A Case for Balancing Traffic Counts with OD Table Estimation

Balancing of traffic counts is an attempt to eliminate errors due to lack of conservation of vehicles through intersections and interchanges.   My friends at the WisDOT swear by it. Most other traffic and travel modelers have never heard of it. One of my co-authors on NCHRP Report 765, Tom Creasey, was charged with writing up balancing, and he could find almost no literature on the subject. Apparently, balanced counts are desirable for obtaining good results from traffic simulation and operational models.

OD table estimation has a side effect of balancing all traffic on the network. When faced with a comparatively messy set of traffic counts for the RADIUS project, I brashly asserted that the assigned volumes at the end of an OD table estimation were better approximations of the actual traffic levels than the counts themselves. Fortunately, there was no way that anybody could refute that statement. However, I thought it would a good idea to set up a simple experiment to check this assertion.

So here is an outline of what I did to validate the concept of balancing. First, I chose a network from Fredericton NB that I had used before for research. Second, I ran a normal base-case forecast through an enormous number of equilibrium iterations to obtain “true” traffic levels on the network. Third, I dirtied the “true” volumes by adding random noise (normally distributed) according to Figure 4-14 from NCHRP Report 765.  Since we never have counts on all links, I chose a 33% random sample of all dirtied link volumes to feed into an OD table estimation. Fourth, I ran an OD table estimation using those chosen link volumes, fitting the counts only to roughly the amount of dirt that I added.

The estimation technique was whole-table least squares. The trip table weight was set to 10 and each “count” was equally weighted as 1. These settings gave me an RMS difference between “count” and volumes of 720 vpd on an average “count” of 5263 vpd or about 13.7%, which is reasonable.

So the question boils down to whether OD table re-estimated volumes are worse than the dirtied volumes which served as our counts for this experiment. A worse comparison would be a negative consideration in the decision to use this technique for balancing.

The RMS differences between “true” volumes and each of my “counts” are shown below, as generated by QRS II. Table 1 is the dirtied counts v. the “true” volumes. The size of the errors pretty much match Figure 4-14, which is not a coincidence, since those differences were created by me and my random number generator.

Table 1. Difference between “True” Volumes and Dirtied Volumes

Table 2 is the re-estimated volumes (on the previously counted links) v. the “true volumes”.

Table 2. Difference between “True” Volumes and Re-estimated Volumes on Links with Counts

It would have been possible to have forced these RMS differences to almost zero by setting the trip table weight in the estimation to a large number (e.g., 10000), but such a setting would have defeated the point of the experiment.

Table 2 shows that the error in the re-estimated “counts” are about the same or slightly better than in the dirtied volumes, except perhaps for the lowest volume roads.

So I would guess, as a result of this one small experiment, that OD table estimation can be used to achieve balanced counts with little loss is accuracy, provided the seed OD table is very good.

Alan Horowitz, Whitefish Bay, August 3, 2015