Analytical Error Propagation in Four-Step Transportation Demand Models

Rezaeestakhruie, Hojjat (2017). Analytical Error Propagation in Four-Step Transportation Demand Models PhD Thesis, School of Civil Engineering, The University of Queensland. doi:10.14264/uql.2017.415

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Author Rezaeestakhruie, Hojjat
Thesis Title Analytical Error Propagation in Four-Step Transportation Demand Models
School, Centre or Institute School of Civil Engineering
Institution The University of Queensland
DOI 10.14264/uql.2017.415
Publication date 2017-03-16
Thesis type PhD Thesis
Supervisor Mahmoud Mesbah
Mark Hickman
Total pages 118
Total colour pages 13
Total black and white pages 105
Language eng
Subjects 0905 Civil Engineering
090507 Transport Engineering
Formatted abstract
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

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.
Keyword Error Propagation
Model Specification Error
Input Measurement Error
Four-Step Transportation Demand Model
Sensitivity Analysis
Monte Carlo Simulation

Document type: Thesis
Collections: UQ Theses (RHD) - Official
UQ Theses (RHD) - Open Access
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Created: Tue, 07 Mar 2017, 11:01:29 EST by Hojjat Rezaeestakhruie on behalf of University of Queensland Graduate School