Abstract
In this paper, we consider a novel reliability-based network equilibrium problem for mixed traffic flows of human-driven vehicles (HVs) and connected autonomous vehicles (CAVs) with endogenous CAV market penetration and stochastic link capacity degradations. Travelers’ perception errors on travel time and their risk-aversive behaviors on mode choice and path choice are incorporated in the model with a hierarchical choice structure. Due to the differences between HVs and CAVs, the perception errors and the safety margin reserved by risk-averse travelers are assumed to be related to the vehicle type. The path travel time distribution is derived by using the moment-matching method based on the assumption that link capacity follows lognormal distribution and link travel times are correlated. Then, the underlying problem is formulated as an equivalent variational inequality problem. A path-based algorithm embedded with the Monte Carlo simulation-based method is proposed to solve the model. Numerical experiments are conducted to illustrate the features of the model and the computational performance of the solution algorithm.
Similar content being viewed by others
Availability of Data and Material
All data generated or analysed during this study are included in this published article.
References
Abdel-Aty MA, Kitamura R, Jovanis PP (1995) Exploring route choice behavior using geographic information system-based alternative routes and hypothetical travel time information input. Transportation Research Record Journal of the Transportation Research Board 1493(1493):74–80
Bifulco GN, Cantarella GE, Simonelli F et al (2016) Advanced traveller information systems under recurrent traffic conditions: network equilibrium and stability. Transp Res B Methodol 92:73–87
Blum J (1954) Multidimensional stochastic approximation methods. Ann Math Stat 25(4):737–744
Brownstone D, Ghosh A, Golob TF et al (2003) Drivers’ willingness-to-pay to reduce travel time: evidence from the San Diego i–15 congestion pricing project. Transp Res A Policy Pract 37(4):37–3387
Chen A, Zhou Z, Lam WHK (2011) Modeling stochastic perception error in the mean-excess traffic equilibrium model. Transp Res B Methodol 45(10):1619–1640
Chen P, Tong R, Lu G et al (2018) The α-reliable path problem in stochastic road networks with link correlations: a moment-matching-based path finding algorithm. Expert Syst Appl 110(Nov.):20–32
Chen S, Wang H, Meng Q (2019) Designing autonomous vehicle incentive program with uncertain vehicle purchase price. Transp Res Part C Emerg Technol 103(Jun.):226–245
Delle Site P (2018) A mixed-behaviour equilibrium model under predictive and static advanced traveller information systems and state-dependent route choice. Transp Res Part C Emerg Technol 86:549–562
Facchinei F, Pang JS (2003) Finite-dimensional variational inequalities and complementarity problems. Springer, New York
Fenton LF (1960) The sum of a log-normal probability distribution in scattered transmission systems. IRE Trans Commun Syst 8:57–67
Fosgerau M, Engelson L (2011) The value of travel time variance. Transp Res B Methodol 45(1):1–8
Ghiasi A, Hussain O, Qian ZS et al (2017) A mixed traffic capacity analysis and lane management model for connected automated vehicles: a Markov chain method. Transp Res B Methodol 106(Dec.):266–292
Haghani M, Shahhoseini Z, Sarvi M (2016) Quantifying benefits of traveler information systems to performance of transport networks prior to implementation: a double-class structured-parameter stochastic trip assignment approach. Transp Lett 8(1):1–12
Hall RW (1983) Travel outcome and performance: the effect of uncertainty on accessibility. Transp Res B Methodol 17(4):275–290
Huang HJ, Liu TL, Yang H (2008) Modeling the evolutions of day-to-day route choice and year-to-year ATIS adoption with stochastic user equilibrium. J Adv Transp 42(2)
Huang HJ, Li ZC (2007) A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS. Eur J Oper Res 176(3):1464–1477
Huang HJ, Liu TL, Guo X et al (2011) Inefficiency of logit-based stochastic user equilibrium in a traffic network under atis. Netw Spat Econ 11(2):255–269
International SAE (2018) Taxonomy and definitions for terms related to driving automation systems for on-road motor vehicles. SAE
Lam W, Shao H, Sumalee A (2008) Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply. Transp Res B Methodol 42(10):890–910
Lazar DA, Coogan S, Pedarsani R (2017) Capacity modeling and routing for traffic networks with mixed autonomy. 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, pp 5678–5683
Levin MW, Boyles SD (2015) Effects of autonomous vehicle ownership on trip, mode, and route choice. Transp Res Rec 2493(1):29–38
Li J, Huang L (2012) Stochastic traffic assignment considering road guidance information. J Transp Syst Eng Inf Technol 12(3):31–35
Liu Z, Song Z (2019) Strategic planning of dedicated autonomous vehicle lanes and autonomous vehicle/toll lanes in transportation networks. Transp Res Part C Emerg Technol 106:381–403
Liu HX, Recker W, Chen A (2004) Uncovering the contribution of travel time reliability to dynamic route choice using real-time loop data. Transp Res A Policy Pract 38(6):435–453
Liu H, He X, He B (2009) Method of successive weighted averages (mswa) and self-regulated averaging schemes for solving stochastic user equilibrium problem. Netw Spat Econ 9(4):485–503
Lo HK, Szeto WY (2004) Modeling advanced traveler information services: static versus dynamic paradigms. Transp Res B Methodol 38(6):495–515
Lo HK, Tung YK (2003) Network with degradable links: capacity analysis and design. Transp Res B Methodol 37(4):345–363
Lo HK, Luo XW, Siu BWY (2006) Degradable transport network: travel time budget of travelers with heterogeneous risk aversion. Transp Res B Methodol 40(9):792–806
Noruzoliaee M, Zou B, Liu Y (2018) Roads in transition: Integrated modeling of a manufacturer-traveler-infrastructure system in a mixed autonomous/human driving environment. Transp Res Part C Emerg Technol 90:307–333
People’s Government of Guangdong Province (2023) Income and consumption expenditure of Guangdong residents in the first half of 2023. http://www.gd.gov.cn/zwgk/sjfb/mssj/rjkzpsr/. Accessed 23 July 2023
Prakash AA, Seshadri R, Srinivasan KK (2018) A consistent reliability-based user-equilibrium problem with risk-averse users and endogenous travel time correlations: Formulation and solution algorithm. Transp Res B Methodol 114:171–198
Rakha H, Farzaneh M, Arafeh M et al (2008) Inclement weather impacts on freeway traffic stream behavior. Transp Res Rec 2071:8–18
Shao H, Lam W, Mei LT (2006) A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand. Netw Spat Econ 6(3):173–204
Shao H, Lam W, Mei LT et al (2008) Modelling rain effects on risk-taking behaviours of multi-user classes in road networks with uncertainty. J Adv Transp 42(3):265–290
Shen L, Hu S, Ting W et al (2020) Finding the reliable shortest path with correlated link travel times in signalized traffic networks under uncertainty. Transp Res E Logist Transp Rev 144(102159):1–23
Shladover SE, Su D, Lu XY (2012) Impacts of cooperative adaptive cruise control on freeway traffic flow. Transp Res Rec 2324(1):63–70
Siu B, Lo H (2006) Doubly uncertain transport network: degradable link capacity and perception variations in traffic conditions. Transp Res Rec 1964:59–69
Srinivasan KK, Prakash AA, Seshadri R (2014) Finding most reliable paths on networks with correlated and shifted log–normal travel times. Transp Res B Methodol 66:110–128
Sumalee A, Uchida K, Lam W (2011) Stochastic multi-modal transport network under demand uncertainties and adverse weather condition. Transp Res Part C Emerg Technol 19(2):338–350
Tan H, Du M, Chen A (2022) Accelerating the gradient projection algorithm for solving the non-additive traffic equilibrium problem with the Barzilai-Borwein step size. Comput Oper Res 141:105723
Tani R, Sumalee A, Uchida K (2021) Travel time reliability-based optimization problem for CAVS dedicated lanes. Transp A Transp Sci 18(3):1569–1600
Verhoef ET et al (2016) Autonomous cars and dynamic bottleneck congestion: the effects on capacity, value of time and preference heterogeneity. Transp Res B Methodol 94:43–60
Wang J, Peeta S, He X (2019) Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles. Transp Res B Methodol 126:139–168
Wang J, Lu L, Peeta S et al (2021) Optimal toll design problems under mixed traffic flow of human-driven vehicles and connected and autonomous vehicles. Transp Res Part C Emerg Technol 125(102952):1–30
Wang J, Wang W, Ren G et al (2022) Worst-case traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles by factoring in the uncertain link capacity. Transp Res Part C Emerg Technol 140(103703):1–18
Xie T, Liu Y (2022) Impact of connected and autonomous vehicle technology on market penetration and route choices. Transp Res Part C Emerg Technol 139:103646
Yang H (1998) Multiple equilibrium behaviors and advanced traveler information systems with endogenous market penetration. Transp Res B Methodol 32(3):0–218
Yin Y, Yang H (2003) Simultaneous determination of the equilibrium market penetration and compliance rate of advanced traveler information systems. Transp Res A Policy Pract 37(2):165–181
Zhang F, Lu J, Hu X (2020) Traffic equilibrium for mixed traffic flows of human-driven vehicles and connected and autonomous vehicles in transportation networks under tradable credit scheme. J Adv Transp 8498561:1–18
Zhang F, Lu J, Hu X et al (2022) Optimal design of differentiated credit charging links in mixed-autonomy transportation networks. Appl Math Model 108:646–669
Zockaie A, Nie YM, Mahmassani HS (2014) Simulation-based method for finding minimum travel time budget paths in stochastic networks with correlated link times. Transp Res Rec 2467(1):140–148
Funding
The authors did not receive support from any organization for the submitted work.
Author information
Authors and Affiliations
Contributions
Qi Zhong: Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing. Lixin Miao: Conceptualization, Methodology, Writing – review & editing, Supervision.
Corresponding author
Ethics declarations
Competing Interests
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhong, Q., Miao, L. Reliability-Based Mixed Traffic Equilibrium Problem Under Endogenous Market Penetration of Connected Autonomous Vehicles and Uncertainty in Supply. Netw Spat Econ 24, 461–505 (2024). https://doi.org/10.1007/s11067-024-09621-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11067-024-09621-7