A generalized Bayesian traffic model

Abstract The rapid growth of transportation data offers new opportunities to analyze the interaction between travel behavior and transportation system performance, and particularly when issues such as uncertainty and reliability are considered. Many previous studies in this area described the stationary behavior of stochastic transportation systems using user equilibrium (UE) conditions. In contrast, this paper develops a generalized Bayesian model to analyze the dynamic behavior of stochastic transportation systems. In the proposed model, the variability of link volume and travel time stems from the stochasticity in travel demand, transportation supply (e.g. link capacity, free flow travel time, etc.) and route choice. To the best of our knowledge, this is among the first work that considers the three sources of stochasticity simultaneously. In addition, we propose a Bayesian updating approach based on the Dirichlet model to describe the route choice behavior. This approach allows researchers to consider a wide range of route choice behavior of bounded rationality in day-to-day traffic dynamics, including a knowledge updating mechanism based on different memory lengths and weighting factors. This framework is particularly suitable for data-driven studies supported by emerging transportation data due to the computing efficiency of the Dirichlet-based Bayesian updating mechanism and the sound behavioral foundation. This paper shows that the proposed Bayesian model with infinite memory leads to UE conditions under stochastic demand and supply. Subsequently, a numerical case study is conducted to illustrate different day-to-day route choice dynamics with different memory lengths of system performance. This paper also discusses the influence of the three sources of stochasticity towards the aggregated variance of link volumes and travel time. With enough longitudinal travel choice and transportation system performance data, the proposed Bayesian framework could be empirically calibrated and tested, which offers an attractive descriptive alternative to the conventional UE-based transportation system models.

[1]  David C. Schmittlein,et al.  Excess Behavioral Loyalty for High-Share Brands: Deviations from the Dirichlet Model for Repeat Purchasing , 1993 .

[2]  F. Feinberg,et al.  Assessing Heterogeneity in Discrete Choice Models Using a Dirichlet Process Prior , 2004 .

[3]  E. Cascetta.  A stochastic process approach to the analysis of temporal dynamics in transportation networks , 1989 .

[4]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[5]  Hai Yang,et al.  Link-based day-to-day network traffic dynamics and equilibria , 2015 .

[6]  David Watling.  Stochastic Network Equilibrium under Stochastic Demand , 2002 .

[7]  Wei Ma,et al.  On the variance of recurrent traffic flow for statistical traffic assignment , 2017 .

[8]  Pu Wang,et al.  Development of origin–destination matrices using mobile phone call data , 2014 .

[9]  Y. Vardi,et al.  Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data , 1996 .

[10]  Jinzhou Cao,et al.  Extracting Trips from Multi-Sourced Data for Mobility Pattern Analysis: An App-Based Data Example. , 2019, Transportation research. Part C, Emerging technologies.

[11]  Cam Rungie,et al.  Calculation of Theoretical Brand Performance Measures from the Parameters of the Dirichlet Model , 2004 .

[12]  Carlos F. Daganzo,et al.  Multinomial Probit: The Theory and its Application to Demand Forecasting. , 1980 .

[13]  Stephen D. Clark,et al.  Modelling network travel time reliability under stochastic demand , 2005 .

[14]  Agachai Sumalee,et al.  Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply , 2008 .

[15]  Samer Madanat,et al.  Perception updating and day-to-day travel choice dynamics in traffic networks with information provision , 1998 .

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

[17]  K. Knopp.  Theory and Application of Infinite Series , 1990 .

[18]  Shoichiro Nakayama,et al.  Consistent formulation of network equilibrium with stochastic flows , 2014 .

[19]  Lei Zhang,et al.  Probabilistic Data Fusion for Short-Term Traffic Prediction With Semiparametric Density Ratio Model , 2019, IEEE Transactions on Intelligent Transportation Systems.

[20]  Gary A. Davis,et al.  Large Population Approximations of a General Stochastic Traffic Assignment Model , 1993, Oper. Res..

[21]  J. Horowitz.  The stability of stochastic equilibrium in a two-link transportation network , 1984 .

[22]  Xiqun Chen,et al.  Short-Term Forecasting of Passenger Demand under On-Demand Ride Services: A Spatio-Temporal Deep Learning Approach , 2017, ArXiv.

[23]  Giulio Erberto Cantarella,et al.  Modelling sources of variation in transportation systems: theoretical foundations of day-to-day dynamic models , 2013 .

[24]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[25]  Agachai Sumalee,et al.  Estimation of mean and covariance of stochastic multi-class OD demands from classified traffic counts , 2015 .

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

[27]  Fan Yang,et al.  Day-to-day stationary link flow pattern , 2009 .

[28]  Martin L. Hazelton,et al.  Asymptotic approximations of transient behaviour for day-to-day traffic models , 2018, Transportation Research Part B: Methodological.

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

[30]  Martin L. Hazelton,et al.  Computation of Equilibrium Distributions of Markov Traffic-Assignment Models , 2004, Transp. Sci..

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

[32]  Henry X. Liu,et al.  Indifference bands for boundedly rational route switching , 2017 .

[33]  Alexander J. Smola,et al.  Scalable distributed inference of dynamic user interests for behavioral targeting , 2011, KDD.

[34]  Hani S. Mahmassani,et al.  DYNAMICS OF COMMUTING DECISION BEHAVIOR UNDER ADVANCED TRAVELER INFORMATION SYSTEMS , 1999 .

[35]  J. Bates,et al.  The valuation of reliability for personal travel , 2001 .

[36]  Agachai Sumalee,et al.  Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts , 2014 .

[37]  Giulio Erberto Cantarella,et al.  Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems , 2015 .

[38]  Chenfeng Xiong,et al.  Agent-Based Microsimulation Approach for Design and Evaluation of Flexible Work Schedules , 2015 .

[39]  Zhen Qian,et al.  Estimating multi-year 24/7 origin-destination demand using high-granular multi-source traffic data , 2018, Transportation Research Part C: Emerging Technologies.

[40]  Xiaojun Chen,et al.  Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach , 2011 .

[41]  Hani S. Mahmassani,et al.  System performance and user response under real-time information in a congested traffic corridor , 1991 .

[42]  Shoichiro Nakayama,et al.  Effect of providing traffic information estimated by a stochastic network equilibrium model with stochastic demand , 2016 .

[43]  Jun-ichi Takayama,et al.  STOCHASTIC NETWORK EQUILIBRIUM MODELS CONSIDERING BOTH STOCHASTIC TRAVEL DEMAND AND ROUTE CHOICE , 2006 .

[44]  Lei Zhang,et al.  Integrating mesoscopic dynamic traffic assignment with agent-based travel behavior models for cumulative land development impact analysis , 2018, Transportation Research Part C: Emerging Technologies.

[45]  Qiang Meng,et al.  General stochastic user equilibrium traffic assignment problem with link capacity constraints , 2008 .

[46]  Hai Yang,et al.  Continuous price and flow dynamics of tradable mobility credits , 2013 .

[47]  Nathan H. Gartner,et al.  Optimal Traffic Assignment with Elastic Demands: A Review Part I. Analysis Framework , 1980 .

[48]  M. Maher.  INFERENCES ON TRIP MATRICES FROM OBSERVATIONS ON LINK VOLUMES: A BAYESIAN STATISTICAL APPROACH , 1983 .

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

[50]  Neil Wrigley,et al.  Dirichlet-Logistic Models of Spatial Choice , 1990 .

[51]  Hai Yang,et al.  Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium , 2017, Transp. Sci..

[52]  A. W. Kemp,et al.  The Dirichlet: A comprehensive model of buying behaviour , 1984 .

[53]  C. Daganzo.  Unconstrained Extremal Formulation of Some Transportation Equilibrium Problems , 1982 .

[54]  Kiyoshi Kobayashi,et al.  Information, rational expectations and network equilibria — an analytical perspective for route guidance systems , 1994 .

[55]  Qiang Meng,et al.  Demand-Driven Traffic Assignment Problem Based on Travel Time Reliability , 2006 .

[56]  Giulio Erberto Cantarella,et al.  Day-to-day dynamic models for intelligent transportation systems design and appraisal , 2013 .

[57]  Shoichiro Nakayama,et al.  Bayesian Learning, Day-to-day Adjustment Process, and Stability of Wardrop Equilibrium , 2009 .

[58]  Martin L. Hazelton,et al.  Bayesian inference for day-to-day dynamic traffic models , 2013 .

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

[60]  D. Watling.  STABILITY OF THE STOCHASTIC EQUILIBRIUM ASSIGNMENT PROBLEM: A DYNAMICAL SYSTEMS APPROACH , 1999 .

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

[62]  Xiqun Chen,et al.  Understanding ridesplitting behavior of on-demand ride services: An ensemble learning approach , 2017 .

[63]  M. Bierlaire,et al.  Discrete Choice Methods and their Applications to Short Term Travel Decisions , 1999 .

[64]  David P. Watling,et al.  A Second Order Stochastic Network Equilibrium Model, I: Theoretical Foundation , 2002, Transp. Sci..

[65]  Richard L. Oliver,et al.  Satisfaction: A Behavioral Perspective On The Consumer , 1996 .

[66]  Seiji Iwakura,et al.  Multinomial probit with structured covariance for route choice behavior , 1997 .

[67]  William H. K. Lam,et al.  Modelling road users’ behavioural change over time in stochastic road networks with guidance information , 2014 .

[68]  Bojian Zhou,et al.  Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics , 2017 .

[69]  Toshihiko Miyagi.  On the Formulation of a Stochastic User Equilibrium Model Consistent with the Random Utility Theory – A Conjugate Dual Approach , 1986 .

[70]  Xiaolei Guo,et al.  A link-based day-to-day traffic assignment model , 2010 .

[71]  Hai Yang,et al.  Physics of day-to-day network flow dynamics , 2016 .

[72]  Martin L. Hazelton.  Day-to-day variation in Markovian traffic assignment models , 2002 .

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

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

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