Analytical Error Propagation in Four-Step Transportation Demand Models

Transportation demand models currently lack a rigorous and analytic treatment to quantify the error propagation from different sources through the models. The error of traffic forecasts is attributed to two main sources: the model specification error and the input variable measurement error. Since Four-Step Transportation Demand Model (FSTDM) is commonly used in practice but its error is not well-studied, the first part of the current study illustrates how the errors of the input variables as well as of the model specification are propagated analytically step by step and how these errors interact to result in inaccurate traffic forecasts. The proposed approach is able to quantify separately and collectively the share of different sources of error in the traffic forecast error. The proposed procedure is an efficient method that is less time consuming than existing simulation-based methods. This enables the proposed procedure to analyse the sensitivity of the traffic forecast to the input measurement error and the quality of modelling in large scale networks. Moreover, comparing the output errors using the proposed approach with the acceptable ranges of error specified in transportation guidelines, decision makers will have a clear opportunity to realise the credibility of a point traffic forecast and its associated variance. The proposed approach derives the variance from calibrated models in each of the four steps, to obtain the variance of the output based on the variance of inputs. The resulting variance formula provides an analytical expression to estimate the forecast errors from the input errors. In addition, the model specification error of each step of the FSTDM is added to the propagated input measurement errors. The proposed approach is applied to the city of Brisbane as a case study spanning the four-step models for eight different trip purposes. As an example, a measurement error of 10 percent for the input variables of the Brisbane FSTDM (BFSTDM) as well as the specification errors of models calibrated for the Home Based Work Blue collar (HBWB) trip purpose were explored. The model specification error produces variances of 1760.77 (trip/h)2, 976.72 (trip/h)2, 0.01082 (trip/h)2 and 0.001327 respectively for trip production, trip attraction, trip distribution and modal split steps. Subsequently, the variance of output errors for the same steps are respectively, on average, 2885.50 (trip/h)2, 7218.70 (trip/h)2, 0.25 (trip/h)2 and 0.18. The variance of output error in the traffic assignment step is calculated to be 2097.20 (veh/h)2 for all trip purposes, while the model specification error of the same step is 1056 (veh/h)2. Having the existing 868 traffic zones, from the first to the third step, a reduction in the variance of trips per origin-destination (O-D) pair is observed. At the same time, in the traffic assignment step, considering all trip purposes, the size of the forecast error variance per link increases. In the second part of the present study, the specification error of a user equilibrium traffic assignment (UETA) is measured using validation techniques. Moreover, the propagation of O-D demand measurement errors to the UETA output is investigated using two different methods: the proposed analytical sensitivity-based method and a simulation-based method. The analytical method uses the results of a sensitivity analysis (SA) on the UETA mathematical program, while the simulation-based method runs a Monte Carlo Simulation (MCS). The proposed method for error propagation is applied to an illustrative example to address three main questions: the number of samples that ensure a reasonably accurate result for the MCS method; the size of the O-D demand measurement error for which the analytical method is valid; and, the share of the path flow rate variance and covariance from the variance of the O-D demand measurement error. Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis. Publications during candidature Conference papers 1. Hojjat Rezaee, Mahmoud Mesbah, Mark Hickman (2016). “Error Propagation in User Equilibrium Traffic Assignment: Comparing an Analytical Sensitivity-based Method with a Simulation-based Method”. Paper presented at the 95th Annual Meeting of the Transportation Research Board, Washington D.C. Publications included in this thesis No publications are included. Contributions by others to the thesis No contributions by others. Statement of parts of the thesis submitted to qualify for the award of another degree None. Acknowledgements Firstly, I would like to express my sincere gratitude to my principle advisor, Dr. Mahmoud Mesbah, and my associate advisor, Prof. Mark Hickman, for the continuous support of my PhD study and related research, for his patience, motivation, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis report. Besides my advisor, I would like to thank my thesis review panel: Prof. David Lockington, and Prof. Carlo Prato, for their insightful comments and encouragement, but also for the hard questions which helped me to widen my research from various perspectives. Last but not the least, I would like to thank my family: my lovely wife, Zeinab, and to my dear parents and sister for supporting me spiritually throughout my studying and writing this thesis report.