How Does a Traffic Signal Become a Traffic Signal?

After a recent presentation to the North Carolina Model Users Group about node delays in travel forecasting networks, I was asked how one knows where traffic signals should be on future-year networks.

This is a complicated question, and my answer was sketchy and not particularly satisfying. I alluded to two papers I wrote on the subject, one with Sam Granato and the other with Minnie Patel, but then I said the modeler needed to iterate. That’s not anywhere near the whole story.

Citations to these two papers are at the bottom of this blog.

The “signal design problem” is closely related to the “network design problem” (NDP) that has attracted the attention of many network theorists over the decades. As far as I know the NDP has never gotten a solution algorithm that could be useful for anything urban transportation planners might consider interesting. However, the signal design problem must be solved reasonably well if we are to have explicit traffic controls in our long-range planning networks.

Signals most often are located at the intersection of two arterial streets. So we need to first ask how does an arterial become an arterial? There are two ways: some street czar decides that a particular road should be an arterial; or a road attracts so much traffic that its arterial status is earned on the road’s merits. This can take time. For the most part, we usually have a pretty good idea of where the arterials might be in the future.

We can assume that all arterial intersections have some form of traffic control, at the very least, stop signs. There are at least two ways to determine whether an arterial intersection needs a signal. I will call the two most obvious ways the “minnie” and the “sam”, as they correspond to my respective coauthors and are easy to remember. The “minnie” tries to locate signals such that a performance measure on the network, such as vehicle-hours-travel, is minimized. The “sam” places signals everywhere they are warranted according to the Manual on Uniform Traffic Control Devices, so long as the traffic situation, overall, is improved. Let it be said at the outset that the “minnie” places far fewer signals than the “sam”, and at the same time the “minnie” achieves considerably lower VHT.

Both methods have a dynamic element. That is, they step through time at multiyear intervals and apply their rules at each interval. Once a signal has been created, it is never destroyed. These assumptions were absolutely necessary to assure convergence of the “minnie”, but they originated in the “sam” as reasonable approximations of the traffic engineering process.

So the “minnie” wins, right? Actually, no. First the “minnie” is extremely computational, even with those simplifications, and likely won’t scale to the largest travel forecasting networks, but that’s not its worst drawback.

The big problem with the “minnie” is that it is an unrealistic representation of how the world of traffic engineering actually behaves. Traffic engineers seldom consider global objectives when placing signals, even if they should.

Here is the “sam” (signal allocation method, maybe?) in detail, as originally implemented. The algorithm is organized into three loops, but I have compressed them here into just an inner loop and an outer loop. The outer loop has two steps.

  1. Divide the forecast horizon period into intervals (such as, 5 years)
  2. Increment though all these intervals, allocating signals at each interval according to the inner loop.

Here is the inner loop.

  1.  Set an initial MUTCD warrant violation threshold (such as, 2.0 times Warrant #3’s numerical values).
  2. Find all intersections beyond this threshold.
  3. Install signals at these intersections
  4. Run a traffic forecast to determine if total network travel time has decreased. If yes, then proceed to step 5, otherwise stop.
  5. Reduce the warrant violation threshold (such as, from 2.0 times Warrant #3 to 1.8 times Warrant #3). If the violation threshold is 1.0 or greater then go to step 1, otherwise stop.

Warrant #3 is the peak hour warrant, which is reasonably consistent with outputs from a peak hour forecast. Since the “sam” reflects the judgement of just a couple guys with some traffic engineering experience, there’s likely a need to vary the rules for many locales. So season to taste.  I have quoted the relevant parts of Warrant #3 at the end of this article.

Keep in mind that installing a signal might require certain logical changes to the network, such as the installation of left-turn lanes.

Alan Horowitz, Chapel Hill, May 13, 2016 (extended, May 16, 2016).


Alan J. Horowitz and Minnie Patel, “The Signal Network Design Problem for Long Range Travel Forecasting”, Journal of Transportation Engineering, Vol. 131, No. 3, March 2005, pp. 183-192.

Alan J. Horowitz and Sam Granato, “Selection of a Traffic Control Strategy for Long-Range Travel Forecasting”, Transportation Research Record Journal, #1706, 2000, pp. 145-151.

Warrant #3 (part).  A signal is warranted if all three of the following conditions exist for the same 1 hour (any four consecutive 15-minute periods) of an average day:
1. The total stopped time delay experienced by the traffic on one minor-street approach (one direction only) controlled by a STOP sign equals or exceeds: 4 vehicle-hours for a one-lane approach or 5 vehicle-hours for a two-lane approach; and
2. The volume on the same minor-street approach (one direction only) equals or exceeds 100 vehicles per hour for one moving lane of traffic or 150 vehicles per hour for two moving lanes; and
3. The total entering volume serviced during the hour equals or exceeds 650 vehicles per hour for intersections with three approaches or 800 vehicles per hour for intersections with four or more approaches.