The Knee Jerk Reaction of an Anti-Fluids Bigot

The following entry is in response to a debate I have been having in a closed blogosphere at work. It is based on a comment I posted to this article.

http://www.popsci.com/cars/article/2010-09/giving-traffic-lights-mind-their-own-can-reduce-congestion-study-says

I will not replicate the blog comments here…you can pick up the gist of the commentary from my narrative below.

First just to be clear I entered into this debate with Bryan on my own free will although he started the argument by baiting me with his tactics. I tend to be an arrogant troll myself on occasion so I am not at all intimidated by his discussion tactics. The evidence of his particular bullying is his use of the term “knee-jerk reaction” which he directed at me for my very quick, and somewhat negative, response to the article posted above by Sphinx. In that comment I stated that modeling the traffic in a city is not like a fluid so they are doing it wrong (Bryan is clearly in “ Stage 3” as given by King and Logan in the book “Tribal Leadership”) It’s not clear that he was rising in defense of Sphinx and that somehow by posting a negative comment to her blog I was attacking her personally (which is certainly not the case) or he is defending the integrity of the authors of the study upon which the article was based (which was most definitely the case) and in both cases, his and mine, we are not in full possession of the facts within the actual study (the actual study can be found here [1]). Nevertheless the debate ensued and I can either stand down or continue to fire back. Obviously I have chosen to fire back.

As an additional note, I also made in my original comment the statement, “If they were saying they model the traffic as a fluid as an analogy” …for laymen to get the picture…that’s Ok. But if they are using fluid dynamics in their actual calculations, as I stated above, they are using a flawed technique.

I followed up my original comment with slightly more detail on my meaning which included the necessity of scaling various traffic modeling problems from intersections with single car/driver interactions through free flowing highways. I said that in the second case fluid dynamics might find some application but they have no place in the former. Although to be even clearer, classic fluid dynamics may seem like they apply in the second case, and are in fact the source of many studies over the past 50 years, in the main they are no longer used by the industry. Occasionally you will see a fluid dynamics PhD student write a paper on some new application of fluid dynamics to traffic flow. However the problem as defined in the original statement, the requirement is to take a systems wide view of a network of urban intersection in order to synchronize the signal lights…but synchronization is the system response…the idea is for each light to work autonomously while considering the bigger picture. This will not work if modeling traffic as a fluid (the algorithm to drive the timing of the lights needs traffic input and output, it will work as a surrogate for traffic but my argument is that it is not a good surrogate and most likely means the algorithm to drive the timing of the lights is also suspect) That of course is my opinion but if you check the core disciplines aligned under fluid dynamics you will not find traffic…because why? It is not a fluid.

Traffic flow on a road is nothing like fluid flow, either compressible or non-compressible fluid flow in a pipe. As you approach free flowing traffic on a highway with smooth curving bends and flow that is uninterrupted it is easy to believe that fluid equations might apply and simplify down to a basic case. This has been the silly mistake of many individuals who have tried. Yes with a lot of trouble you can show flow with the equations, but then you have modeled a system that is not grounded in reality and most certainly does not represent real traffic. One might read [2] to see how all the math might predict the motion of cars modeled as a compressible fluid in a closed circuit for instance, as a soliton (wave) …but it’s not reality and it’s far too complex to be practical.

Starting from first principles all of fluid dynamics arises from the Ideal Gas Law which states:

pV = nRT

Pressure x Volume = Molecular Mass x Gas Constant x Temperature

Pressure doesn’t apply to traffic. Volume doesn’t apply to traffic. Molecular Mass doesn’t apply. The Gas Constant doesn’t apply. Temperature doesn’t apply.

This is where Bryan tries to convert cars to molecules, traffic speed to temperature, and traffic density to pressure x volume. Go for it. Obviously I can’t deny that folks have done just that…just as folks have tried to drive a nail with a set of pliers as well. I contend there are better and much more accurate methods.

But that’s just the start with fluids…How about viscosity? How about friction? How about the length of the pipe and the inlet/outlet pressures? The list goes on. You can find all the equations for pipe flow “Q” here in this reference below [3].  But here is a look at it.

Now if you throw out everything but traffic density and speed you are reduced to this equation:

Q = D x V

And who would argue that traffic volume/flow in not a function of the number of cars on the highway and their speed…which is traffic but it doesn’t behave like a fluid in any way other than it moves from point A to point B, sometimes. Sometimes it turns, sometimes it crashes. But one “fluid like” equation, is far too simplistic to model or predict the behavior of cars on a road, highway, or at an intersection. A great deal of work has gone into describing traffic mathematically in its many forms. All of that work is better than fluids but none of it better than discrete event simulation which is the standard for the industry and what has been used in thousands of transportation and traffic studies worldwide. A survey of the tools available is given here [4].

But it doesn’t end there. As we use discrete event simulation tools to model the interactions of the individual cars in a network in order to effectively model what is happening more and more autonomy has to be given to the individual elements. Not only do the cars have to behave independently, speed, direction, etc., they have to think for themselves interact with what happening around them. They have to receive feedback as well (try that with a fluid). A better way to do it is by treating the traffic network as a complex adaptive system with the use of agent based modeling to simulate the traffic in the network. Here is a traffic application and references [5]. That is the full sum of what I was trying to say with my comment.

Before I started my simulation company in 1994, I first described agent based modeling in discrete event simulation for traffic flow research I was conducting for Dr. E.B White at George Mason University during my masters program. I have an obvious bias against fluids which I studied in several courses during my undergraduate work in Mechanical Engineering at Texas A&M University. My traffic research was entitled the Strategic Transportation Operational Planning Simulator (STOPS) [6]. Alas the computing power for complex adaptive simulations and agent based modeling was not sufficient in 1992. It is now. But now the field is abounding with these techniques. Couple these techniques with the power of cloud computing and the power of netted information coming from an urban traffic grid and the solution to decentralization of traffic control systems is upon us. Again, all I was saying in my original comment was that fluids are bad and complex adaptive systems are good.

As I have now read the original study it is obvious that the cars are indeed treated as discrete events and were modeled using a simulation called PTV Vissim [7]. My original thought that the use of the word “Fluid” was simply an analogy is true. However it would be interesting to treat this system with a complex adaptive simulation as I have suggested. If my reaction was “knee-jerk” I apologize to those I offended. I am an “Anti-Fluid Bigot” when it comes to traffic modeling.

For those of you who do not like to start with first principles and do the thinking for yourselves, a criticism of using fluids to model traffic, that is not my own, they can be found under Daganzo’s Requiem [8]. Coincidently I observed in several studies that Helbing [9], a coauthor of the subject study, has been a vocal critic of Daganzo’s criticism of fluid dynamics for traffic modeling. This is truly odd since Bryan and I have inadvertently entered into a microcosm of this same debate. Since Helbing choose a direction other than fluid modeling in his most recent work can we assume he is now on-board? Since the word “Fluid” does not appear a single time in the recent report, I have to wonder why it was used at all in the subject article.  To venture a guess would be to suggest the use of the word fluid is an echo from a once lively debate between Daganzo and Helbing.

In the end I must now thank Bryan for forcing me to expand upon my comment so everyone has a better understanding upon which I based my “knee-jerk” reaction.

References:

[1] Lammer & Helbing, Self-Stabilizing Decentralized Signal Control of Realistic Saturated Network Traffic, 2010

[2] Saavedra & Velasco, Solitons in a macroscopic traffic model, 2010

[3] Schroder, A Tutorial of Pipe Flow Equations, 2001

[4] Jones, et al. Traffic Simulation Software Comparison Study

[5] Khalesian & Delavar, A Multi-agent Based Traffic Network Micro-simulation using Spatio-temporal GIS.

[6] Muccio, Strategic Transportation Operational Planning Simulator, 1992

[7] http://www.ptvag.com/software/transportation-planning-traffic-engineering/software-system-solutions/vissim/technical-details/

[8] Daganzo, Requiem for second-order fluid approximations of traffic flow, 1995

[9] Helbing & Johansson, On the controversy around Daganzo’s Requiem for and Aw-Rascle’s resurrection of second-order traffic flow models, 2008