A unified equilibrium framework of new shared mobility systems

Abstract Modeling congestion effects arising from multiple travel modes, shared mobility modes in particular, is non-trivial because of the complex interactions among diverse agents and distinct traffic flow compositions. This research aims to provide a theoretical framework of generic traffic network equilibria to unify these services and hopefully become a step stone to modeling shared mobility services in congested road network. In the proposed framework, we mainly focus on three modes: driving solo, ridesharing, and e-hailing service. The four types of traffic flows are: personal vehicle drivers, e-hailing drivers, ridesharing riders, and e-hailing passengers. The first two flows contribute to traffic congestion while the latter two do not. To capture their interactions, a super extended network is created with four copied networks each of whom represents one type of traffic flow. The equilibrium of new mobility systems can then be reformulated as a quasi-variational inequality and solution existence is discussed. The numerical results are tested in both Braess network and Sioux Falls network to illustrate the impact of different parameters on equilibrium outcomes, including modal cost, system travel time and deadhead miles. The results of this model will help assist transportation planners in making policy and regulation decisions regarding shared mobility services.

[1]  Xiaolei Guo,et al.  Braess paradox under the boundedly rational user equilibria , 2014 .

[2]  Richard E. Rosenthal,et al.  GAMS -- A User's Guide , 2004 .

[3]  Shing Chung Josh Wong,et al.  Modeling urban taxi services in congested road networks with elastic demand , 2001 .

[4]  P. Harker.  Generalized Nash games and quasi-variational inequalities , 1991 .

[5]  Shing Chung Josh Wong,et al.  Equlibrium of Bilateral Taxi-Customer Searching and Meeting on Networks , 2010 .

[6]  Hai Yang,et al.  Taxi services with search frictions and congestion externalities , 2014 .

[7]  Hani S. Mahmassani,et al.  Dynamic Traffic Assignment in Design and Evaluation of High-Occupancy Toll Lanes , 2000 .

[8]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..

[9]  Hai Yang,et al.  Equilibrium properties of taxi markets with search frictions , 2011 .

[10]  Stephen D. Boyles,et al.  A general framework for modeling shared autonomous vehicles with dynamic network-loading and dynamic ride-sharing application , 2017, Comput. Environ. Urban Syst..

[11]  W. Y. Szeto,et al.  A two-stage approach to modeling vacant taxi movements , 2015 .

[12]  Lin Sun,et al.  Hunting or waiting? Discovering passenger-finding strategies from a large-scale real-world taxi dataset , 2011, 2011 IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOM Workshops).

[13]  Maged Dessouky,et al.  Complementarity models for traffic equilibrium with ridesharing , 2015 .

[14]  Yili Hong,et al.  How Do On‐demand Ridesharing Services Affect Traffic Congestion? The Moderating Role of Urban Compactness , 2016, Production and Operations Management.

[15]  Bin Ran,et al.  Evaluation of Value Pricing Using a Multiclass Dynamic Network Model , 2003 .

[16]  Yi-Chang Chiu,et al.  Modeling Routing Behavior for Vacant Taxicabs in Urban Traffic Networks , 2012 .

[17]  Liang Liu,et al.  Uncovering cabdrivers' behavior patterns from their digital traces , 2010, Comput. Environ. Urban Syst..

[18]  Hai Yang,et al.  Ridesharing User Equilibrium and Its Implications for High-Occupancy Toll Lane Pricing , 2017 .

[19]  Henry X. Liu,et al.  Boundedly Rational User Equilibria (BRUE): Mathematical Formulation and Solution Sets , 2013 .

[20]  Torbjörn Larsson,et al.  Side constrained traffic equilibrium models: analysis, computation and applications , 1999 .

[21]  Susan Shaheen,et al.  Shared Mobility: Current Practices and Guiding Principles , 2016 .

[22]  Xuan Di,et al.  Second best toll pricing within the framework of bounded rationality , 2016 .

[23]  Shing Chung Josh Wong,et al.  Modeling Urban Taxi Services with Multiple User Classes and Vehicle Modes , 2008 .

[24]  Favyen Bastani,et al.  Towards Reducing Taxicab Cruising Time Using Spatio-Temporal Profitability Maps , 2011, SSTD.

[25]  Rui Ma,et al.  A link-node reformulation of ridesharing user equilibrium with network design , 2018, Transportation Research Part B: Methodological.

[26]  W. Y. Szeto,et al.  A time-dependent logit-based taxi customer-search model , 2013 .

[27]  Fang Liu,et al.  A Two-Layer Model for Taxi Customer Searching Behaviors Using GPS Trajectory Data , 2016, IEEE Transactions on Intelligent Transportation Systems.

[28]  M. Ferris,et al.  Complementarity problems in GAMS and the PATH solver 1 This material is based on research supported , 2000 .

[29]  Hai Yang,et al.  DEMAND-SUPPLY EQUILIBRIUM OF TAXI SERVICES IN A NETWORK UNDER COMPETITION AND REGULATION , 2002 .

[30]  Zuo-Jun Max Shen,et al.  Modeling taxi services with smartphone-based e-hailing applications , 2015 .

[31]  W. Y. Szeto,et al.  A cell-based logit-opportunity taxi customer-search model , 2014 .

[32]  Fernando Ordóñez,et al.  Ridesharing: The state-of-the-art and future directions , 2013 .

[33]  Kara M. Kockelman,et al.  The Travel and Environmental Implications of Shared Autonomous Vehicles, Using Agent-Based Model Scenarios , 2014 .

[34]  Meng Li,et al.  A restricted path-based ridesharing user equilibrium , 2020, J. Intell. Transp. Syst..

[35]  Henry X. Liu,et al.  Risk Averse Second Best Toll Pricing , 2009 .

[36]  Jong-Shi Pang,et al.  Nonconvex Games with Side Constraints , 2011, SIAM J. Optim..

[37]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[38]  W. Y. Szeto,et al.  Modelling multi-period customer-searching behaviour of taxi drivers , 2014 .

[39]  Hani S. Mahmassani,et al.  Methodology for Assessing High-Occupancy Toll-Lane Usage and Network Performance , 2001 .

[40]  Carlos Riquelme,et al.  Dynamic pricing in ridesharing platforms , 2016, SECO.

[41]  W. Y. Szeto,et al.  Sequential Logit Approach to Modeling the Customer-Search Decisions of Taxi Drivers , 2015 .

[42]  Hai Yang,et al.  Empirical evidence for taxi customer-search model , 2010 .

[43]  Francisco Facchinei,et al.  Nash equilibria: the variational approach , 2010, Convex Optimization in Signal Processing and Communications.

[44]  Henry X. Liu,et al.  Boundedly rational route choice behavior: A review of models and methodologies , 2016 .

[45]  Shing Chung Josh Wong,et al.  A NETWORK MODEL OF URBAN TAXI SERVICES , 1998 .

[46]  W. Y. Szeto,et al.  Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance , 2014, 1402.1211.

[47]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[48]  Carlos F. Daganzo,et al.  EQUILIBRIUM MODEL FOR CARPOOLS ON AN URBAN NETWORK , 1981 .

[49]  S. Ukkusuri,et al.  Taxi market equilibrium with third-party hailing service , 2017 .

[50]  Yafeng Yin,et al.  Optimal Deployment of Managed Lanes in General Networks , 2015 .