A recent post to the TMIP Forum by Suzanne Childress and subsequent replies gave me pause. The question was innocent enough: what VDF (volume-delay function) should be used with a 100% autonomous vehicle traffic stream. Two people answered that this was the wrong question to ask, but I don’t think this question is going away any time soon.
Of course, a 100% autonomous vehicle fleet is science fiction. We have been talking seriously about such a scenario for over 40 years, and we are approaching realization of this scenario at a snail’s pace. The implementation problems are as much institutional as they are technical, maybe more so.
In late 1974, as a freshly minted PhD, I arrived at General Motors Research Laboratories to find, among other things, my new colleagues killing off an unpopular research project on autonomous vehicles. Somebody, and I don’t know who, had publicly stated that it was possible to build computer-controlled freeways that could achieve speeds of up to 150 mph while also achieving flow rates of up to 10,000 passengers cars per hour per lane. GM felt the need to investigate. The staff used the best car-following theories available (GM was a leader in car-following research at the time) and found that these numbers had been ridiculously inflated. GM’s staff required near absolute safety. Even though they could assume drivers were perfect, they could not assume that either the vehicle or the electronics were perfect. Thus, reasonably safe headways between cars were imposed. They picked operating parameters that could be defended in court, hypothetically.
VDFs apply to uninterrupted traffic flow, only, as was pointed out in one response to the question. Intersection delay is much more important in urban settings. Autonomous vehicles would likely require newer intersection delay relationships, too. Reliability is another consideration.
For many years, I gave a homework assignment in my Transportation Engineering class asking students to estimate the very high-speed capacity of a freeway lane by using a vehicle following equation found in our textbook and by adopting conventionally accepted safety standards. (If you are interested in retracing the logic, the textbook is by Papacostas and Prevedouros, our infamous friend Panos.) The capacities were shockingly low.
A much simpler question, I sometimes used as an extra credit problem on exams, is to estimate the service flow at a given speed when everyone adheres to the “rule of the road”. There are actually two of these rules depending upon how old you are. When I took driver’s training I was told to leave one car length of space ahead of me for every 10 mph of speed. My children learned to leave 2 seconds of gap, regardless of speed. (The National Safety Council recommends 3 seconds.) In any case, it is possible to derive a VDF from only this information and the length of a car.
So for example, a 2 second gap at 60 mph for a 15-foot long car gives a spacing of 2*88 + 15 = 191 feet. This is a density of 27.6 cars per mile, and using the fundamental equation of traffic flow, 60*27.6 = 1659 pcphpl (passenger cars per hour per lane) flow rate. Not an unexpected number. This is, perhaps, one point on our human-driver VDF.
I have not seen a treatise on the legal issues surrounding autonomous vehicles. Everything is speculative since there is no case law. Automobile manufactures successfully avoid a lot of liability by claiming their vehicles are safe when operated and maintained properly. A crash is almost always the fault of a person, not a machine. But with an autonomous vehicle, a crash is caused exclusively by the machine. To avoid crashes, the system needs to be fail safe under all environmental conditions. A decent set of safety parameters in a vehicle following equation might come from an assumption of the lead vehicle coming to a stonewall stop and the following vehicle braking moderately aggressively after a reasonable reaction/perception time. So if we were to choose a reaction time of say 1 second and a coefficient of friction during the skid of 0.3 (wet flat road), the required spacing is 1*88 + 88*88/(2*32.2*0.3) + 15 = 460 feet. This corresponds to a density of just 11.5 cars per lane mile and a flow rate of a paltry 689 passenger cars per hour per lane.
100% means 100%. There can be absolutely no human-controlled vehicles. As pointed out to me by my friend Ed Beimborn, these 460-foot spacings (31 car lengths) would be very attractive to a human driver who could easily weave through them to go much faster than the design speed and those poor occupants who are faithfully allowing their cars to drive themselves. The temptation to defeat the computer controls would be overwhelming.
These analyses suggest to me that autonomous vehicles could never outperform a bunch of native Californians in traffic flow efficiency, given our litigious society.
As always, I am interested in hearing your comments.
Alan Horowitz, Whitefish Bay, April 21, 2018
I think the best hope for the “travel forecasting industry” to understand the impacts that autonomous vehicles have on causing changes to person travel (changes to person travel patterns, as well as the time and costs to travel) will be through the power of observing what is (or is not) actually changing over time. Perhaps speculation as to what might or might not happen 30-plus years from now can be best handled through some sort of “exploratory scenario planning” process that recognizes the huge range of uncertainties that may exist, but yet does not even rely on the actual prediction of person travel tables.
In other words, if you’re in a vehicle that consistently “plays by the rules,” you’ll be taken advantage of not only by emboldened pedestrians but also the same old “road warriors.” Even commuters who travel the semi-saturated routes of the mid-size cities should be able to understand that, let alone those in LA or NY.