Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles

Abstract Compared to existing human-driven vehicles (HDVs), connected and autonomous vehicles (CAVs) offer users the potential for reduced value of time, enhanced quality of travel experience, and seamless situational awareness and connectivity. Hence, CAV users can differ in their route choice behavior compared to HDV users, leading to mixed traffic flows that can significantly deviate from the single-class HDV traffic pattern. However, due to the lack of quantitative models, there is limited knowledge on the evolution of mixed traffic flows in a traffic network. To partly bridge this gap, this study proposes a multiclass traffic assignment model, where HDV users and CAV users follow different route choice principles, characterized by the cross-nested logit (CNL) model and user equilibrium (UE) model, respectively. The CNL model captures HDV users’ uncertainty associated with limited knowledge of traffic conditions while overcoming the route overlap issue of logit-based stochastic user equilibrium. The UE model characterizes the CAV's capability for acquiring accurate information on traffic conditions. In addition, the multiclass model can capture the characteristics of mixed traffic flow such as the difference in value of time between HDVs and CAVs and the asymmetry in their driving interactions, thereby enhancing behavioral realism in the modeling. The study develops a new solution algorithm labeled RSRS-MSRA, in which a route-swapping based strategy is embedded with a self-regulated step size choice technique, to solve the proposed model efficiently. Sensitivity analysis of the proposed model is performed to gain insights into the effects of perturbations on the mixed traffic equilibrium, which facilitates the estimation of equilibrium traffic flow and identification of critical elements under expected or unexpected events. The study results can assist transportation decision-makers to design effective planning and operational strategies to leverage the advantages of CAVs and manage traffic congestion under mixed traffic flows.

[1]  Xiangdong Xu,et al.  A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem , 2012, Comput. Oper. Res..

[2]  E. Martins,et al.  An algorithm for the ranking of shortest paths , 1993 .

[3]  Hai-Jun Huang,et al.  A Multi-Class Dynamic User Equilibrium Model for Queuing Networks with Advanced Traveler Information Systems , 2003, J. Math. Model. Algorithms.

[4]  Stephen D. Boyles,et al.  Improved bush-based methods for network contraction , 2016 .

[5]  William H. K. Lam,et al.  A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand , 2006 .

[6]  Terry L. Friesz,et al.  A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem , 1995, Transp. Sci..

[7]  Yu Zhou,et al.  Real-world fuel consumption and CO2 (carbon dioxide) emissions by driving conditions for light-duty passenger vehicles in China , 2014 .

[8]  Yoshiaki Nemoto,et al.  Development of a Small-Distance Vehicle Platooning System , 2009 .

[9]  Anna Nagurney,et al.  A MULTICLASS, MULTICRITERIA TRAFFIC NETWORK EQUILIBRIUM MODEL WITH ELASTIC DEMAND , 2002 .

[10]  Hans Fritz,et al.  Fuel Consumption Reduction in a Platoon: Experimental Results with two Electronically Coupled Trucks at Close Spacing , 2000 .

[11]  Hai Yang,et al.  Sensitivity analysis for the elastic-demand network equilibrium problem with applications , 1997 .

[12]  E. Cascetta,et al.  A MODIFIED LOGIT ROUTE CHOICE MODEL OVERCOMING PATH OVERLAPPING PROBLEMS. SPECIFICATION AND SOME CALIBRATION RESULTS FOR INTERURBAN NETWORKS , 1996 .

[13]  Heinz H. Bauschke,et al.  Projection and proximal point methods: convergence results and counterexamples , 2004 .

[14]  Terry L. Friesz,et al.  Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems , 1994, Oper. Res..

[15]  Michael Scott Ramming,et al.  NETWORK KNOWLEDGE AND ROUTE CHOICE , 2002 .

[16]  Larry Joseph Leblanc,et al.  MATHEMATICAL PROGRAMMING ALGORITHMS FOR LARGE SCALE NETWORK EQUILIBRIUM AND NETWORK DESIGN PROBLEMS , 1973 .

[17]  S. Peeta,et al.  Stability issues for dynamic traffic assignment , 2003, Autom..

[18]  Jian Wang,et al.  Sensitivity analysis based approximation models for day-to-day link flow evolution process , 2016 .

[19]  Stephen D. Boyles,et al.  Effects of Autonomous Vehicle Ownership on Trip, Mode, and Route Choice , 2015 .

[20]  T de la Barra,et al.  Multidimensional path search and assignment , 1993 .

[21]  Richard Mounce,et al.  On the Convergence of the Method of Successive Averages for Calculating Equilibrium in Traffic Networks , 2015, Transp. Sci..

[22]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[23]  S. Dafermos.  The Traffic Assignment Problem for Multiclass-User Transportation Networks , 1972 .

[24]  Nicholas F. Maxemchuk,et al.  Highway Capacity Benefits from Using Vehicle-to-Vehicle Communication and Sensors for Collision Avoidance , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[25]  Hai Yang,et al.  Sensitivity Analysis of Network Traffic Equilibrium Revisited: The Corrected Approach , 2007 .

[26]  S. Khan,et al.  Real time lane detection for autonomous vehicles , 2008, 2008 International Conference on Computer and Communication Engineering.

[27]  Haijun Huang,et al.  Combined Activity/Travel Choice Models: Time-Dependent and Dynamic Versions , 2003 .

[28]  Jianqiang Wang,et al.  Economy-oriented vehicle adaptive cruise control with coordinating multiple objectives function , 2013 .

[29]  Daniel J. Fagnant,et al.  Preparing a Nation for Autonomous Vehicles: Opportunities, Barriers and Policy Recommendations , 2015 .

[30]  M. J. Smith,et al.  A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium , 1995, Ann. Oper. Res..

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

[32]  M. Florian.  A Traffic Equilibrium Model of Travel by Car and Public Transit Modes , 1977 .

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

[34]  Yuchuan Du,et al.  Optimal design of autonomous vehicle zones in transportation networks , 2017 .

[35]  Hai Yang,et al.  A discrete rational adjustment process of link flows in traffic networks , 2013 .

[36]  Satish V. Ukkusuri,et al.  Multiclass, simultaneous route and departure time choice dynamic traffic assignment with an embedded spatial queuing model , 2019 .

[37]  Anthony V. Fiacco,et al.  Introduction to Sensitivity and Stability Analysis in Nonlinear Programming , 2012 .

[38]  Mike J. Smith,et al.  A route-swapping dynamical system and Lyapunov function for stochastic user equilibrium , 2016 .

[39]  Michael J. Smith,et al.  The Stability of a Dynamic Model of Traffic Assignment - An Application of a Method of Lyapunov , 1984, Transp. Sci..

[40]  Terry L. Friesz,et al.  Sensitivity Analysis for Equilibrium Network Flow , 1988, Transp. Sci..

[41]  Henry X. Liu,et al.  Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem , 2009 .

[42]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[43]  Hai-Jun Huang,et al.  A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS , 2007, Eur. J. Oper. Res..

[44]  Hong Kam Lo,et al.  Global Optimum of the Linearized Network Design Problem with Equilibrium Flows , 2010 .

[45]  Yafeng Yin,et al.  Optimal deployment of autonomous vehicle lanes with endogenous market penetration , 2016 .

[46]  W. Y. Szeto,et al.  DYNAMIC TRAFFIC ASSIGNMENT: PROPERTIES AND EXTENSIONS , 2006 .

[47]  S F Catalano,et al.  A FORECASTING MODEL FOR INLAND NAVIGATION BASED ON ROUTE ENUMERATION , 2001 .

[48]  Alain L. Kornhauser,et al.  Assigning traffic over essentially-least-cost paths , 1996 .

[49]  Hong Kam Lo,et al.  Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion , 2006 .

[50]  Satish V. Ukkusuri,et al.  Dynamic User Equilibrium Model for Combined Activity-Travel Choices Using Activity-Travel Supernetwork Representation , 2010 .

[51]  M. Ben-Akiva,et al.  MODELLING INTER URBAN ROUTE CHOICE BEHAVIOUR , 1984 .

[52]  Stephen D. Clark,et al.  Probit-Based Sensitivity Analysis for General Traffic Networks , 2000 .

[53]  Stephen D. Boyles,et al.  Dynamic traffic assignment of cooperative adaptive cruise control , 2018 .

[54]  A. Papola,et al.  On the covariance structure of the Cross-Nested Logit model , 2008 .

[55]  Hai-Jun Huang,et al.  Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues , 2002 .

[56]  Stephen D. Boyles,et al.  A multiclass cell transmission model for shared human and autonomous vehicle roads , 2016 .

[57]  Shlomo Bekhor,et al.  Stochastic User-Equilibrium Formulations for Extended-Logit Assignment Models , 1999 .

[58]  Stephen D. Boyles,et al.  Bush-based sensitivity analysis for approximating subnetwork diversion , 2012 .

[59]  R. Tobin.  Sensitivity analysis for variational inequalities , 1986 .

[60]  Srinivas Peeta,et al.  Combined multinomial logit modal split and paired combinatorial logit traffic assignment model , 2018 .

[61]  Athanasios K. Ziliaskopoulos,et al.  Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future , 2001 .

[62]  Majid Sarvi,et al.  Path sets size, model specification, or model estimation: Which one matters most in predicting stochastic user equilibrium traffic flow? , 2016 .

[63]  Erik T. Verhoef,et al.  Robot Cars and Dynamic Bottleneck Congestion: The Effects on Capacity, Value of Time and Preference Heterogeneity , 2016 .

[64]  W. Y. Szeto,et al.  Multi-class dynamic traffic assignment with physical queues: intersection-movement-based formulation and paradox , 2016 .

[65]  Haijun Huang,et al.  A discrete dynamical system of formulating traffic assignment: Revisiting Smith’s model , 2016 .

[66]  Xiangdong Xu,et al.  Modeling Mode and Route Similarities in Network Equilibrium Problem with Go-Green Modes , 2016 .

[67]  Zhaowang Ji,et al.  Path finding under uncertainty , 2005 .