing the driving performance and fairness of CAVs under different strategies, the merits and drawbacks of each strategy were scrutinized. To mitigate the influence of stochastic factors, each scenario underwent simulation for a duration of 15 min. Performance metric 1, denoted as the travel delay \(dl_{i}\) of CAV \(i\), reflects the performance of the strategy in terms of traffic efficiency. It is defined as follows:  
\[dl_{i}=t_{i}^{m}-t_{i}^{min} \tag{23}\]  
The term \(t_{i}^{min}\) denotes the minimum time required for CAV \(i\) to reach the MZ while traveling at \(u_{max}\) and \(v_{max}\) within the CZ. Performance metric 2, referred to as fuel consumption \(FC_{i}\) of CAV \(i\), elucidates the strategy's efficacy concerning energy efficiency. It is derived by computing the definite integral of the fuel consumption rate function \(fc_{i}(t)\) over the interval \([t_{i}^{0},t_{i}^{m}]\). It is pertinent to acknowledge that the fuel consumption of HEVs encompasses not solely the fuel consumption of the internal combustion engine but also the commensurate fuel consumption of the electric motors:  
\[FC_{i}=\int_{t_{i}^{0}}^{t_{i}^{m}}fc_{i}(t)dt \tag{24}\]  
The fuel consumption rate is contingent upon the velocity and power of the vehicle, and is defined as follows [25]:  
\[fc_{i}(t)= \begin{cases}fc_{ev}&\text{for}\bigg{\{}\begin{aligned} P _{i}(t)\leq 0\\ P_{i}(t)<P_{ev}\text{ and }v_{i}(t)<v_{ev}\\ e_{1}+e_{2}*v_{i}(t)+e_{3}*P_{i}(t)+e_{4}*P_{i}^{2}(t)&\text{for} \begin{aligned} P_{i}(t)>0\text{ and }v_{i}(t)\geq v_{ev}\\ P_{i}(t)\geq P_{ev}\text{ and }v_{i}(t)<v_{ev}\end{aligned}\end{cases}  \tag{25}\]  
The equivalent fuel consumption rate of the 2010 Toyota Prius in EV mode, denoted as \(fc_{ev}\), represents a key parameter. Here, \(P_{i}(t)\) signifies the instantaneous power of CAV \(i\), while \(P_{ev}\) denotes the maximum power achievable in EV mode, and \(v_{ev}\) stands for the maximum velocity attainable in EV mode. When \(P_{i}(t)\) is negative or \(v_{i}(t)\) falls below \(v_{ev}\) with power lower than \(P_{ev}\), the HEV transitions to EV mode. We adopted the parameters summarized from the experiments conducted by researchers, as documented in reference [25], where the specific values for \(v_{ev}\) and \(P_{ev}\) of the 2010 Toyota Prius are 32 km/h and 10 kW, respectively, with \(fc_{ev}\) set at 0.006. Additionally, the coefficients \(e_{1}\), \(e_{2}\), \(e_{3}\), and \(e_{4}\) were determined to be 0.006, 0.003998, 0.077092, and \(-9.155\times 10^{-5}\). Researchers have elucidated the relationship between \(P_{i}(t)\), \(v_{i}(t)\), and \(u_{i}(t)\) in reference [26]:  
\[P_{i}(t)=\bigg{(}mu_{i}(t)+mg\cdot\cos(\theta)\cdot\frac{C_{r}}{1000}(C_{c}v_{ i}(t)+C_{t})\,+\,\frac{1}{2}\rho_{Air}A_{f}\mathcal{C}_{D}{v_{i}}^{2}(t)+mg\cdot \sin(\theta)\bigg{)}\cdot v_{i}(t) \tag{26}\]  
We designated the mass of the Toyota Prius as \(m=1521\) kg, the gravitational acceleration \(g\) as 9.8066 m/s\({}^{2}\), and the road slope \(\theta\) as 0.