The Influence of the Impedance Function on Uncertainty Propagation Through a Four-step Model
O Petrik, F Moura, J de Abreu e Silva, Instituto Superior Técnico, PT
This work analyzes the impact of impedance function inputs and specifications on the output uncertainty of a four-step model and identifies the relevant major error contributors.
Transport demand models imply a wide range of uncertainties originated from the variability of natural processes, imperfection of knowledge about the phenomenon to be modeled and exogenous factors influencing it. The greater the uncertainty on the demand estimates is the higher will be the requirements on the needs of robustness and flexible design for the final project.
The variety of different types and sources of uncertainty helps its propagation through the travel modeling steps, and contributes to the overall output uncertainty. There is often a possibility for a decision-maker to reduce the input and calibration uncertainty by gaining additional information (e.g. conducting a survey, collecting expert judgments, etc.). However, every piece of supplementary data has its cost and so the decision-maker should thoroughly scope for which information any improvement efforts need to be concentrated. Two major rules on this choice were suggested in the literature: (1) focusing on the variables with a larger uncertainty, and (2) focusing on the variables influencing the dependent variables most. The former means that the variables with larger error first should be identified and the latter advocates model parsimony.
This work analyzes the impact of impedance function inputs and specifications on the uncertainty of a four-step model and identifies the relevant major error contributors. For that, we consider different specifications of the impedance function (including its choice and parameters distribution) and uncertainty of its attribute (which are the generalized costs). To illustrate our analyses, we use as case study data from the city of Aveiro which is a medium sized city in Portugal with a multimodal transportation system available.
First the paper presents the inventory of all possible sources of uncertainty involved in each stage of the classical four step modeling process and identification of the ones uncovered or very meagerly addressed in previous studies. Also we provide a review of the literature on uncertainty propagation in transport modeling. Based on this review we trace the development of the uncertainty propagation studies with evolution of models, methods and increasing coverage of uncertainties of different sources highlighting the issues which still need to be addressed.
We analyze uncertainty propagation through the steps of four-step travel model omitting the classical generation step, which is conditioned by the given data, namely the mobility survey, from which the information on trip generation can be obtained directly. Based on the inventory of different sources of uncertainty provided in the first part, we categorize the uncertainties originated from the use of the generalized cost formula and impedance function on three last stages of the model. We consider different approaches to the impedance function specification, in order to compare the resulting output uncertainties and find a trade-off between simpler models and models with greater number of parameters providing better fit to the sample but, possibly, with larger output error on the aggregated level.
One way to quantify and to correct for the model specification error is to use a resampling method, e.g. bootstrapping, which allows estimation of the distribution of the model parameters.
It is suggested in the literature that such simulation techniques ?can provide useful insights into the stability of model parameters to data errors?. By using bootstrapping we construct different OD-matrices based on the subsamples from the original survey and calibrate the respective impedance functions obtaining the range of its parameters.
As a result of the input and specification variations related to the impedance function we obtain the output variations for link flows depending on their type (highways, motorways or urban streets) and on one of two levels of congestion (namely, congested or free flow). We also analyze the type of relationships (linear or non-linear) between the input uncertainty related to the impedance function and the result error. The sensitivity analysis of model outputs to varying inputs and parameters is also implemented in order to define the major contributors to the final uncertainty.
The uncertainty is expressed in form of variance of the forecast provided by the model and its variance, its 95% confidence interval and percentiles of its distribution (the lowest 5% for the links flow predictions).
All the simulations are performed using MATLAB which provides flexibility and transparency of the modeling and uncertainty evaluation processes.
Association for European Transport