Efficient frontier of route choice for modeling the equilibrium under travel time variability with heterogeneous traveler preferences

Abstract Travelers consider the average duration and the reliability of travel time when choosing their route. However, the relative importance of average travel time and reliability not only depends on the purpose of the trip, but also varies from one person to another. Users seek to minimize their travel costs leading to an equilibrium condition in which they choose routes in such a way that they cannot reduce the general cost of their own trip. In this paper, we adopt the concept of the efficient frontier to represent the equilibrium route choice of the heterogeneous users in a network under travel time variability. Then, we use the primary properties of the efficient frontier to propose a mathematical formulation for the route choice problem for a discrete or continuous distribution of sensitivity of users to variations in route travel times. An analytical-based algorithm is designed to assign the heterogeneous demand to the network. Efficiency of the proposed algorithm in solving the route choice problem is also compared in a numerical example with a classic iterative method with a smoothing factor.

[1]  Xuesong Zhou,et al.  Incorporating Stochastic Road Capacity into Day-to-Day Traffic Simulation and Traveler Learning Framework , 2011 .

[2]  Carlos F. Daganzo,et al.  Morning Commute with Competing Modes and Distributed Demand: User Equilibrium, System Optimum, and Pricing , 2012 .

[3]  R. Bellman.  Dynamic programming. , 1957, Science.

[4]  H. Oliver Gao,et al.  Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach , 2017 .

[5]  Yafeng Yin,et al.  Robust congestion pricing under boundedly rational user equilibrium , 2010 .

[6]  Piet Rietveld,et al.  Road Congestion and Incident Duration , 2013 .

[7]  Kenneth A. Small,et al.  THE SCHEDULING OF CONSUMER ACTIVITIES: WORK TRIPS , 1982 .

[8]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[9]  A. Anas.  The optimal pricing, finance and supply of urban transportation in general equilibrium: A theoretical exposition , 2012 .

[10]  David P. Watling,et al.  User equilibrium traffic network assignment with stochastic travel times and late arrival penalty , 2006, Eur. J. Oper. Res..

[11]  Eric J. Gonzales,et al.  Analytical equilibrium of bicriterion choices with heterogeneous user preferences: application to the morning commute problem , 2017 .

[12]  Meead Saberi,et al.  Connecting Networkwide Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow , 2013 .

[13]  Hong Kam Lo,et al.  Network with degradable links: capacity analysis and design , 2003 .

[14]  Hai Yang,et al.  PROFITABILITY AND WELFARE GAIN OF PRIVATE TOLL ROADS IN A NETWORK WITH HETEROGENEOUS USERS , 2002 .

[15]  R B Noland.  INFORMATION IN A TWO-ROUTE NETWORK WITH RECURRENT AND NON-RECURRENT CONGESTION. IN: BEHAVIORAL AND NETWORK IMPACTS OF DRIVER INFORMATION SYSTEMS , 1999 .

[16]  Zhong Zhou,et al.  The [alpha]-reliable Mean-Excess Traffic Equilibrium Model with Stochastic Travel Times , 2010 .

[17]  Hong K. Lo,et al.  Doubly uncertain transportation network: Degradable capacity and stochastic demand , 2008, Eur. J. Oper. Res..

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

[19]  Anders Karlström,et al.  The value of reliability , 2007 .

[20]  Robin Lindsey,et al.  Road pricing and investment , 2012 .

[21]  Pitu Mirchandani,et al.  Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions , 1987, Transp. Sci..

[22]  Hong Kam Lo,et al.  Adaptive Vehicle Routing for Risk-averse Travelers☆ , 2013 .

[23]  Hai Yang,et al.  Pareto efficiency of reliability-based traffic equilibria and risk-taking behavior of travelers , 2014 .

[24]  Xiaoning Zhang,et al.  Multiclass Network Toll Design Problem with Social and Spatial Equity Constraints , 2002 .

[25]  Bi Yu Chen,et al.  An efficient solution algorithm for solving multi-class reliability-based traffic assignment problem , 2011, Math. Comput. Model..

[26]  Kenneth A. Small,et al.  The bottleneck model: An assessment and interpretation , 2015 .

[27]  Zhong-Ren Peng,et al.  Using Global Positioning System Data to Understand Variations in Path Choice , 2000 .

[28]  Michael Patriksson,et al.  The Traffic Assignment Problem: Models and Methods , 2015 .

[29]  Xing Wu,et al.  Modeling Heterogeneous Risk-Taking Behavior in Route Choice: A Stochastic Dominance Approach , 2011 .

[30]  Mohamed Abdel-Aty,et al.  INVESTIGATING EFFECT OF TRAVEL TIME VARIABILITY ON ROUTE CHOICE USING REPEATED-MEASUREMENT STATED PREFERENCE DATA , 1995 .

[31]  Ning Jia,et al.  A rank-dependent bi-criterion equilibrium model for stochastic transportation environment , 2014, Eur. J. Oper. Res..

[32]  Mogens Fosgerau,et al.  The value of travel time variance , 2010 .

[33]  Chung-Cheng Lu,et al.  Dynamic pricing, heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment , 2013 .

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

[35]  Joshua Auld,et al.  Dynamics of Activity Time-of-Day Choice , 2017 .

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

[37]  Robert B. Noland,et al.  Simulating Travel Reliability , 1997 .

[38]  C. Fisk.  Some developments in equilibrium traffic assignment , 1980 .

[39]  Mogens Fosgerau.  On the relation between the mean and variance of delay in dynamic queues with random capacity and demand , 2008 .

[40]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[41]  D. Boyce.  Beckmann's transportation network equilibrium model: Its history and relationship to the Kuhn–Tucker conditions , 2013 .

[42]  A J Richardson,et al.  TRAVEL TIME VARIABILITY ON COMMUTER JOURNEYS , 1978 .

[43]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[44]  W. Vickrey.  Congestion Theory and Transport Investment , 1969 .

[45]  Matthias Ehrgott,et al.  A bi-objective user equilibrium model of travel time reliability in a road network , 2014 .

[46]  Mahyar Amirgholy,et al.  Multi-objective cordon price design to control long run adverse traffic effects in large urban areas , 2015 .

[47]  Yu Nie,et al.  Multi-class percentile user equilibrium with flow-dependent stochasticity , 2011 .

[48]  Carlos F. Daganzo,et al.  On Stochastic Models of Traffic Assignment , 1977 .

[49]  David M Levinson,et al.  A Portfolio Theory of Route Choice , 2013 .

[50]  Stephen D. Boyles,et al.  An outer approximation algorithm for the robust shortest path problem , 2013 .

[51]  Robert B. Dial,et al.  Bicriterion Traffic Assignment: Basic Theory and Elementary Algorithms , 1996, Transp. Sci..

[52]  Vincent A. C. van den Berg,et al.  Congestion Tolling in the Bottleneck Model with Heterogeneous Values of Time , 2011 .