I don't want to move tim off the first post this quick, but...
I've often wondered (and often quite publicly, on this blog, and to friends) why the M5 goes so slow. I've had a variety of explanations, most claiming that merging at the tunnel is the problem. I've often rejected these theories, for reasons I'll outline below. Then Michael mentioned "traffic waves", which I also rejected, since the title itself is an inkling to the content, and I didn't think that they caused the problem. Eventually, though, curiosity got the better of me, and I ended up visiting this site
. This article is about why I don't believe it.
Firstly, I'd like to say I've got nothing against William Beaty, the guy who wrote it. I kind of take the piss a bit, but it's all in good fun. The first step to figuring out something new is to write down everything you know, and he's done that. It's just that some of the things he wrote don't apply everywhere, and more specifically, don't apply in the M5 (imho). Secondly, please read the site, as I'm not about to repeat everything he says here. There'll be a small summaries to get to my points, though.
William starts by explaining what traffic waves are, and how they work. This is mostly fine, but he seems to make some assumptions that lead to strange conclusions. Most of these stem from the lack of mathematics present. I would
use mathematics, but I'm also an engineer, and at least as lazy as Bill. I will, however, explain where he's misguided.
The first part deals with the energy of the wave. Under "Not caused by accidents", Bill states that traffic waves can be caused by anything, even minor things. However, this implies that as they propagate, they gain energy. First, even intuitively, this is patently absurd. Why you'd brake harder and accelerate faster than the person in front of you doesn't really make sense. A little more mathematically, the energy of a wave (really a pulse) is defined by it's amplitude and frequency. However, these are cars, and the waves are compression waves. The amplitude is the difference between the two cars that are closest and the two cars that are furthest away. The frequency is the acceleration of the cars. This means that for the amplitude to increase, a car won't accelerate as fast as the car in front of it when leaving (thereby increasing the peak distance), or won't decelerate as fast when joining (thereby decreasing the minimum). For the frequency to increase, a car must decelerate faster when joining, and accelerate faster when leaving. Kaching! Note how the energy is constant. You can't increase it, you can't decrease it.
Energy, by the way, is pretty much the analog of the value that tells you how fast you'll get to work. I'm not exactly contending that traffic waves can't get worse (they can, and do, but there are sensible limits, and this generally doesn't occur). What I'm saying is this won't get you to work any later, because every time you slow down before the wave, you also speed up after the wave.
What Bill's doing by slowing down is increasing the amplitude of the wave and decreasing the frequency. He's acting as a smoothing capacitor (slower speed / lower voltage, but smoother falloff / less deceleration / acceleration). However, the energy is the same, so you're not getting anywhere any faster. In any case, I don't think Bill would contend this. Smoothing a wave in and of itself will not fix anything. However, there are supposed benefits to doing this which will increase the flow of traffic.
The second experiment deals with the "standing wave" scenario. Let's get this straight from the beginning: That's not a standing wave. A standing wave occurs when there are waves going in both
directions, unless Bill's Electrical Engineering degree states otherwise (seriously, Bill, WTF?). Even according to his own initial analysis, a wave can only go backwards. However, to be fair, I don't think he meant "standing wave" in technical terms, and the diagram shows a situation which could "possibly happen". I contend this, and say that it can't happen. At least, not forever. With sensible drivers, the wave must
move back. In order for it to stay constant, you must accelerate sinusoidally, which is very difficult to do perfectly. The wave definitely cannot go forward, unless someone is deliberately driving slowly (like Bill in his experimentation).
Incidently, I was going to suggest a generalised sinusoidal acceleration strategy to "fix" his smoothing capacitor idea, but it looks like I would've been wrong. (acceleration is a function of the distance between you and the car in front of you. I think that's exponential, but I didn't really think about it that much).
Another problem with Bill's model is stiffness. We all know that the stiffer the medium, the faster the wave (that's why sound travels faster underwater). We can see this in a big truck vs 3 cars. The front of the truck accelerates at the same speed as the back of the truck, whereas the 3 cars all accelerate at different speeds (each slower than the last). Therefore, the wave actually travels back faster through a truck (take a look one day). The implication is, if we accelerated and decelerated faster (increased the frequency), and with quicker responses, we'd push the wave back quicker, and hence get rid of it faster, than if we accelerate / decelerate slowly. Note that Bill's way of increasing the amplitude does exactly the opposite.
Note, however, that Bill's also trying to get a more comfortable drive, get longer life out of his engine and brakes, better fuel economy, etc. Also, in a network that's not jam-packed, this method actually works, since there's plenty of empty spaces to fill up.
The final problem is that his model only works on freeways / motorways. Traffic lights are wave generators, and they have a very low frequency. Bill's "drive slowly" method is royally fucked with traffic lights. Any high frequency stuff is completely overriden by the immensely powerful traffic waves that traffic lights generate.
Now let's get to some Australia specific issues, and some ideas. The M5 has a lot of trucks. A lot
. A truck, if you think about it, is a lot like Bill. It accelerates and decelerates slowly, and generally keeps a constant speed. That's why you'll notice that the M5 isn't very start stop (it is, but not very). That's because the trucks absorb most of this. Trucks are also large and have the stiffness property mentioned above. Bill's model doesn't consider them at all.
Also, I don't know about America, but in Australia, we change lanes. This is also to do with the trucks. We contend with them every day, so we go around them. We also go around slow drivers. Anyone keeps a large spot in front of them, someone will fill up that slot. There are unwritten rules about queue-jumping, so we're not arseholes about it (generally), but if there's a ridiculous empty space, it's un-Australian to not
take that space. In addition, there are often faster and slower lanes, and people will often switch to the faster lane. This'll happen all the time, and it's a bit like a shuffle of space. You can't expect keep a cache of space in front of your car.
Notice how he mentions the "evaporation" after the wave? The bit where you're supposed to go fast? Where does that
happen on the M5?
One other thing he mentioned was merging. First, stare at the animation for a while. Notice how the arsehole drivers in the middle lane suddenly become nice when the absolute end of the left lane comes? Strange how they pick that exact time... Anyway, we know that wouldn't happen realistically. Either there'd be starvation of the merging lane or more cars would enter earlier. The other thing is, notice how the cars disappear just as they start going fast?
Have you ever slowed down while merging, then immediately started going faster? I haven't. Then again, I haven't merged into the harbour tunnel at peak hour before. However, I've changed lanes quite often beforehand, and this is what I've noticed: People are generally nice. This is my "Aussies aren't arseholes" postulation. Anyway, after a bit of thinking, I figured that either trucks are merging, which is something they shouldn't do (but would anyway, because trucks are
arseholes), or that there's a problem further up.
I'm still convinced that the problem is a network related one. ie: that the system can't handle this many people, and the rate at which the city can take cars is far lower than the rate at which the M5 can provide cars to the city. This leaves it backed up the whole way out. tim and Trevardy might know for sure, but I'm still in doubt that it's a merging issue.