How to get matrix development outputs for UK Department for Transport standards (TAG)

August 2023 — Technical note #81

Tessa Hayman

Product Specialist

Transport projects or studies that require UK government approval are expected to follow official transport analysis guidance (commonly referred to as TAG). In the newly released version 23 of Aimsun Next, it is now easier to create outputs recommended by the UK Modelling and Appraisal guidance from the Department for Transport (DfT) for monitoring changes in matrices. In this technical note, Tessa Hayman will explain the new features and how to use them.  

In TAG Unit M3.1 Highway Assignment Modelling it is recommended that the changes from matrix adjustment (matrix estimation) should be monitored using: 

  • Scatter graphs comparing OD pair values before and after adjustment. 
  • Scatter graphs comparing origin destination totals (zonal trip ends) before and after adjustment. 
  • Comparisons of trip length distribution changes 
  • Comparisons of sector-to-sector level matrices before and after adjustment 

Matrix adjustment shouldn’t make significant changes to the structure of matrices as these can cause significant changes in route choice or restrict the changes in route choices that may occur due to a scheme. It is therefore recommended that any adjustment is well supervised and the criteria for the significance of changes brought about by matrix estimation is given by TAG in the following table: 

Measure 

Significance criteria 

Matrix zonal cell values  

Slope within 0.98 and 1.02 

Intercept near zero 

R2 >0.95 

Matrix zonal trip ends 

Slope within 0.99 and 1.01 

Intercept near zero  

R2 > 0.98 

Trip length distributions 

Means within 5% 

Standard deviations within 5% 

Sector to sector level matrices 

Differences within 5% 

 

Where the changes are greater than the significance criteria, then these should be explored by the modeller to understand if these will influence the purpose of the model. If they are deemed to be significant then the development of the prior matrix should be reassessed, the real data set checked. Any exceedances that are not deemed to be important should be explained and documented in the validation report for the model.  

Matrix adjustment shouldn’t be allowed to make significant changes to the prior matrices, if calibration and validation targets are not able to be met without these changes then a lower level of validation should be reported. 

To enable the modeller to monitor this more easily within Aimsun Next, several new features have been added. The first was added in v22, but should be highlighted, is the option to have a reference matrix that is different from your input matrix.  

Within the static OD departure adjustment experiment and dynamic OD adjustment experiment windows, there is a dropdown that allows you to select the reference matrix for the adjustment. This is used to calculate the elasticities and constrain the matrix. This should be used when you are adjusting the matrix with multiple steps e.g., static OD adjustment then static OD departure adjustment and finally dynamic OD adjustment. It means that the adjustment will try to stay as close to the prior matrix used as input for step 1, rather than moving further and further away from the prior matrix at each step.  

 

 

Then to monitor the adjustment, there are additional outputs in the outputs tab of all the adjustments within Aimsun Next.  

 

Matrix cell values 

To see the changes in matrix cell values, select Cell-by-Cell and the user class that you would like to analyse, then select the scatter graph option. This creates a scatter graph comparing the original and adjusted demands and gives the line of best fit, R2 as well as additional information such as the RMSE. 

 

 

It can be seen here that the slope of the line of best fit is 1.306 which is above the significance value (0.99-1.01). The user should check that the correct prior matrix was used and why the adjustment is increasing the traffic so much. A change to the slope that is this high, suggests there is a mismatch in what is being compared e.g., time of day, user class, year and that the real data set, centroid configuration and prior matrix methodology should be evaluated. 

 

Trip ends

To see the changes in matrix trip ends, select Trip Ends and the user class that you would like to analyse, then select the scatter graph option. This creates a scatter graph comparing the original and adjusted demands, aggregated by the origin and destination total. It gives the line of best fit, R2 as well as additional information such as the RMSE of these totals.

 

 

It can be seen here that the slope of the line of best fit is 1.306 which is above the significance value (0.99-1.01). The user should check that the correct prior matrix was used and why the adjustment is increasing the traffic so much. A change to the slope that is this high, suggests there is a mismatch in what is being compared e.g., time of day, user class, year and that the real data set, centroid configuration and prior matrix methodology should be evaluated.

 

Trip length distribution 

Note: This is only currently available in the Static OD adjustment as this is the adjustment most likely to change the trip length distribution.  

To see the changes made to the trip length distribution, go to the trip length distribution tab and select the user class you would like to analyse. A graph is histogram is shown showing the original and adjusted matrix distributions. It should be noted that the bars for the original demand in the histogram are displaced along the x axis by 0.5km so that both histograms can be easily seen. The data can be exported to show externally using the copy distribution data button.  

The mean and standard deviation of both the adjusted and original trip length distributions are displayed below the chart to allow the modeler to easily check the significance of the changes to the trip length distribution after the adjustment. 

 

 

The changes to the trip length distribution mean and standard deviation (1.12% and -4.45%) are under the significance levels given by TAG.  

 

Sector to sector 

To see the changes at a sector-to-sector level, select cell by cell, the user class that you would like to analyse and the grouping category which defines your sectors; then select the list option. This shows the percentage difference between the sector-to-sector totals. 

 

 

Many of the sector-to-sector pairs have changes above the significance level given by TAG (5%). As this measure looks at the structural change to the matrix, the modeler must look at the prior matrix and real data set to understand why there is such a difference between that and what is needed to meet the calibration and validation counts. 

All these outputs can be retrieved from an adjustment when the results are saved into an .adj file by right clicking the replication and clicking retrieve adjustment results. 

 

Trip distribution without running the model 

It is also now possible to compare the trip distribution of two matrices without running the model by using the shortest path calculator. This can be used to evaluate the trip length distribution for instance after a departure adjustment or dynamic OD adjustment. It does not take into account multiple routing options that may be used in assignment, but it can be a good method to check the trip distribution of a matrix for a large-scale model without having to wait to run the model.  

1. Go to data analysis > shortest path calculator 

 
2. Select the skim matrix option
 
3. Select the correct centroid configuration, set cost to distance; you can also set a vehicle type if needed. Click calculate. This creates a skim matrix in that centroid configuration with the shortest path (by distance) between each OD pair.  
 
4. Go to the skim matrix object
 
 
5. Go to the histogram tab and change the weighted by Matrix to the trip matrix for the vehicle type or a total trip matrix for all vehicle types if you wish to evaluate it for all vehicle types.
 
 
 
6. You can change the bin size and definition by changing the number of intervals or clicking calculate ranges ad selecting a method e.g., 10 quantiles
 
 

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Aimsun Next 23

Aimsun (2023). Aimsun Next 23 User’s Manual, Aimsun Next Version 23.0.0, Barcelona, Spanien. Zugriff am: July. 19, 2023. [Online].
Verfügbar: https://docs.aimsun.com/next/23.0.0/


Aimsun Next 20.0.5

Aimsun (2021). Aimsun Next 20.0.5 User’s Manual, Aimsun Next Version 20.0.3, Barcelona, Spanien. Accessed on: May. 1, 2021. [In software].
Available: qthelp://aimsun.com.aimsun.20.0/doc/UsersManual/Intro.html

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