Skip to main content

Advertisement

SpringerLink
Log in

Range-Constrained Traffic Assignment with Multi-Modal Recharge for Electric Vehicles

  • Published:
Networks and Spatial Economics Aims and scope Submit manuscript

Abstract

Plug-in electric vehicles (PEVs) are sustainable alternatives to internal combustion engine vehicles thanks to the use of environmentally-friendly electric energy and the reduction of off-gas emissions. One of the major concerns associated with the adoption of PEVs is the distance limit, i.e. the fact that PEVs may not be able to complete trips without recharging. In this study, we propose to model the assignment of mixed-vehicular traffic of PEVs with two different charging capabilities accounting for PEV range constraints. We consider two recharge modes: charging stations with recharge time and modern charging lanes where PEVs are recharged automatically by traversing the lanes. The main objective of this study is to explore the influences of multi-modal recharge service provision on individual trips and network performance. First, a network transformation method is proposed to incorporate recharge decisions within the PEV route choice model. Second, we develop a novel convex programming formulation for mixed-vehicular traffic assignment accounting for en-route multi-modal recharge, derive mathematical properties and propose solution algorithms. In this rich traffic assignment framework, PEV route choice is represented as a resource-constrained shortest path subproblem with recharge time and we identify a suitable exact algorithm to solve this subproblem during the assignment process. Finally, computational experiments are conducted to demonstrate the performance of the proposed models and algorithms. The numerical results reveal that the incorporation of PEV multi-modal recharge has a significant impact on both route choice strategies and equilibrium flow patterns, wherein influencing factors include the distance limit, deployment of charging stations and charging lanes, and recharge time. In addition, we identify counter-intuitive configurations with regard to the way range constraints and recharge time reshape the equilibrium network flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Adler JD, Mirchandani PB, Xue G, Xia M (2016) The electric vehicle shortest-walk problem with battery exchanges. Netw Spatial Econ 16(1):155–173

    Article  Google Scholar 

  • Agrawal S, Zheng H, Peeta S, Kumar A (2016) Routing aspects of electric vehicle drivers and their effects on network performance. Transp Res Part D: Transp Environ 46:246–266

    Article  Google Scholar 

  • Artmeier A, Haselmayr J, Leucker M, Sachenbacher M (2010) The shortest path problem revisited: optimal routing for electric vehicles. KI 2010: Adv Artif Intell:309–316

  • Assad AA (1978) Multicommodity network flows—a survey. Networks 8(1):37–91

    Article  Google Scholar 

  • Bar-Gera H. Transportation Network Test Problems. http://www.bgu.ac.il/~bargera/tntp/. Accessed April 12, 2016

  • Beckmann M, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Yale University Press, New Haven

    Google Scholar 

  • Bi Z, Kan T, Mi CC, Zhang Y, Zhao Z, Keoleian GA (2016) A review of wireless power transfer for electric vehicles: prospects to enhance sustainable mobility. Appl Energy 179:413–425

    Article  Google Scholar 

  • Bonges HA III, Lusk AC (2016) Addressing electric vehicle (EV) sales and range anxiety through parking layout, policy and regulation. Transp Res A Policy Pract 83:63–73

    Article  Google Scholar 

  • Bunce L, Harris M, Burgess M (2014) Charge up then charge out? Drivers’ perceptions and experiences of electric vehicles in the UK. Transp Res A Policy Pract 59:278–287

    Article  Google Scholar 

  • Burns LD (2013) Sustainable mobility: a vision of our transport future. Nature 497(7448):181–182

    Article  Google Scholar 

  • Cabral EA (2005) Wide area telecommunication network design: problems and solution algorithms with application to the Alberta SuperNet. University of Alberta

  • Cantarella GE, Watling DP (2016) Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete-and continuous-time models. EURO J Trans Logist 5(1):69–98

    Article  Google Scholar 

  • Castillo E, Menéndez JM, Sánchez-Cambronero S (2008) Traffic estimation and optimal counting location without path enumeration using Bayesian networks. Comput Aided Civil Infrastruct Eng 23(3):189–207

    Article  Google Scholar 

  • Chen BY, Lam WH, Sumalee A, Li Q, Shao H, Fang Z (2013a) Finding reliable shortest paths in road networks under uncertainty. Netw Spatial Econ 13(2):123–148

    Article  Google Scholar 

  • Chen N, Duell M, Waller ST, Gardner L (2013b) Evaluating the impact of electric vehicle charging infrastructure design alternatives on transport network performance. In Proceedings of Australasian Transport Research Forum

  • Chen Z, Liu W, Yin Y (2017) Deployment of stationary and dynamic charging infrastructure for electric vehicles along traffic corridors. Trans Res Part C: Emerging Technol 77:185–206

    Article  Google Scholar 

  • Climaco JCN, Martins EQV (1982) A bicriterion shortest path algorithm. Eur J Oper Res 11(4):399–404

    Article  Google Scholar 

  • Dafermos SC (1972) The traffic assignment problem for multiclass-user transportation networks. Transp Sci 6(1):73–87

    Article  Google Scholar 

  • Desrosiers J, Lübbecke ME (2005) A primer in column generation. InColumn generation (1–32). Springer US

  • Dong J, Liu C, Lin Z (2014) Charging infrastructure planning for promoting battery electric vehicles: An activity-based approach using multiday travel data. Trans Res Part C: Emerging Technol 38:44–55

    Article  Google Scholar 

  • Duell M, Gardner LM, Waller ST (2018) Policy implications of incorporating distance constrained electric vehicles into the traffic network design problem. Trans Lett 10(3):144–158

    Article  Google Scholar 

  • Dumitrescu I, Boland N (2003) Improved preprocessing, labeling and scaling algorithms for the weight-constrained shortest path problem. Networks 42(3):135–153

    Article  Google Scholar 

  • Erdoğan S, Miller-Hooks E (2012) A green vehicle routing problem. Trans Res Part E: Logist Trans Rev 48(1):100–114

    Article  Google Scholar 

  • Fan Y, Nie Y (2006) Optimal routing for maximizing the travel time reliability. Netw Spatial Econ 6(3–4):333–344

    Article  Google Scholar 

  • Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks 44(3):216–229

    Article  Google Scholar 

  • Franke T, Krems JF (2013) Interacting with limited mobility resources: psychological range levels in electric vehicle use. Transp Res A Policy Pract 48:109–122

    Article  Google Scholar 

  • Gardner LM, Duell M, Waller ST (2013) A framework for evaluating the role of electric vehicles in transportation network infrastructure under travel demand variability. Transp Res A Policy Pract 49:76–90

    Article  Google Scholar 

  • Gellermann T, Sellmann M, Wright R (2005) Shorter path constraints for the resource constrained shortest path problem. In International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming (pp. 201–216). Springer Berlin Heidelberg

  • Hamdouch Y, Marcotte P, Nguyen S (2004) A strategic model for dynamic traffic assignment. Netw Spatial Econ 4(3):291–315

    Article  Google Scholar 

  • Handler GY, Zang I (1980) A dual algorithm for the constrained shortest path problem. Networks 10(4):293–309

    Article  Google Scholar 

  • He F, Yin Y, Lawphongpanich S (2014) Network equilibrium models with battery electric vehicles. Transp Res B Methodol 67:306–319

    Article  Google Scholar 

  • He F, Yin Y, Zhou J (2015) Deploying public charging stations for electric vehicles on urban road networks. Trans Res Part C: Emerging Technol 60:227–240

    Article  Google Scholar 

  • He F, Yin Y, Wang J, Yang Y (2016) Sustainability SI: optimal prices of electricity at public charging stations for plug-in electric vehicles. Netw Spatial Econ 16(1):131–154

    Article  Google Scholar 

  • Highways England. Off Road Trials for ‘Electric Highways’ Technology. https://www.gov.uk/government/news/off-road-trials-for-electric-highways-technology. Accessed August 11, 2015

  • Jafari E, Boyles SD (2017) Multicriteria stochastic shortest path problem for electric vehicles. Netw Spatial Econ 17(3):1043–1070

    Article  Google Scholar 

  • Jaffe JM (1984) Algorithms for finding paths with multiple constraints. Networks 14(1):95–116

    Article  Google Scholar 

  • Jiang N (2012) Constrained traffic equilibrium: impact of electric vehicles. PhD Thesis at the University of Texas at Austin

  • Jiang N, Xie C, Waller S (2012) Path-constrained traffic assignment: model and algorithm. Trans Res Record: J Trans Res Board 2283:25–33

    Article  Google Scholar 

  • Jiang N, Xie C, Duthie JC, Waller ST (2014) A network equilibrium analysis on destination, route and parking choices with mixed gasoline and electric vehicular flows. EURO J Trans Logist 3(1):55–92

    Article  Google Scholar 

  • Jing W, An K, Ramezani M, Kim I (2017) Location Design of Electric Vehicle Charging Facilities: a path-distance constrained stochastic user equilibrium approach. J Adv Transp 2017

  • Lacomme P, Moukrim A, Quilliot A, Vinot M (2017) A new shortest path algorithm to solve the resource-constrained project scheduling problem with routing from a flow solution. Eng Appl Artif Intell 66:75–86

    Article  Google Scholar 

  • Laporte G, Pascoal MM (2011) Minimum cost path problems with relays. Comput Oper Res 38(1):165–173

    Article  Google Scholar 

  • Larsson T, Patriksson M (1999) Side constrained traffic equilibrium models—analysis, computation and applications. Transp Res B Methodol 33(4):233–264

    Article  Google Scholar 

  • Larsson T, Lundgren JT, Rydergren C, Patriksson M (2001) Most likely traffic equilibrium route flows analysis and computation. In Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models (pp. 129–159). Springer US

  • Li Y, Waller ST, Ziliaskopoulos T (2003) A decomposition scheme for system optimal dynamic traffic assignment models. Netw Spatial Econ 3(4):441–455

    Article  Google Scholar 

  • Li S, Tong L, Xing J, Zhou Y (2017) The market for electric vehicles: indirect network effects and policy design. J Assoc Environ Resour Econ 4(1):89–133

    Google Scholar 

  • Li S, Sun F, An D, He S (2018) Increasing efficiency of a wireless energy transfer system by spatial translational transformation. IEEE Trans Power Electron 33(4):3325–3332

    Article  Google Scholar 

  • Liu H, Wang DZ (2017) Locating multiple types of charging facilities for battery electric vehicles. Transp Res B Methodol 103:30–55

    Article  Google Scholar 

  • Madawala UK, Thrimawithana DJ (2011) A bidirectional inductive power interface for electric vehicles in V2G systems. IEEE Trans Ind Electron 58(10):4789–4796

    Article  Google Scholar 

  • McNally MG (2007) The four step model. Handbook Trans Model 1:35–41

    Article  Google Scholar 

  • Miller JM, Onar OC, White C, Campbell S, Coomer C, Seiber L, Sepe R, Steyerl A (2014) Demonstrating dynamic wireless charging of an electric vehicle: the benefit of electrochemical capacitor smoothing. IEEE Power Electron Mag 1(1):12–24

    Article  Google Scholar 

  • Miralinaghi M, Lou Y, Keskin BB, Zarrinmehr A, Shabanpour R (2017) Refueling station location problem with traffic deviation considering route choice and demand uncertainty. Int J Hydrog Energy 42(5):3335–3351

    Article  Google Scholar 

  • Mirchandani P, Adler J, Madsen OB (2014) New logistical issues in using electric vehicle fleets with battery exchange infrastructure. Procedia Soc Behav Sci 108:3–14

    Article  Google Scholar 

  • Mock P, Yang Z (2014) Driving electrification: a global comparison of fiscal incentive policy for electric vehicles. International Council on Clean Transportation, Washington, DC

    Google Scholar 

  • Mock P, Schmid S, Friedrich HE (2010). Market prospects of electric passenger vehicles. Hybrid and Electric Vehicles, POWER SOURCES, MODELS, SUSTAINABILITY, INFRASTRUCTURE AND THE MARKET

  • Nagurney AB (1984) Comparative tests of multimodal traffic equilibrium methods. Transp Res B Methodol 18(6):469–485

    Article  Google Scholar 

  • Neubauer J, Wood E (2014) The impact of range anxiety and home, workplace, and public charging infrastructure on simulated battery electric vehicle lifetime utility. J Power Sources 257:12–20

    Article  Google Scholar 

  • Newmobility.news. World’s First Public ‘Electric Road’ for Charging in Sweden. https://newmobility.news/2018/04/12/sweden-opens-worlds-first-public-electric-road-for-charging/. Accessed April 12, 2018

  • Nie Y, Zhang HM, Lee DH (2004) Models and algorithms for the traffic assignment problem with link capacity constraints. Transp Res B Methodol 38(4):285–312

    Article  Google Scholar 

  • Niroumand R, Bahrami S, Aashtiani HZ, Roorda MJ (2018) Battery Electric Vehicles Network Equilibrium with Flow-Dependent Energy Consumption (No. 18–04519)

  • Park CK, Lee S, Park S (2004) A label-setting algorithm for finding a quickest path. Comput Oper Res 31(14):2405–2418

    Article  Google Scholar 

  • Patriksson M (2015) The traffic assignment problem: models and methods. Courier Dover Publications

  • Raith A, Ehrgott M (2009) A comparison of solution strategies for biobjective shortest path problems. Comput Oper Res 36(4):1299–1331

    Article  Google Scholar 

  • Ramadurai G, Ukkusuri S (2010) Dynamic user equilibrium model for combined activity-travel choices using activity-travel supernetwork representation. Netw Spatial Econ 10(2):273–292

    Article  Google Scholar 

  • Sheffi Y (1985) Urban transportation networks. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Smith OJ, Boland N, Waterer H (2012) Solving shortest path problems with a weight constraint and replenishment arcs. Comput Oper Res 39(5):964–984

    Article  Google Scholar 

  • Tesla Motors. Wired-up Roads Will Soon Charge Your Electric Car – While You’re Driving. https://theconversation.com/wired-up-roads-will-soon-charge-your-electric-car-while-youre-driving-72625. Accessed February 8, 2017

  • Tran DH, Choi W (2018) Design of a High-Efficiency Wireless Power Transfer System with Intermediate Coils for the on-board chargers of electric vehicles. IEEE Trans Power Electron 33(1):175–187

    Article  Google Scholar 

  • Unnikrishnan A, Waller ST (2009) User equilibrium with recourse. Netw Spatial Econ 9(4):575–593

    Article  Google Scholar 

  • Waller ST, Ziliaskopoulos AK (2002) On the online shortest path problem with limited arc cost dependencies. Networks 40(4):216–227

    Article  Google Scholar 

  • Wang TG, Xie C, Xie J, Waller T (2016) Path-constrained traffic assignment: a trip chain analysis under range anxiety. Trans Res Part C: Emerging Technol 68:447–461

    Article  Google Scholar 

  • Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civ Eng 1(3):325–362

    Google Scholar 

  • Xie C, Jiang N (2016) Relay requirement and traffic assignment of electric vehicles. Comput Aided Civil Infrastruct Eng 31(8):580–598

    Article  Google Scholar 

  • Xie C, Wang TG, Pu X, Karoonsoontawong A (2017) Path-constrained traffic assignment: modeling and computing network impacts of stochastic range anxiety. Transp Res B Methodol 103:136–157

    Article  Google Scholar 

  • Xu M, Meng Q, Liu K (2017) Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints. Transp Res B Methodol 99:138–166

    Article  Google Scholar 

  • Yang H, Huang HJ (2004) The multi-class, multi-criteria traffic network equilibrium and systems optimum problem. Transp Res B Methodol 38(1):1–15

    Article  Google Scholar 

  • Zheng H, He X, Li Y, Peeta S (2017) Traffic equilibrium and charging facility locations for electric vehicles. Netw Spatial Econ 17(2):435–457

    Article  Google Scholar 

  • Ziliaskopoulos AK, Waller ST, Li Y, Byram M (2004) Large-scale dynamic traffic assignment: implementation issues and computational analysis. J Transp Eng 130(5):585–593

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (project DP190102873).

Author information

Authors and Affiliations

  1. Research Centre for Integrated Transport Innovation, School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia

    Xiang Zhang, David Rey, S. Travis Waller & Nathan Chen

Authors
  1. Xiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Rey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Travis Waller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nathan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang Zhang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Rey, D., Waller, S.T. et al. Range-Constrained Traffic Assignment with Multi-Modal Recharge for Electric Vehicles. Netw Spat Econ 19, 633–668 (2019). https://doi.org/10.1007/s11067-019-09454-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11067-019-09454-9

Keywords

Search

Navigation