Need a PhD Topic? How about cops in traffic | Hacker News Reader

Need a PhD Topic? How about cops in traffic

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63 pointsgothmog42 comments

As it happens, I studied traffic flow back when I was an undergrad in the context of "agent based modeling".

Agent-based models are basically computer simulations where you throw N 'agents' into an environment with pre-defined rules and then watch how they interact with each other. This setup lends itself perfectly to vehicle-flow; each agent is a car, each car has a model for when it accelerates, when it slows down, when it turns, and so forth. Create enough of them, and you can start to simulate traffic jams and other interesting traffic phenomena.

Now, I have not studied this problem in particular. My research was on the effect of excessive lane-changing on overall traffic throughput (Spoiler: lane-changing tends to cause traffic to slow down behind the lane-changer, which means that system-wide lane-changing leads to traffic jams, but changing lanes is a strictly superior strategy for individual drivers in most situations. The classic collective-action problem. Economics!)

However, it seems to me that it would be relatively simple to extend a traditional AB traffic model to include special vehicles that impose constraints on nearby cars.

If any of you are interested, there is an excellent java library developed at UChicago called Repast [http://repast.sourceforge.net/index.html] which contains a framework for building agent-based models.

You may also be interested in my favorite book on the subject, "Micromotives and Macrobehavior" [http://www.amazon.com/Micromotives-Macrobehavior-Lectures-Pu...] which is more rigorous than its Amazon description would have you believe.

I don't think you need agent models. You can probably study this directly with the nonlinear transport equation (Lighthill-Witham, I think), or one of the more detailed versions (the Rascall model?).

All you need to do is impose a police-created boundary condition at x=cop_location(t) instead of solving the pde on free space:

    velocity(density)|x=cop_location(t) = cop_velocity(t).

Would that model take into account the number of lanes and the lane position of the cop?

It's been a while since I looked, so I'd need to think carefully. But very likely, yes, you could incorporate such things.

What I'd do is in the speed control term V(1-u(x,t)), I'd probably make V vary w.r.t the distance to the cop. I.e., same lane, you'd take something like:

    [V+(V_cop-V)bump(x-cop_position)](1-u(x,t))

Whereas in different lanes, you'd take:

    [V+alpha(V_cop-V)bump(x-cop_position)](1-u(x,t))

where alpha < 1 measures the reduced effect the cop has on different lanes. (Alpha might vary from lane to lane if you have more than 2 lanes, i.e. if the cop is in lane 1, alpha_lane_5 might be much smaller than alpha_lane_1.)

Here, bump(z) is some sort of bump function - 1 near z=0, dropping off as z moves away.

I was expecting a question about how cops will manage to travel significantly faster than the "wave" by pushing it aside or maybe just using the shoulder. I wonder if that's already been studied.

>a police car introduces certain mental restrictions which prevent people from behaving how they naturally would.

Just FYI, there's a reason for the mental restriction. If you pass a cop and you're in his jurisdiction and you're going faster than the speed limit you have about a 80% chance of getting a speeding ticket.

80% is the shaky number I came up with based on witnessing 5 occurrences. I was a one driver that got pulled over. I've seen 4 other drivers attempt it and only one didn't get pulled over.

Here in Massachusetts, the staties blow by you at 100MPH (and when people don't move over, sit on their tail and probably give them a good scare when they finally realize what's behind them). I generally see them coming from pretty far back (a car closing at ~25mph is pretty noticeable), move over, let them pass, then see how long I can follow. I figure that the cop must be following the law and going a safe speed for the conditions of the road, so I can use them as a benchmark for what is considered acceptable instead of having to rely on the purely advisory signs.

Funnily enough, the slow cops and coplike vehicles that bunch up traffic are usually the ones with the least jurisdiction and least likely to give out tickets. Town cops going one exit on a state road, inmate transfer, game wardens, etc. This could of course all be fixed by having speed limits that reflected society, and GPS tracking of cops to make sure they're not immune from the law. But more likely self driving cars will make the whole situation moot - I'd gladly save fuel and make a 2hr trip in 3hrs if I didn't have to waste my attention on the vehicle.

Yeah, I'm from the Cape. Never had to pass a state cruiser. I dive a lot in CT though and their staties never drive fast without their lights going.

One time I had to call 911 for a drunk driver and the dispatcher asked me to follow the guy saying I could drive as fast as I felt safe. I was about 1/2 mile behind the guy going 95 mph when the cruiser passed me like I was standing still (with no siren or lights). I'd swear he was going 140.

"I'd gladly save fuel and make a 2hr trip in 3hrs if I didn't have to waste my attention on the vehicle."

Isn't that the bus/train?

bus/train won't get you door to door, so you get further expense (monetary or social) at both ends (coupled with more pay-attention time). plus the added coordination time due to not wanting to miss your departure. i've done the bus, and i'd estimate it's more like adding 2hr of non-attention to the existing 2hr of pay-attention.

bus/train also requires packing/bundling and simultaneous handling of cargo, where with a car, you can just throw everything in the trunk/back seat at your leisure.

I've often tested the theory myself, without breaking the speed limit. If the cop is driving just under the limit, I set my speed exactly on the limit, and overtake if I need to.

Of the ~10 times I've done this, I once got pulled over and abused by the cop for being a "freaking idiot". No ticket.

>without breaking the speed limit

Yeah, I pass cops all the time without breaking the limit and have yet to get pulled over.

Though, I did get the "freaking idiot" riot act the time I got pulled over for passing above the limit.

So actually your number, by Laplace's law of succession (http://en.wikipedia.org/wiki/Rule_of_succession), would be 71%: you saw 4 other instances and you were another instance, so that's 5 instances, and you say you and 3 others were pulled over for 4 pull overs, so in the formula 's +1 / n + 2' we get ' 4+1 / 5+2' or 0.71 or 71%.

Interesting. I'm a simpleton when it comes to this stuff.

Surely this depends a lot on where in the world you are? I regularly break the speed limit while overtaking police cars in the UK and have never been pulled over (but never by much - I figure there's too much work involved to give me a ticket for only going 5 miles an hour over the limit). In fact, I've unintentionally overtaken police while going over the limit in Qatar and the US as well without being pulled over - both places where I'm more fearful of the police than when in the UK.

True. All observations were in New England.

>I figure there's too much work involved to give me a ticket for only going 5 miles an hour over the limit

True. I typically drive past speed traps at ~10MPH over the limit with no problem. Passing a cop seems to be showing disrespect and I think that's why it'll get you pulled over.

Here's a brief demo [video] of how these jams can start for no apparent reason http://www.youtube.com/watch?v=Suugn-p5C1M

It must have taken careful coordination to get them into the starting position too.

I'd be interested to see videos of solutions they've come up with. They could even try solutions that exist today (variable speed limits, hard shoulder openings, ramps with traffic lights when adding cars, etc.).

An interesting question, but I must ask — why is the answer important?

I could see this being possibly useful in traffic "wave" disruption. I've read on the traffic wave theory before and there has been some ideas that if the wave could be disrupted long enough to clear out that it would dissolve and traffic would start to flow again at its normal pace. I suppose that disruption could be done by police cars allowing buffers to build thus disrupting the wave.

Can you tell I find this field fascinating? Full disclosure I have a degree in Operations Research.

One of those papers mentioned in the article described "negative traffic" as the gaps in an otherwise saturated segment of road. Vehicles travelling behind the gap tended to have smoother acceleration curves.

I've used this idea to great effect when stuck in traffic by moving into the far left lane, building up a nice gap in front of me, and then cruising at a steady 2-3mph instead of stop-and-go. I've noticed that people generally recognize this as a net-positive and will "follow the leader" with only one or two cheaters (cars which pass me and move into the gap) -- usually the cars immediately behind me.

In order to pull this off, the lane leader needs to maintain a variable length buffer of gap-space in order to prevent their velocity from falling to zero ("stopping").

As the traffic density drops, the gap increases, and you can speed up which ups the average velocity of all of the cars in the lane. Eventually, traffic density will drop down to "normal" conditions at which point cars begin to cheat with increasing frequency until a normal traffic equilibrium is reached (e.g. "not in traffic").

I would love to see an interactive model of this strategy, specifically to figure out the optimum number of lane leaders; less than the total number of lanes, I suspect.

Here is a DIY traffic wave experiement I read on this topic. http://www.eskimo.com/~billb/amateur/traffic/traffic1.html. Pretty interesting results.

bump: sorry. the remaining links look broken

I read the same article a while ago and added it to my (long) list of business proto-ideas. Here are the notes I scribbled a few years ago:

"Build a web app/site that allows people to practice smoothing out waves, speed up time to see effects easily, animate the process for visual understanding, etc., etc. Maybe even issue stickers so one can identify people who are smoothers rather than just people cutting in line."

Lately, a mobile app or an app built into the car's computer system could coordinate smoothing actions with other cars, and give some feedback on real time smoothing.

Sounds like a great idea. If anything it could be a really interesting augmented reality game.

I try to do that as well but it's hard to built up a big enough gap especially in LA where a 'stop' can last up to 15+ seconds. Trying to make a gap big enough without seeming like a complete douche is hard and it makes it that much harder that I have been conditioned to speed up as much as possible.

I myself try to do that in my lane. Building up a gap so I don't have to use the clutch and can just idle through traffic. I've had varying success with this technique.

One of my pet peeves is seeing other drivers tailgate. My hypothesis is that all congested would be alleviated if everyone followed the 2 second rule.

Sans the copper, they do this over here in the UK by using variable speed limits, hard shoulder 'opening' and the real threat of speed cameras.

Seems to work in my albeit anecdotal and very occasional experience of driving near Birmingham in rush hour. Would be interested to hear the perspective on UK HNers who were aorund before/after they implemented this.

And they're using it more and more:

http://www.bbc.co.uk/news/uk-england-13426799

I must say I've long assumed that they also used police cars for flow control - now of course they have the Highways Agency vehicles¹ which look so much like police cars as to cause the same slowing to <70mph from what's often an average in the outer lanes of 85.

---

¹ -- I can't see how the Highways Agency are not running fowl of the law against "impersonating a police officer" by the livery of their vehicles.

Notice how truckers work with highway congestion too. They tend to slow down to allow congestion in front of them to flow. This might look at first to allow braking space for the big trucks but I think it has a lot to do with the traffic flow as well.

Truckers don't like to change gears. It's much more efficient for them to stay in a lower gear and coast at a consistent speed than it is to constantly change gears and brake.

One reason might be that if you can reduce the effects of traffic you can make our economy more efficient and improve civic life.

Also, the theory that is used to model the behavioral aspects of traffic flow could very well apply to other areas of the social sciences. So a researcher trying to solve a different problems might read this problem and be able to apply the model to his own area of research.

lots of manhours are lost in traffic

http://www.foreignpolicy.com/articles/2010/08/24/the_world_s...

I would say understanding the dynamics of it is a perfectly important question for a PhD thesis

not sure this hasn't already been studied

there is probably some theory of traffic that this strategy is based on

http://espn.go.com/action/freeskiing/story/_/id/7128930/colo...

http://www.slate.com/articles/life/transport/2011/10/rolling...

I saw something like this the other day at a stop sign. Normally there is a lot of traffic going through this stop sign at rush hour, but it doesn't get backed up. The other day there was a police car sitting near the stop sign. It caused a huge backup that stretched for several blocks. Turns out people were being extra careful to come to a complete stop for a few seconds because of the police car, and that caused the line to move more slowly than normal.

Déjà vu: http://news.ycombinator.com/item?id=1626403

Burger's Equation predicts a backwards propagating density wave when there's a discontinuity, eg a traffic jam even after the original accident has cleared.

(Whenever I'm out in LA I think about it, calms me down.)

http://en.wikipedia.org/w/index.php?title=Burgers%27_equatio...

My personal pet peeve is the number of times I've seen police officers breaking traffic regulations. I was hoping someone would study that (and actually make them stop). Speeding, tailgating, illegal lane changes, etc. etc. They're not supposed to do any of that without a siren.

> How do you model a traffic scenario where certain vehicles introduce more stringent constraints on the vehicles around them that are not purely limited to their physical place on the road?

Would this really qualify as a PhD topic these days? Serious question.

I don't have any expertise, but... I think it would.

A dissertation proving that cops on the road slow down traffic might be able to effect public policy. We might be able to get cops off the road during rush hour! We might realize that the benefits of tracking down speeding drivers don't outweight the benefits of having a copless road.

It's probably be worthwhile as a paper (journal article or peer-reviewed conference paper), but it doesn't seem enough for a competitive PhD dissertation.

I'd be very surprised if nobody's done this yet.

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