Period-to-period toll adjustment schemes for mixed traffic with time-varying electric vehicle penetration

Abstract As electric vehicle (EV) penetration increases, the mixed traffic of EVs and gasoline vehicles (GVs) will be prevalent in roadway systems for a long time. Meanwhile, EV incentive policies, adjusted adaptively as a response to EV market growth, will perturb the mixed traffic pattern periodically. Such periodic perturbation will cause mixed traffic to evolve from disequilibrium to a new equilibrium. This equilibration is theoretically indeterminate due to the non-uniqueness of mixed traffic equilibria and the dynamic interaction between operational policy and underlying mixed traffic. The non-unique mixed-traffic equilibrium in the previous period influences the traffic stationary state and traffic evolution trajectory in the next period, which is also non-unique. Thereby, the indeterminacy in the equilibration process affects the long-term mixed traffic performance that should be factored into the period-to-period adjustment of EV incentive policies. This effect calls for the study of mixed traffic equilibration as a theoretical foundation for long-term policymaking, which has not received significant attention. This paper explores the properties of mixed traffic equilibria and proposes a mixed traffic evolution model considering time-varying EV penetration. The mixed traffic evolution model is then integrated into a control framework to support the period-to-period adjustment of EV-promoting tolling policy. Numerical examples illustrate the effects of non-unique mixed traffic equilibria and period-to-period toll adjustment schemes on long-term mixed traffic performance.

[1]  W. Y. Szeto,et al.  Profit optimization of public transit operators: examining both interior and boundary solutions , 2020, Transportmetrica A: Transport Science.

[2]  David M Levinson,et al.  The Traffic and Behavioral Effects of the I-35W Mississippi River Bridge Collapse , 2010 .

[3]  Satish V. Ukkusuri,et al.  Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium , 2020, Comput. Oper. Res..

[4]  Hai Yang,et al.  The multi-class, multi-criteria traffic network equilibrium and systems optimum problem , 2004 .

[5]  Srinivas Peeta,et al.  Multi-period equilibrium modeling planning framework for tradable credit schemes , 2016 .

[6]  Yeongmin Kwon,et al.  Evaluation of incentive policies for electric vehicles: An experimental study on Jeju Island , 2018, Transportation Research Part A: Policy and Practice.

[7]  J. J. Trip,et al.  Policy options to support the adoption of electric vehicles in the urban environment , 2013 .

[8]  H. Oliver Gao,et al.  Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses , 2018, Transportation Research Part B: Methodological.

[9]  Yu Nie,et al.  A class of bush-based algorithms for the traffic assignment problem , 2010 .

[10]  Hai-Jun Huang,et al.  Day-to-Day Flow Dynamics and Congestion Control , 2016, Transp. Sci..

[11]  G. Santos,et al.  Incentives for quick penetration of electric vehicles in five European countries: Perceptions from experts and stakeholders , 2020, Transportation Research Part A: Policy and Practice.

[12]  Yang Yu,et al.  Day-to-day dynamic traffic assignment with imperfect information, bounded rationality and information sharing , 2018, Transportation Research Part C: Emerging Technologies.

[13]  Yusak O. Susilo,et al.  The effect of policy incentives on electric vehicle adoption , 2016 .

[14]  Jun Bi,et al.  Day-to-Day Assignment Models and Traffic Dynamics Under Information Provision , 2018 .

[15]  Anna Nagurney,et al.  A multiclass, multicriteria traffic network equilibrium model , 2000 .

[16]  Mariano Nieto,et al.  Performance analysis of technology using the S curve model: the case of digital signal processing (DSP) , 1998 .

[17]  Fan Yang,et al.  Day-to-day stationary link flow pattern , 2009 .

[18]  Lin Cheng,et al.  Travelers’ Risk-Taking Behaviors in Day-to-Day Dynamic Evolution Model , 2016 .

[19]  Nan Jiang,et al.  Computing and Analyzing Mixed Equilibrium Network Flows with Gasoline and Electric Vehicles , 2014, Comput. Aided Civ. Infrastructure Eng..

[20]  Shanyong Wang,et al.  The impact of policy measures on consumer intention to adopt electric vehicles: Evidence from China , 2017 .

[21]  Bo Gao,et al.  Modeling Day-to-day Flow Dynamics on Degradable Transport Network , 2016, PloS one.

[22]  Haiying Shen,et al.  Opportunistic Energy Sharing Between Power Grid and Electric Vehicles: A Game Theory-Based Pricing Policy , 2017, 2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS).

[23]  Ning Jia,et al.  Day-to-day traffic dynamics considering social interaction: From individual route choice behavior to a network flow model , 2016 .

[24]  Fritz Busch,et al.  Optimal location of wireless charging facilities for electric vehicles: Flow-capturing location model with stochastic user equilibrium , 2015 .

[25]  Jieping Ye,et al.  Modelling drivers’ working and recharging schedules in a ride-sourcing market with electric vehicles and gasoline vehicles , 2019, Transportation Research Part E: Logistics and Transportation Review.

[26]  Gilbert Laporte,et al.  The electric vehicle routing problem with energy consumption uncertainty , 2019, Transportation Research Part B: Methodological.

[27]  Hai Yang,et al.  Exploration of day-to-day route choice models by a virtual experiment , 2018, Transportation Research Part C: Emerging Technologies.

[28]  Anne C. Lusk,et al.  Addressing electric vehicle (EV) sales and range anxiety through parking layout, policy and regulation , 2016 .

[29]  Konstantinos G. Zografos,et al.  The electric vehicle routing problem with time windows and synchronised mobile battery swapping , 2020 .

[30]  W. Y. Szeto,et al.  Day-to-day modal choice with a Pareto improvement or zero-sum revenue scheme , 2018 .

[31]  Qiang Meng,et al.  Fleet sizing for one-way electric carsharing services considering dynamic vehicle relocation and nonlinear charging profile , 2019, Transportation Research Part B: Methodological.

[32]  Nikolas Geroliminis,et al.  An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations , 2017 .

[33]  Yanfeng Ouyang,et al.  Refueling infrastructure planning in intercity networks considering route choice and travel time delay for mixed fleet of electric and conventional vehicles , 2020 .

[34]  Hong Zheng,et al.  Traffic Equilibrium and Charging Facility Locations for Electric Vehicles , 2016, Networks and Spatial Economics.

[35]  Inês L. Azevedo,et al.  The impact of federal incentives on the adoption of hybrid electric vehicles in the United States , 2013 .

[36]  Jorge E. Mendoza,et al.  The electric vehicle routing problem with non-linear charging functions , 2015 .

[37]  Yingyan Lou,et al.  Stable dynamic pricing scheme independent of lane-choice models for high-occupancy-toll lanes , 2020 .

[38]  Huijun Sun,et al.  Day-to-Day Evolution Model Based on Dynamic Reference Point with Heterogeneous Travelers , 2020, Networks and Spatial Economics.

[39]  Agachai Sumalee,et al.  Dynamic feedback control of day-to-day traffic disequilibrium process , 2020 .

[40]  Hai Yang,et al.  Optimal deployment of wireless charging lanes considering their adverse effect on road capacity , 2020 .

[41]  Caroline Prodhon,et al.  The electric vehicle routing problem with time windows, partial recharges and satellite customers , 2019, Transportation Research Part E: Logistics and Transportation Review.

[42]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[43]  Lixing Yang,et al.  An integrated framework for electric vehicle rebalancing and staff relocation in one-way carsharing systems: Model formulation and Lagrangian relaxation-based solution approach , 2018, Transportation Research Part B: Methodological.

[44]  José M. Grisolía,et al.  The impact of service and government-policy attributes on consumer preferences for electric vehicles in China , 2019, Transportation Research Part A: Policy and Practice.

[45]  Qiang Meng,et al.  A day-to-day route flow evolution process towards the mixed equilibria , 2017 .

[46]  Qiang Meng,et al.  Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints , 2017 .

[47]  Hai Yang,et al.  Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity , 2015 .

[48]  Haijun Huang,et al.  Mathematical and Economic Theory of Road Pricing , 2005 .

[49]  A. Skonhoft,et al.  The Norwegian support and subsidy policy of electric cars. Should it be adopted by other countries , 2014 .

[50]  S. Travis Waller,et al.  Range-Constrained Traffic Assignment with Multi-Modal Recharge for Electric Vehicles , 2019, Networks and Spatial Economics.

[51]  Yang Liu,et al.  Vehicle assignment and relays for one-way electric car-sharing systems , 2019, Transportation Research Part B: Methodological.

[52]  Agachai Sumalee,et al.  Pricing Environmental Externality in Traffic Networks Mixed With Fuel Vehicles and Electric Vehicles , 2021, IEEE Transactions on Intelligent Transportation Systems.

[53]  Tetsuo Tezuka,et al.  Optimization of shared autonomous electric vehicles operations with charge scheduling and vehicle-to-grid , 2019, Transportation Research Part C: Emerging Technologies.

[54]  Stephen D. Boyles,et al.  Deep Reinforcement Learning Algorithm for Dynamic Pricing of Express Lanes with Multiple Access Locations , 2019, ArXiv.

[55]  Hai-Jun Huang,et al.  An optimal charging station location model with the consideration of electric vehicle’s driving range , 2018 .

[56]  Ziyou Gao,et al.  Bounded-rationality based day-to-day evolution model for travel behavior analysis of urban railway network , 2013 .

[57]  H. Lo,et al.  Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria , 2017 .

[58]  Yafeng Yin,et al.  Network equilibrium models with battery electric vehicles , 2014 .

[59]  Haijun Huang,et al.  A cumulative prospect theory approach to commuters’ day-to-day route-choice modeling with friends’ travel information , 2018 .

[60]  S. Peeta,et al.  A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand , 2015 .

[61]  Ning Wang,et al.  Effectiveness of policy incentives on electric vehicle acceptance in China: A discrete choice analysis , 2017 .

[62]  W. Y. Szeto,et al.  Trial-and-error operation schemes for bimodal transport systems , 2020 .

[63]  Hai Yang,et al.  Day-to-day dynamics with advanced traveler information , 2021 .

[64]  Hai Yang,et al.  Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium , 2017, Transp. Sci..

[65]  Yafeng Yin,et al.  Optimal deployment of charging lanes for electric vehicles in transportation networks , 2016 .

[66]  Soyoung Ahn,et al.  Receding Horizon Stochastic Optimal Control Strategy for ACC and CACC under Uncertainty , 2017 .

[67]  Henry X. Liu,et al.  Modeling the day-to-day traffic evolution process after an unexpected network disruption , 2012 .

[68]  G. Cantarella,et al.  A general stochastic process for day-to-day dynamic traffic assignment: Formulation, asymptotic behaviour, and stability analysis , 2016 .

[69]  Yafeng Yin,et al.  Deploying public charging stations for electric vehicles on urban road networks , 2015 .

[70]  Khaled Abdelghany,et al.  Strategic network design and analysis for in-motion wireless charging of electric vehicles , 2021 .

[71]  Bojian Zhou,et al.  Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics , 2017 .

[72]  Stephen D. Boyles,et al.  Dynamic pricing for managed lanes with multiple entrances and exits , 2018, Transportation Research Part C: Emerging Technologies.

[73]  Lin Cheng,et al.  Reformulating Environmentally Constrained Traffic Equilibrium via a Smooth Gap Function , 2015 .

[74]  Wanjing Ma,et al.  Vehicle relocation in one-way station-based electric carsharing systems: A comparative study of operator-based and user-based methods , 2020 .