Norman Marshall’s article, “Forecasting the impossible: The status quo of estimating traffic flows with static traffic assignment and the future of dynamic traffic assignment,” slams conventional modeling practices. Marshall states that MPOs routinely test alternatives that create unrealistically large flows on freeways and the consequential delays are so erroneous as to invalidate any impact analysis that uses them. The culprit is static traffic assignment (STA), and the fix is dynamic traffic assignment (DTA).
I have been a strong advocate of DTA in planning studies of all types. I do recognize that DTA is highly computational and that some larger MPOs might be better off putting their resources elsewhere. In Ohio, several small MPOs have used area-wide DTA for their modeling for years by now, with excellent results. NCHRP 765 notes examples of this and incorporates DTA into the “travel forecasting model ideal” for project-level work.
I am quite familiar with alternatives that assign traffic well beyond a volume-to-capacity ratios (v/c) of 1, and I cannot fathom why anybody would take any of this seriously, either as a realistic representation of the future or as a strawman case study. When a lot of facilities are badly over-assigned, then the model is broken somewhere. The failure may not be in the traffic assignment step but may be in the land-use allocation step or elsewhere. Ideally, any alternative should have all important facilities operating somewhere close to their design capacity. If this were the case, STA would suffice for most planning.
The problem largely stems from inaccurate estimates of delay from queuing in STA. I have always believed that the funny shape of the BPR curve is intended to account for moderate amounts of queuing, albeit rather roughly. If 6000 cars try to squeeze through a facility with a capacity of 4000 vehicles per hour, they will all eventually do it. These vehicles will encounter a long queue that will finally dissipate when volumes drop below capacity. The BPR curve is not misguided, it is just a poor guess of queuing delay for many situations. I will illustrate my point with a numerical example.
Consider a freeway with a lane drop causing a bottleneck, going from 3 lanes to 2 lanes. The link upstream of the lane drop is very long. There are four links, each 1-mile long downstream of the lane drop. The capacity of each lane is 2000 vph and the free speed is 60 mph. The upstream volume is 6000 vph during the peak hour. Call this Case 1. What is the downstream delay with STA or DTA? I will adopt a BPR curve with “standard” freeway coefficients as republished in NCHRP Report 365. The free-speed multiplier (“alpha”) is 0.83 and the v/c exponent (“beta”) is 5.5. (See Note 1)
STA Case 1. Each of the 4 downstream links will have a v/c ratio of 1.5. A strict application of the BPR curve, as required by STA, gives a single-link travel time of about 8.7 minutes and a 4-link time of 34.9 minutes.
DTA Case 1. DTA calculates delay differently. Each of the 4 links will have a v/c = 1 (approximately) and there will be an average queuing delay of exactly 15 minutes. (see Note 2). A downstream link travel time is 1.83 minutes, so the four-link travel time is 7.3 minutes, and the total travel time is 22.3 minutes.
STA overestimates delay.
Now consider almost the same situation, but there is a work zone of 1 mile in length, thereby closing 1 lane of a 3-lane freeway for just this one link. Call this Case 2. Otherwise, Case 2 is the same as Case 1.
STA Case 2. One of the downstream links will have a v/c of 1.5 and the other 3 links will have a v/c of 1.0. The total delay is 8.7 + 3*1.83 = 14.9 minutes.
DTA Case 2. One link will have a v/c = 1 (see Note 3) and the three downstream-most links will have a v/c = 0.67. Those further downstream links will have a travel time of 1.09 minutes, so the total average travel time is 3*1.09 + 1.83 + 15 = 20.1 minutes.
STA now underestimates delay.
So, you can see that STA and the BPR curve together create wildly inconsistent travel time estimates for over-capacity situations.
STA will also tolerate over-capacity volume estimates when the queuing penalty is not sufficiently large, even though there is plenty of capacity on parallel routes.
All these problems go away when there is ample capacity in the system to handle all traffic.
Here are Alan’s guidelines for the use of STA in long range transportation planning.
- Choose DTA over STA whenever possible.
- If you must use STA, do not publish any alternative/scenarios with facilities loaded beyond a v/c ratio of 1.1.
- If an alternative/scenario is forecasting over-capacity conditions, look for the problem in other modeling steps and fix it.
- If you cannot fix it within the model, then modify or discard the alternative/scenario.
- If you are close to getting a believable model, but you still have multiple facilities that are well over capacity, consider using arbitrary penalties, as a last resort, to force traffic onto parallel facilities.
Some of these guidelines apply to DTA, as well.
Alan Horowitz, Whitefish Bay, March 28, 2019
Note 1. These parameters were estimated by matching the speed/volume curve for freeways in the 1985 HCM from v=0 to v=capacity. I used them in WisDOT’s RADIUS model, and they worked quite well. BTW, the RADIUS model was DTA.
Note 2. I am assuming that the v/c ratio is well below 1 for the hours before and after our peak hour. There will be no queue at the beginning of the hour and it will grow uniformly until 2000 vehicles are queued. The maximum wait will be 30 minutes (2000/4000 hours), so the average wait will be 15 minutes.
Note 3. This is a slight over-simplification. The capacity of the bottleneck itself is usually lower than the capacity of the downstream link. The v/c for the link past the bottleneck should be a little smaller than 1.0, but not enough to invalidate these examples.