# Traffic Volume Balancing

## Introduction

This document discusses a procedure for balancing traffic volume data along an access-controlled facility such as a freeway. If directional data is available, balancing can also be applied to arterials or other non-access-controlled facilities, provided that traffic generators such as side streets and major driveways are treated in a manner similar to "ramps" in the discussion that follows.

Field-collected traffic volumes for the Wisconsin freeway system almost always contain mathematical inconsistencies. For example, if we start with the observed volume at an Automatic Traffic Recorder (ATR) station and proceed in the direction of travel, adding the on-ramp volumes and subtracting the off-ramp volumes, the running total almost never matches the observed volume at the next ATR.

These inconsistencies arise primarily from the fact that currently it is not possible to count the entire network simultaneously. Instead, data must be assembled from multiple dates and sources. The sources include continuous freeway mainline counts from ATRs, supplemental 48-hour mainline counts collected using portable radar units, 48-hour ramp counts collected using portable pneumatic tube counters, and perhaps intersection turning movement counts. Because this data is collected at different times and with different technologies, it must be adjusted or "balanced" to obtain a mathematically consistent data set.

## Benefits of Balancing

When implemented judiciously, the balancing process helps "clean" the traffic volume data. It tempers the effects of outliers (such as counts collected on non-representative days) and counting errors (such as counts affected by equipment problems). To a limited degree it also allows imputation of missing volumes, for example using last year's data as a preliminary estimate of the volume at a site where a detector has recently failed.

Balancing the data also results in faster convergence of OD matrix estimation. This is because when matrix estimation is applied to unbalanced count data, the software can oscillate between different solutions as it attempts to match conflicting numerical targets.

## The Balancing Process

Manually balancing a large freeway network is an extremely labor-intensive and frustrating task, with no unique mathematical solution. Freeway-to-freeway interchanges pose a particular challenge for manual balancing, since each ramp affects three or more computations. An automated mathematical balancing solution was developed to overcome these issues. The main steps in this process are as follows:

1. Importing the raw traffic data from TRADAS, VSPOC, and other sources such as intersection turning movement counts.
2. Computing the imbalance in the imported data set by means of running totals. Generally speaking, trusted ATR sites are used as reference points for this computation.
3. Adjusting the counts using mathematical optimization, subject to the constraint that the imbalance must be zero. The objective function for the optimization is to minimize the difference between the adjusted and unadjusted volume sets, as measured by the GEH formula. More specifically the GH formula is applied to hourly data (such as the AM peak hour) and the GD formula is applied to daily data.

## Setting Up A Volume Balancer

Volume balancing can be implemented using purpose-built software or in a spreadsheet. In either case an optimization algorithm needs to be available. If the corridor consists only of service interchanges and ordinary freeway segments, each travel direction can be balanced separately. If the study area includes freeway-to-freeway interchanges, the entire study area must be balanced simultaneously. Special care must be taken when coding freeway-to-freeway movements to assure that the adjusted volumes are consistent for all routes involving that movement.

The sequence of counts along a corridor is important to the balancing process. The most straightforward process is to begin at a mainline location where the numerical value of the count is known and trusted. Next, compute running totals by proceeding in the direction of travel, adding the entrance ramp volumes and subtracting the exit ramp volumes. In this way, volumes usually can be computed for all (or nearly all) ramps and freeway segments.

In many cases this sequential procedure allows computation of volumes for segments where count data is missing. For example, most Wisconsin freeways have counts on ramps and basic freeway segments, but not on the short segments between ramps at an interchange. This commonly occurs at diamond interchanges, but the volume on the short segment between ramps can be estimated as the upstream mainline volume minus the exit ramp volume (or if necessary, as the downstream mainline volume minus the entrance ramp volume).

In some instances balancing is thwarted by incomplete data. For example, if an exit splits into two downstream ramps and only one of them has been counted, the missing ramp's volume will need to be collected in order to determine the total volume (without this data the balancing process can produce misleading results or fail entirely). Collector-distributor roads are another situation where the data set may be incomplete; such areas should be reviewed before starting to set up the balancing process.

Setting up the balancing process will generate a data matrix that includes each ramp and each freeway segment. In some cases a location will have both observed and computed volumes, while in other cases only a computed volume will be available. The balancing process involves developing adjusted volumes for each ramp and segment, keeping the adjusted volumes as close as possible to the observed volumes while zeroing out the difference between the running totals and the volume at the last station in the sequence. By "as close as possible" we mean that wherever possible we compute the GEH between the adjusted volume and the original observation, and within the optimization algorithm we keep trying different adjustments until we find the one that minimizes the sum of the GEH values along the entire corridor.

## Worked Example

Table 1 shows an example of the balancing process. In this table, station type "A" means an ATR, "B" means a basic freeway segment, "M" means a short segment between ramps at an interchange, "0" means an exit ramp, and "1" means an entrance ramp.

Suppose we begin at station 99-0001, where the observed volume was 66206 vehicles per day. Let's assume that this is a trusted ATR station known to be in good working order. We then deduct the 5440 vehicles exiting at Bravo Blvd, for a running total of 60766 on the short freeway segment inside the Bravo Blvd interchange. Next we add the Bravo Blvd entrance ramp volume of 8141, bringing the running total to 68907. But this contradicts the field count at station 99-1918, which was 75381. Something is wrong! If we continue to compute running totals, by the time we get to the end of this corridor at Delta Road the running total will be 77356, which is 861 more than the observed volume at the final ATR station.

In this case the imbalance is a positive number, so to balance the volume set it will be necessary to reduce the entrance ramp volumes and/or increase the exit ramp volumes. In addition, the mainline count between Bravo Blvd and Charlie Parkway appears to be much too high. That is a type "B" site, which means it's a short-duration count and probably not as trustworthy as the ATR data (perhaps it was taken when there was a special event that pushed up the volumes). Through the optimization process the software adjusts the ramp volumes to resolve the imbalance. The process also re-estimates the mainline volume at site 99-1918; in essence the software concludes that the field count at that site was inconsistent with the rest of the data set and adjusts it sharply downward.

 Station ID Type Location Observed Volume Adjusted Volume Change GD 99-0001 A I-999 NB between Alpha Ave and Bravo Blvd 66206 66206 0 0.0 99-3173 0 Bravo Blvd exit ramp 5440 5440 0 0.0 M Between ramps at Bravo Blvd interchange (no data) 60766 99-3174 1 Bravo Blvd entrance ramp 8141 8137 -4 0.0 99-1918 B I-999 NB between Bravo Blvd and Charlie Parkway 75381 68903 -6474 7.6 99-3178 0 Charlie Parkway eastbound exit ramp 20826 20826 0 0.0 M Between ramps at Charlie Parkway interchange (no data) 48077 99-3178 0 Charlie Parkway westbound exit ramp 12957 13018 +43 0.2 M Between ramps at Charlie Parkway interchange (no data) 35059 99-3371 1 Charlie Parkway westbound entrance ramp 16990 16237 -753 1.8 M Between ramps at Charlie Parkway interchange (no data) 51297 99-3677 1 Charlie Parkway eastbound entrance ramp 25242 25203 -45 0.1 99-0002 A I-999 NB between Charlie Parkway and Delta Road 76495 76495 0 0.0