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Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (5): 977-988    DOI: 10.3785/j.issn.1008-973X.2026.05.007
    
Dynamic pricing model for expressway toll rates in connected traffic environment
Xiancai JIANG(),Xinyao HE,Xinyue ZHANG
College of Civil Engineering and Transportation, Northeast Forestry University, Harbin 150040, China
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Abstract  

Differentiated tolling at various time periods neglects issues related to traffic efficiency and operational safety, resulting in no fundamental improvement in the utilization efficiency of road resources. To address this gap, a dynamic pricing model for expressway toll rates (DPM-ET) was proposed within the context of connected transportation. Operational safety was characterized by the standard deviation of vehicle speed, while traffic efficiency was reflected through vehicle speed along with vehicle platoon dynamics. Single-factor pricing models were constructed separately, then integrated with pricing to develop a multi-factor dynamic toll rate model. To enhance expressway resource utilization efficiency, Stackelberg price game theory was used to encourage optimized driving behavior, maintain stable and uniform speeds, and improve traffic flow safety. Simulation results show that compared to the benchmark scheme, DPM-ET improves the average lane speed by 2.01%-6.74% and speed stability by 5.22%, and achieves a maximum platooning rate of 0.9. Compared to similar pricing schemes, DPM-ET improves the value of optimal speed difference (VoOSD) by 4.68-5.37 times, speed stability by 21.17%, and the average lane speed by 5.22%-11.05%. DPM-ET achieves its optimal applicability when the platoon mileage weight is 0.7, the platoon size coefficient is 0.6, the reward coefficient is 0.8, the exponential decay rate coefficient is 0.67, and the maximum standard deviation pricing factor is 3.2.



Key wordsintelligent transportation      dynamic pricing      toll rate      Stackelberg game      expressway     
Received: 16 September 2025      Published: 06 May 2026
CLC:  U 491  
Fund:  黑龙江省自然科学基金资助项目(PL2024E012).
Cite this article:

Xiancai JIANG,Xinyao HE,Xinyue ZHANG. Dynamic pricing model for expressway toll rates in connected traffic environment. Journal of ZheJiang University (Engineering Science), 2026, 60(5): 977-988.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.05.007     OR     https://www.zjujournals.com/eng/Y2026/V60/I5/977


网联环境下高速公路收费费率动态定价模型

时段差异化收费方式忽略了通行效率与运行安全问题,未使道路资源利用效率得到根本提升. 为此以网联交通为背景,提出高速公路收费费率的动态定价模型(DPM-ET). 以车速标准差刻画运行安全,车速及车辆编队体现通行效率,分别构建单因子定价模型、联合定价的多因子动态费率模型. 以提升高速公路道路资源利用效率为目标,采用斯塔克尔伯格价格博弈驱动驾驶者优化驾驶行为,保持车速平稳、统一,提升高速公路交通流的运行安全. 仿真结果表明,DPM-ET相较于基准方案,车道平均速度提升了2.01%~6.74%,速度稳定性提升了5.22%,编队率最高达到0.9. DPM-ET相较于同类定价方案,最优速差异价值(VoOSD)效果提升了4.68~5.37倍,速度稳定性提升了21.17%,车道平均速度提升了5.22%~11.05%. 当编队里程权重参数为0.7、编队规模定价系数为0.6、奖励系数为0.8、指数衰减速率系数为0.67、标准差定价因子上限为3.2时,DPM-ET处于最佳适用状态.


关键词: 智能交通,  动态定价,  收费费率,  斯塔克尔伯格博弈,  高速公路 
Fig.1 Conceptual diagram of dynamic pricing model for expressway toll rates in connected traffic environment
Fig.2 Schematic of vehicle platooning scenario
Fig.3 Vehicle state selection under price game mechanism (vehicle speed)
Fig.4 Vehicle state selection under price game mechanism (vehicle platoon)
驾驶者运营方
hclc
hmCd(hm, hc), Ch(hc, hm)Cd(hm, lc), Ch(lc, hm)
lmCd(lm, hc), Ch(hc, lm)Cd(lm, lc), Ch(lc, lm)
Tab.1 Outcome of both sides’ strategic choices
参数数值参数数值
0车道最高限速/(m·s?1)250车道最低限速/(m·s?1)16.67
1车道最高限速/(m·s?1)30.561车道最低限速/(m·s?1)25
2车道最高限速/(m·s?1)33.332车道最低限速/(m·s?1)30.56
最大加速度/(m·s?2)3.0最小加速度(m·s?2)?5
CAV平均时距/s1/2CAV反应时间/s0.1
CHV平均时距/s2/3CHV反应时间/s1.0
低交通流量/(pcu·h?1)1 500中流量/(pcu·h?1)2 000
高交通流量(pcu·h?1)2 500重复次数5
仿真时长/s3 600车辆长度/m5/12
Tab.2 Parameter settings for model simulation and analysis
Fig.5 Platooning rate over time
Fig.6 Comparison of vehicle speed and vehicle inventory in each lane
Fig.7 Comparison of toll fees, travel time, and average speed deviation under different traffic volumes
Fig.8 Distribution of value of optimal speed difference (three schemes)
Fig.9 Distribution of acceleration (three schemes)
Fig.10 Comparison of average vehicle speed across different schemes (three lanes)
Fig.11 Comparison of objective function values for different parameter combinations
组别参数数值组别参数数值
1m0.23d10.90
φ10.8d20.85
φ22.0d30.75
φ31.7ζ10.0
2w2.0?h1.3
Δx1000?f1.0
σl3.24nh1.05
k0.67nm1.00
3sα0.7nl0.90
Tab.3 Results of parameter sensitivity analysis
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