21st International Symposium on Transportation and Traffic TheoryEstimation of mean and covariance of stochastic multi-class OD demands from classified traffic counts

This paper proposes a new model to estimate the mean and covariance of stochastic multi-class (multiple vehicle classes) origin–destination (OD) demands from hourly classified traffic counts throughout the whole year. It is usually assumed in the conventional OD demand estimation models that the OD demand by vehicle class is deterministic. Little attention is given on the estimation of the statistical properties of stochastic OD demands as well as their covariance between different vehicle classes. Also, the interactions between different vehicle classes in OD demand are ignored such as the change of modes between private car and taxi during a particular hourly period over the year. To fill these two gaps, the mean and covariance matrix of stochastic multi-class OD demands for the same hourly period over the year are simultaneously estimated by a modified lasso (least absolute shrinkage and selection operator) method. The estimated covariance matrix of stochastic multi-class OD demands can be used to capture the statistical dependency of traffic demands between different vehicle classes. In this paper, the proposed model is formulated as a non-linear constrained optimization problem. An exterior penalty algorithm is adapted to solve the proposed model. Numerical examples are presented to illustrate the applications of the proposed model together with some insightful findings on the importance of covariance of OD demand between difference vehicle classes.

[1]  David Watling,et al.  MAXIMUM LIKELIHOOD ESTIMATION OF AN ORIGIN-DESTINATION MATRIX FROM A PARTIAL REGISTRATION PLATE SURVEY , 1994 .

[2]  Charles Audet,et al.  Analysis of Generalized Pattern Searches , 2000, SIAM J. Optim..

[3]  Enrique Castillo,et al.  Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations , 2008 .

[4]  Will Recker,et al.  Travel Time Reliability with Risk-Sensitive Travelers , 2001 .

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

[6]  Shing Chung Josh Wong,et al.  Advances in equilibrium models for analyzing transportation network reliability , 2014 .

[7]  Kara M. Kockelman,et al.  The propagation of uncertainty through travel demand models: An exploratory analysis , 2000 .

[8]  Bi Yu Chen,et al.  A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty , 2014 .

[9]  Agachai Sumalee,et al.  Journey time estimator for assessment of road network performance under demand uncertainty , 2013 .

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

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

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

[13]  F. Viti,et al.  Dynamic origin–destination estimation in congested networks: theoretical findings and implications in practice , 2013 .

[14]  Bernhard Friedrich,et al.  A combined method to forecast and estimate traffic demand in urban networks , 2013 .

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

[16]  Shing Chung Josh Wong,et al.  Estimation of multiclass origin-destination matrices from traffic counts , 2005 .

[17]  Enrique F. Castillo,et al.  Traffic Estimation and Optimal Counting Location Without Path Enumeration Using Bayesian Networks , 2008, Comput. Aided Civ. Infrastructure Eng..

[18]  Agachai Sumalee,et al.  Stochastic Multi-Modal Transport Network under Demand Uncertainties and Adverse Weather Condition , 2011 .

[19]  Bin Yu,et al.  Bus arrival time prediction at bus stop with multiple routes , 2011 .

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

[21]  Peter Bühlmann.  Regression shrinkage and selection via the Lasso: a retrospective (Robert Tibshirani): Comments on the presentation , 2011 .

[22]  Agachai Sumalee,et al.  Stochastic cell transmission model for traffic network with demand and supply uncertainties , 2013 .

[23]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[24]  R. Tibshirani,et al.  Regression shrinkage and selection via the lasso: a retrospective , 2011 .

[25]  Hai Yang,et al.  Efficiency of a highway use reservation system for morning commute , 2015 .

[26]  Yafeng Yin,et al.  Sensor location problems in path-differentiated congestion pricing , 2015 .

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

[28]  Shiliang Sun,et al.  A bayesian network approach to traffic flow forecasting , 2006, IEEE Transactions on Intelligent Transportation Systems.

[29]  Moshe E. Ben-Akiva,et al.  Estimation and Prediction of Time-Dependent Origin-Destination Flows with a Stochastic Mapping to Path Flows and Link Flows , 2002, Transp. Sci..

[30]  Haijun Huang,et al.  A combined trip distribution and assignment model for multiple user classes , 1992 .

[31]  S. Travis Waller,et al.  Evaluation with Traffic Assignment Under Demand Uncertainty , 2001 .

[32]  Yafeng Yin,et al.  Expirable parking reservations for managing morning commute with parking space constraints , 2014 .

[33]  Moshe E. Ben-Akiva,et al.  Alternative Approaches for Real-Time Estimation and Prediction of Time-Dependent Origin-Destination Flows , 2000, Transp. Sci..

[34]  William H. K. Lam,et al.  USING AUTOMATIC VEHICLE IDENIFICATION DATA FOR TRAVEL TIME ESTIMATION IN HONG KONG , 2008 .

[35]  Baibing Li.  Markov models for Bayesian analysis about transit route origin-destination matrices , 2009 .

[36]  Shou-Ren Hu,et al.  A generalized sensor location model for the estimation of network origin–destination matrices , 2014 .

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

[38]  Hai-Jun Huang,et al.  Calibration of the combined trip distribution and assignment model for multiple user classes , 1992 .

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

[40]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[41]  Domenico Sassanelli,et al.  A Fixed Point Approach to Origin-Destination Matrices Estimation Using Uncertain Data and Fuzzy Programming on Congested Networks , 2013 .

[42]  E. Cascetta.  Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator , 1984 .

[43]  H. Spiess.  A MAXIMUM LIKELIHOOD MODEL FOR ESTIMATING ORIGIN-DESTINATION MATRICES , 1987 .

[44]  Henk J van Zuylen,et al.  The most likely trip matrix estimated from traffic counts , 1980 .

[45]  Kelvin K W Yau,et al.  Multiple-vehicle traffic accidents in Hong Kong. , 2006, Accident; analysis and prevention.

[46]  M. Bell.  THE ESTIMATION OF ORIGIN-DESTINATION MATRICES BY CONSTRAINED GENERALISED LEAST SQUARES , 1991 .

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