A Modest Reinterpretation of “Traffic Assignment and Feedback Research to Support Improved Travel Forecasting”

It is not so much that the recent report for FTA “Traffic Assignment and Feedback” is wrong. (I will call it the TAF report from here on.)  The TAF report is just not sufficiently prescriptive. It is absolutely clear from the TAF report that traffic assignments, as practiced by many large MPOs, are ill; but the TAF report’s recommendations are akin to taking two aspirin, drinking fluids, and getting lots of bed rest, when chemotherapy is needed.

Nothing I am going to say is academic. My whole message can be reduced to four words:

Do It Like Parkersburg.

Parkersburg is the best validated travel model ever, as far as I can ascertain. Not only do volumes validate well, but speeds validate well. And, critically important, the Parkersburg model has the correct sensitivity between speeds and volumes, which I doubt that any of those five tested MPO models can claim.

Let me dispose of some smaller issues first.

The TAF report describes misuse of “relative gap”, then makes no recommendations regarding it. Relative gap is a terrible indicator of assignment convergence. Few people understand it, and it has little relationship to our primary means of validating models. Let’s consign relative gap to technical papers in the academic literature, where it can have considerable value. (I wrote a previous blog on this subject.)

The TAF report complains that MPO models are not converged enough. Most of the models investigated seem to use a double-loop feedback scheme. The double-loop feedback scheme is really clunky. It works, but it moves along very slowly. The TAF report praises MSA (method of successive averages), but then fails to recommend it. Let me state this a plainly as I can. MPOs need to replace their double-loops with MSA.           (There is an odd disconnect in the TAF report regarding the use by some MPOs of Frank-Wolfe (FW) decomposition along with MSA, which has me perplexed, since MSA should be supplanting FW.)

TAZ size and topological accuracy, potentially important topics, were largely ignored by the TAF report.

Now let’s move on to some heavier issues.

Where the TAF report is seriously overly tolerant is in the area of volume-delay functions (VDFs). VDF’s have their place in travel models, but they are really bad at estimating delay when there is conflicting or opposing traffic. If your model doesn’t have any conflicting or opposing traffic, then you don’t need to read any further. Otherwise, please pay attention. (I am being sarcastic, every travel model has opposing and conflicting traffic.)

Many traffic assignment algorithms, particularly those derived from Martin Beckmann’s theory such as Frank-Wolfe decomposition, require VDFs following strict mathematical requirements. (These requirements are given in the TAF report, so I won’t bore you with them again.) Beckmann formulated the traffic assignment problem as an optimization, but we now know that Beckmann’s formulation is flat-out incorrect for urban situations. Urban traffic assignment is much more correctly dealt with as a variational inequality. The difference between these two theories from a practical viewpoint is huge.

To properly incorporate conflicting and opposing traffic, you need node delays that come from accurate applications of traffic flow theory, such as the operations analysis procedures of the Highway Capacity Manual for signals and stop signs. Such node delays cause two problems for any algorithm derived from Beckmann’s theory. First, the better node delay equations don’t behave according to those nice mathematical properties that Beckmann required. Second, optimization algorithms cannot handle better node delays; for these you need an algorithm consistent with variational inequality theory. Incidentally, MSA is consistent with variational inequality theory.

Beckmann’s theory fails for two-lane roads; however, the capacity of a two-lane road segment in an urban area is likely controlled by the intersection as either end.  But then again…

The TAF report laments that speeds (or travel times) from MPO models aren’t good. The report states that two of the tested models have node delays, but these “node delays” are not described anywhere in the TAF report and may still be derived from a VDF-like equation, in principle*. VDFs can be tweaked to make them look OK on urban arterials right now, but the traffic theory underlying them is mostly wrong at intersections, so there is no confidence they can forecast speeds well for future cases. For good speed forecasts, high-quality node delays are essential.

Just to belabor this point a little more, Frank-Wolfe decomposition cannot handle good node delay equations. So if your traffic assignment technique has “FW” in its acronym, you will get bad speed forecasts. And if it is not entirely obvious, bad speed calculations during the assignment process lead to crummy volume forecasts. Of course, the converse is not always true.  The absence of “FW” does not necessarily get you good forecasts.

The TAF report correctly states that 24-hour assignments are obsolete. Why’s that? Directional splits of turning movement and mainline flows are mostly incorrect for peak hours when we care most about delays. Let me go one step further. Multihour traffic assignments of any length of time are deficient. The longest time period for any traffic assignment should be 1 hour, especially if there are good node delay equations. The TAF report suggests that dynamic traffic assignment is an emerging technology. While not every MPO needs it for its intrinsic advantages, DTA does have the virtue of conveniently breaking multihour forecasts into single hours (or less).

If you want technical details that underlie my assertions here, see the short bibliography below.

I will encourage the people who built the Parkersburg model to post their specifications where everyone can see them.  As always, I welcome comments and corrections.

Alan Horowitz, Whitefish Bay, September 10, 2015

See my other blog posts at ajhassoc.com.

*I was able to find online separate documentation for one of the two MPO models; the second MPO did not answer my e-mail messages.


Alan J. Horowitz, “Internodal Delay Issues in Long-Range Adaptive Travel Forecasts”, Transportation Research Record Journal #1783, 2002, pp. 49-54.

Alan J. Horowitz, “Intersection Delay in Regionwide Traffic Assignment: Implications of the 1994 Update of the Highway Capacity Manual”, Transportation Research Record 1572, 1997, pp 1-8.

Alan J. Horowitz, “Implementing Travel Forecasting with Traffic Operational Strategies”, Transportation Research Record, No. 1365, 1992, pp. 54-61.

Alan J. Horowitz, “Convergence of Certain Traffic/Land-Use Equilibrium Assignment Models”, Environment and Planning A, Vol. 23, 1991, pp. 371-383.

Alan J. Horowitz, “Convergence Properties of Some Iterative Traffic Assignment Algorithms”, Transportation Research Record, No. 1220, 1989, pp. 21-27.