Calibration of large-scale transport planning models: a structured approach

Abstract

Traditionally, transport planning model systems are estimated and calibrated in an unstructured way, which does not allow for interactions among included parameters to be considered. Furthermore, the computational burden of model systems plays a key role in choosing a calibration approach, and usually forces modellers to calibrate demand-side and network models separately. Also, trial-and-error methods and expert opinion are currently the backbones of transport model calibration, which leaves room for error in the calibrated parameters. This paper addresses these challenges and suggests a structured approach for determining optimal calibrated transport model parameters. This approach involves joint estimation and calibration of demand and network models, with a major focus on avoiding any manipulation of the OD matrix. The approach can be applied to static or dynamic traffic assignments. The approach is applied by calibrating GTAModel—an example of a large-scale agent-based model system from Toronto, Canada.

Appendices

Appendix 1

See Tables 3 and 4.

Table 3 Selected parameters, their deviation limits, and the solution in the first iteration of the algorithm

Table 4 Selected parameters, their deviation limits, and the solution in the second iteration of the algorithm

Appendix 2

To fit any functional relationship between a set of dependent and independent variables, we need a set of observed values for the variables. In the context of this paper, the calibration parameters and calibration criteria (as the responses of interest) are independent and dependent variables, respectively. Each of the experiments in CCD analysis provides an observed set of values for the parameters and performance criteria (as in Table 1). Although the values for the parameters are determined by central composite designs, the response values for each of the experiments should be calculated. Different formulations can be used for calculating the response values; we use mean Euclidean distance (MED) indicator to calculate the responses of interest for all the criteria. In other words, MED indicators are functions to quantify the performance criteria. In our case study, there are 18 criteria (see Table 2); therefore, 18 MED indicators should be calculated for each of the experimental runs. We use MED indicator using the 1-norm distance measure, as per Eq. (7).

$$MED_{ij} = \frac{{\mathop \sum \nolimits_{k} \left| {\Delta v_{ijk} } \right|}}{{n_{j} }}\quad \forall i \in I\;and\; \forall j \in J$$

(7)

where $i$ is the experiment number, $j$ is the response measure, $k$ is the observed statistic number, $n_{j}$ is the total number of records for response measure $j$, and $\Delta v$ represents the difference between the observed and simulated values. To illustrate this further, consider an observed screenline dataset with 500 records. In this example, reproducing screenline counts is one of the response measures. Each of the records is an observed statistic, and the total number of records in the dataset is 500.

Since the MED values are often of different units and scales (depending on the scales of $n$ and $\Delta v$), it could significantly affect the output of Eq. (2). Therefore, the performance indicators of the experiments should be scaled before importing them into the optimisation formula. As a result, the performance indicators are replaced with the normalised indicators as in Eq. (8).

$$NMED_{ij} = \frac{{MED_{ij} - \mu_{j} }}{{\sigma_{j} }}\quad \forall i \in I\;and\;\forall j \in J$$

(8)

where $\mu_{j}$ and $\sigma_{j}$ are the mean and standard deviation of the performance indicators (MED) for response $j$ over all the experiments. The smaller NMED means a lower difference between the simulated and observed statistics and, therefore, better performance.