Model Calibration

The Origin-Destination (OD) matrix calibration is performed by a suite of Python and MATLAB programs integrating with DynusT to perform the DynusT embedded linearized quadratic optimization with the objective function to minimize the absolute deviation between the simulated and actual link counts. The user can specify the tolerable maximum deviation with respect to the total trips or individual zone-pair trips per iteration. At each OD calibration iteration, DynusT is called to run DTA based on the existing OD matrices. With the simulated link counts for the user-selected screen lines, the OD calibration program calls for the optimization solver to solve the linearized quadratic minimization program, resulting in new OD matrices. The iterations continue until the total deviation (e.g. the objective function value) is less than a user-defined threshold or the maximum number of iterations is reached.

In order to operate this Calibration Tool, installation of MATLAB (7.0 or later), Python (2.5 or later), and Mozek Optimization Tools (4 or later) is required. The calibration routines iteratively utilize these softwares throughout the process; therefore, these are all necessary to use this particular tool. Once these softwares are online, an Excel spreadsheet (provided with the tool) is used to prepare input information and user-specified parameters for the MATLAB code to read. The spreadsheet, as seen in the image below, provides the necessary information such as:

• number of calibration iterations,
• the adjustment allowance factors, Alpha and Beta, for auto demand,
• and the adjustment allowance factors for truck and HOV demand, if being calibrated simultaneously.
• PLEASE NOTE, the other listed parameters are not currently used, and will be later removed.

The adjustment allowance factors Alpha and Beta are user-specified and give the upper and lower bound constraints in an OD pair's deviation from on calibration iteration to the next in the linearized quadratic optimization problem. The Alpha is the bounding constraint for individual OD pairs. This allows the range of alteration in an OD pair from iteration to iteration. The smaller the factor, the tighter the allowance for an OD pair to reach the optimal. The Beta is the bounding constraint for all affected OD pairs. So for all OD pairs that will be altered, the total amount of change for all those OD pairs is bounded as well. The choosing of the Alpha and Beta parameters should be balanced with the number of calibration iterations. In other words, giving large Alpha and Beta parameters will allow large swings in OD volume which may push toward a faster convergence, therefore less iterations; however, this may also shift OD volumes further away from a calibrated OD table and a less comparable simulated network.

The next figure below shows the spreadsheet tab in which the SL count information is placed. The first column gives the SL ID in which the user can specify the ID's of each SL. Next, the From and To Nodes of the Sl links are listed, followed by the SL traffic count.

The MATLAB routines are the main procedures that perform the whole calibration process. When running, the main routine will ask for the spreadsheet and the dataset folder in which the demand data being calibrated should be in. Next, the automated process will continue to run through the specified iterations until completed. The status of the procedure will be updated in the MATLAB command window. Please keep in mind that this procedure is a timely process. Within each calibration iteration,

The figure below shows the scattergram for simulated and actual counts over iterations for a 157-TAZ network with 90 screen lines. One can see that the simulated link counts are well inline with the actual link counts (e.g. on the 45-degree line) at the 16th OD calibration iteration. The band along the 45-degree line indicates the +- 10% error. The majority of the screen lines are well within the 10% absolute error range. All the high-volume screen lines are within the 10% deviation band.

The diagram blow shows that the total number of trips increase in the first 10 OD iterations, but becomes stabilized afterward.

The diagram below is the histogram of the errors of all screen lines at the 16th iteration. The results show that 98% of the screen lines are within 10% error. 55% are within 5% error.

The mesoscopic traffic simulation in DynusT is based on the Anisotropic Mesoscopic Simulation (AMS) model, which moves vehicles according to the speed-density (v-k) relationship. The typical v-k relationship used in DynusT is the Greensheild's type equation, i.e. .

The v-k relationship can be calibrated using typical tube counter data in which the average speed and counts are reported per user-defined interval.

First, the counts can be converted to flow rates. If the reported speed is the space-mean-speed (total distance divided by total time that the speed trap is occupied), then the density can be calculated by taking k = q/v. If the average is the time-mean-speed (e.g. the average speed is the arithmetic mean of the individual speed measures) then 3%-5% reduction from the time-mean-speed can be used to approximate the space-mean-speed.

The data points can be prepared in MS Excel and plotted as shown below. The calibration can be performed by either using MS Excel or other curve fitting tools such as Matlab or Mathematica.