Observability quantification of public transportation systems with heterogeneous data sources: An information-space projection approach based on discretized space-time network flow models

Abstract Focusing on how to quantify system observability in terms of different interested states, this paper proposes a modeling framework to systemically account for the multi-source sensor information in public transportation systems. By developing a system of linear equations and inequalities, an information space is generated based on the available data from heterogeneous sensor sources. Then, a number of projection functions are introduced to match the relation between the unique information space and different system states of interest, such as, the passenger flow/density on the platform or in the vehicle at specific time intervals, the path flow of each origin-destination pair, the earning collected from the tickets to different operation companies etc., in urban rail transit systems as our study object. Their corresponding observability represented by state estimate uncertainties is further quantified by calculating its maximum feasible state range in proposed space-time network flow models. All of proposed models are solved as linear programming models by Dantzig–Wolfe decomposition, and a k-shortest-path-based approximation approach is also proposed to solve our models in large-scale networks. Finally, numerical experiments are conducted to demonstrate our proposed methodology and algorithms.

[1]  Steven M. LaValle,et al.  Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces , 2012, Found. Trends Robotics.

[2]  Nigel H. M. Wilson,et al.  Analyzing Multimodal Public Transport Journeys in London with Smart Card Fare Payment Data , 2009 .

[3]  Haris N. Koutsopoulos,et al.  A probabilistic Passenger-to-Train Assignment Model based on automated data , 2017 .

[4]  Xuesong Zhou,et al.  Dynamic programming-based multi-vehicle longitudinal trajectory optimization with simplified car following models , 2017 .

[5]  Yasuo Asakura,et al.  Behavioural data mining of transit smart card data: A data fusion approach , 2014 .

[6]  Nicholas Jing Yuan,et al.  Reconstructing Individual Mobility from Smart Card Transactions: A Space Alignment Approach , 2013, 2013 IEEE 13th International Conference on Data Mining.

[7]  Jiangtao Liu,et al.  Capacitated transit service network design with boundedly rational agents , 2016 .

[8]  Xuesong Zhou,et al.  Solving simultaneous route guidance and traffic signal optimization problem using space-phase-time hypernetwork , 2015 .

[9]  Alexandre M. Bayen,et al.  Lax–Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton–Jacobi Equation. Part I: Theory , 2010, IEEE Transactions on Automatic Control.

[10]  Lester Randolph Ford,et al.  A Suggested Computation for Maximal Multi-Commodity Network Flows , 2004, Manag. Sci..

[11]  Liu Jianfeng,et al.  Boarding Stop Inference Based on Transit IC Card Data , 2015 .

[12]  Chung-Cheng Lu,et al.  Dynamic origin-destination demand flow estimation under congested traffic conditions , 2013 .

[13]  Takamasa Iryo,et al.  Estimation method for railway passengers’ train choice behavior with smart card transaction data , 2010 .

[14]  M. Fukushima.  A modified Frank-Wolfe algorithm for solving the traffic assignment problem , 1984 .

[15]  Gerald L. Thompson,et al.  A Dynamic Space-Time Network Flow Model for City Traffic Congestion , 1987, Transp. Sci..

[16]  Hani S. Mahmassani,et al.  Dynamic origin-destination trip demand estimation for subarea analysis , 2006 .

[17]  Michael Bierlaire,et al.  The total demand scale: a new measure of quality for static and dynamic origin–destination trip tables , 2002 .

[18]  Enrique F. Castillo,et al.  Observability in linear systems of equations and inequalities: Applications , 2007, Comput. Oper. Res..

[19]  Alexandre M. Bayen,et al.  Guaranteed bounds on highway travel times using probe and fixed data , 2009 .

[20]  Pan Shang,et al.  Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach , 2019, Transportation Research Part B: Methodological.

[21]  Marcela Munizaga,et al.  Estimation of a disaggregate multimodal public transport Origin-Destination matrix from passive smartcard data from Santiago, Chile , 2012 .

[22]  Catherine Morency,et al.  Smart card data use in public transit: A literature review , 2011 .

[23]  Xin Wu,et al.  Hierarchical travel demand estimation using multiple data sources: A forward and backward propagation algorithmic framework on a layered computational graph , 2018, Transportation Research Part C: Emerging Technologies.

[24]  Elise Miller-Hooks,et al.  Large-Scale Vehicle Sharing Systems: Analysis of Vélib' , 2013 .

[25]  Hai Yang,et al.  An analysis of the reliability of an origin-destination trip matrix estimated from traffic counts , 1991 .

[26]  Martin Trépanier,et al.  Individual Trip Destination Estimation in a Transit Smart Card Automated Fare Collection System , 2007, J. Intell. Transp. Syst..

[27]  Jinhua Zhao,et al.  Estimating a Rail Passenger Trip Origin‐Destination Matrix Using Automatic Data Collection Systems , 2007, Comput. Aided Civ. Infrastructure Eng..

[28]  Che-Fu Hsueh,et al.  A model and an algorithm for the dynamic user-optimal route choice problem , 1998 .

[29]  W. Y. Szeto,et al.  A State-of-the-Art Review of the Sensor Location, Flow Observability, Estimation, and Prediction Problems in Traffic Networks , 2015, J. Sensors.

[30]  Chung-Cheng Lu,et al.  Eco-system optimal time-dependent flow assignment in a congested network , 2016 .

[31]  Torbjörn Larsson,et al.  Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem , 1992, Transp. Sci..

[32]  J. Desrosiers,et al.  A Primer in Column Generation , 2005 .

[33]  Giuseppe Confessore,et al.  A Network Based Model for Traffic Sensor Location with Implications on O/D Matrix Estimates , 2001, Transp. Sci..

[34]  George F. List,et al.  An Information-Theoretic Sensor Location Model for Traffic Origin-Destination Demand Estimation Applications , 2010, Transp. Sci..

[35]  Zhenliang Ma,et al.  Activity detection and transfer identification for public transit fare card data , 2015 .

[36]  Harvey J. Miller,et al.  Transportation network design for maximizing space–time accessibility , 2015 .

[37]  Alexandre M. Bayen,et al.  Convex Formulations of Data Assimilation Problems for a Class of Hamilton-Jacobi Equations , 2011, SIAM J. Control. Optim..

[38]  Licia Capra,et al.  Urban Computing: Concepts, Methodologies, and Applications , 2014, TIST.

[39]  William H. K. Lam,et al.  An activity-based time-dependent traffic assignment model , 2001 .

[40]  Carlos F. Daganzo,et al.  Urban Gridlock: Macroscopic Modeling and Mitigation Approaches , 2007 .

[41]  Monica Gentili,et al.  Locating sensors on traffic networks: Models, challenges and research opportunities , 2012 .

[42]  Torbjörn Larsson,et al.  A column generation procedure for the side constrained traffic equilibrium problem , 2004 .

[43]  Yanshuo Sun,et al.  Rail Transit Travel Time Reliability and Estimation of Passenger Route Choice Behavior , 2012 .

[44]  Hani S. Mahmassani,et al.  Multiple user classes real-time traffic assignment for online operations: A rolling horizon solution framework , 1995 .

[45]  Omar Drissi-Kaïtouni,et al.  A Dynamic Traffic Assignment Model and a Solution Algorithm , 1992, Transp. Sci..

[46]  Enrique F. Castillo,et al.  The Observability Problem in Traffic Network Models , 2008, Comput. Aided Civ. Infrastructure Eng..

[47]  Pan Shang,et al.  Equity-oriented skip-stopping schedule optimization in an oversaturated urban rail transit network , 2018 .

[48]  Chung-Cheng Lu,et al.  Robust Multi-period Fleet Allocation Models for Bike-Sharing Systems , 2016 .

[49]  Hai Yang,et al.  Departure time, route choice and congestion toll in a queuing network with elastic demand , 1998 .

[50]  John Zimmerman,et al.  Swarthmore College , 2012 .

[51]  Ning Zhu,et al.  Data-driven distributionally robust optimization approach for reliable travel-time-information-gain-oriented traffic sensor location model , 2018, Transportation Research Part B: Methodological.

[52]  Chris Smith,et al.  Avoiding the crowds: understanding Tube station congestion patterns from trip data , 2012, UrbComp '12.

[53]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[54]  Xiaolei Ma,et al.  Mining smart card data for transit riders’ travel patterns , 2013 .

[55]  Xuesong Zhou,et al.  Network-oriented household activity pattern problem for system optimization , 2017 .

[56]  Hani S. Mahmassani,et al.  A structural state space model for real-time traffic origin–destination demand estimation and prediction in a day-to-day learning framework , 2007 .

[57]  Christian G. Claudel,et al.  Networked Traffic State Estimation Involving Mixed Fixed-mobile Sensor Data Using Hamilton-Jacobi equations , 2016, 1606.03332.

[58]  Haris N. Koutsopoulos,et al.  Inferring left behind passengers in congested metro systems from automated data , 2017 .

[59]  Feng Chen,et al.  Transit smart card data mining for passenger origin information extraction , 2012, Journal of Zhejiang University SCIENCE C.

[60]  Xuesong Zhou,et al.  Robust single-track train dispatching model under a dynamic and stochastic environment: a scenario-based rolling horizon solution approach , 2011 .

[61]  Xuesong Zhou,et al.  Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach , 2013 .