πŸ”₯ Yore driving, Deez roasted Nuts! πŸ”₯


  • β™Ώ (Parody)

    @Kian said:

    All that matters is how many cars are coming out of the constriction. If more cars are trying to go in than can come out, no merging strategy is going to make a meaningful impact.

    True if you only consider that little bit of the road.



  • @Kian said:

    They can go at the speed limit and they don't need to slow down any more. Even if the constriction never ends, they're going to be cruising comfortably.

    You'd think that, but these "shockwaves" magically move in both directions somehow. Meaning you hit the constriction and sometimes have a hundred meters before you start to speed up again.

    @Kian said:

    All that matters is how many cars are coming out of the constriction. If more cars are trying to go in than can come out, no merging strategy is going to make a meaningful impact.

    Other that "road utilization" which is marginal, because it just means you can load a few dozen more cars onto a highway where people are coming in and slowing down anyway.

    It may make the difference in a exit or entrance further back.

    But if your entire highway is congested, where this would make a difference, you are fucked anyway.


  • Winner of the 2016 Presidential Election

    @Kian said:

    As the speed increases, the distance between cars has to increase proportionally.

    Not really (the highlighted part).

    @Kian said:

    Increasing the speed limit lets you cover longer distances, but when it comes to capacity (cars/hour), you need to add lanes to increase it.

    The capacity is the maximum number of cars per hour. It's a constant if you assume that there's no speed limit. Depending on how low the speed limit is, it might actually impact the capacity of the road.


  • area_deu

    @Kian said:

    An interesting fact I realized while writing is that a road's capacity is actually a constant

    No.

    independent of the posted speed limit.
    Maybe. But not independent of the actual speed.
    Once the cars are inside the constriction, other cars won't be merging in. They can go at the speed limit and they don't need to slow down any more.
    Uh-huh. Have you even ever driven a car? There are no buses, lorries, vans, hills, corners or caravans where you live?
    Even if the constriction never ends, they're going to be cruising comfortably.
    No. They're going to be stuck behind a fucking lorry and hating every minute of it.
    All that matters is how many cars are coming out of the constriction.
    No.
    If more cars are trying to go in than can come out, no merging strategy is going to make a meaningful impact.
    It WILL make an impact to the poor suckers who are stuck in the pile-up BEFORE the constriction because SOME FUCKHEAD decided to half-merge early and WASTED PRECIOUS ROAD SPACE. IT WILL ALSO MAKE an impact to the poor suckers who are stuck behind the HUGE-ASS accident caused by two people deciding to merge early into the same gap because they couldn't wait until the end of the lane where it would have been clear who has to merge when.

    Seriously. This feels like discussing traffic theory with a bunch of school children who have never driven anything else than a fucking bicycle.


  • Discourse touched me in a no-no place

    I like that diagram. It feels physics-y. πŸ˜„


  • Winner of the 2016 Presidential Election

    It's a very simplistic model, but it works well enough. ;) It also shows the relationship between mean speed and other quantities.

    A long time ago, in high school, I had to write a paper about traffic analysis and modeling.


  • β™Ώ (Parody)

    @Kian said:

    That's a consequence of road over-utilization. An interesting fact I realized while writing is that a road's capacity is actually a constant, independent of the posted speed limit. The safe distance between cars is determined by human reflexes and how comfortable they feel with cars being close at different speeds. As the speed increases, the distance between cars has to increase proportionally.

    Yes, but that assumes that spacing remains "constant." I learned that you were supposed to leave a 3 second gap. Obviously, the distance increases as speed does (which is what you were talking about). However, that's not how stuff works in real life.


  • area_deu

    @boomzilla said:

    Yes, but that assumes that spacing remains "constant." I learned that you were supposed to leave a 3 second gap.

    Really? It's 2 seconds here in Germany. Guess our brakes are better.


  • β™Ώ (Parody)

    Well, I might also be misremembering. Both numbers are in my head. :belt_onion:



  • @asdf said:

    >As the speed increases, the distance between cars has to increase proportionally.

    Not really (the highlighted part).

    I don't know if you misunderstood what I said, or the wiki article you linked. From your own link:

    There is a connection between traffic density and vehicle velocity: The more vehicles are on a road, the slower their velocity will be.
    [...]
    The speed-density relationship is linear with a negative slope

    Saying that "the more vehicles are on a road, the slower their velocity will be" is the same as saying "the faster they go, the fewer vehicles are on the road". Which means that as speed increases, distance between them increases, which causes density to fall. Density is the inverse of distance between cars.

    Saying that the speed-density relationship is linear literally means that the relationship is proportional. Twice the speed leads to half the density. Do you even maths?



  • @boomzilla said:

    However, that's not how stuff works in real life.

    In theory, theory and practice are the same. In practice, they aren't πŸ˜›


  • Winner of the 2016 Presidential Election

    @Kian said:

    Which means that as speed increases, distance between them increases, which causes density to fall.

    No. First of all, free-flow traffic and congested traffic are completely different, so you have to look at them separately. Look at the lower diagram, they're not comparable at all. You're also confusing cause and effect. The mean speed is the effect.



  • @asdf said:

    You're also confusing cause and effect.
    How am I confusing cause and effect when I never said that one caused the other? OH! You mean when I said "which causes density to fall"? I meant that greater distance between cars is literally the same thing as lower density. They're two ways of measuring the same thing. I didn't mean to imply that there's a causal relationship between increasing distance and decreasing density.


  • Winner of the 2016 Presidential Election

    @Kian said:

    How am I confusing cause and effect when I never said that one caused the other?

    Let me quote you again, exact same quote:

    @Kian said:

    Which means that as speed increases, distance between them increases, which causes density to fall.

    Do you even read what you write?


  • Winner of the 2016 Presidential Election

    An increase/decrease of traffic density influences the mean speed and the probability that the traffic changes into another state.

    (Bit more realistic version of the fundamental diagram of traffic flow, arrows are state transitions.)





  • @xaade said:

    @Kian said:
    Meaning every car should have be, on average, two minimum safe distances behind the car ahead.

    In a real world situation, increasing the safe distance to a proper follow distance would help accommodate that, as the constriction may not be long enough to impact cars for too long.

    :wtf: TDEMSYR.
    @xaade said:

    people don't even follow minimum safety distance either, which is why most of these constrictions end up congesting traffic.

    No, the constrictions congest traffic if there are enough cars on the road that there is less than two "comfort" distances between them, such there is less than one after merging. If the merged distance is less than the comfort distance, traffic will slow, regardless of whether that distance is greater than, equal to, or less than the safe distance. Even if everyone had self-driving cars that perfectly maintained minimum safe spacing and perfectly zipper-merged (early or late is irrelevant), traffic would be forced to slow if the number of cars exceeded the number that could be accommodated in the restricted region at full speed.

    @xaade said:

    people are bad drivers
    This, while true in and of itself, is not the reason for congestion. There are just too many drivers (good or bad) for the restricted capacity of the road. Bad drivers can (and do) make the situation worse, but even if people drove perfectly, the congestion would still occur.



  • @asdf said:

    Do you even read what you write?

    I edited my post as you were posting. I said that greater distance between cars causes lower density in the sense that, for example, increasing the frequency of something "causes" the period to decrease. They're two ways of measuring the same thing. I didn't mean to imply that there's a causal relationship between increasing distance and decreasing density. And I also didn't mean to say that driving faster pushes cars away from you magically either.



  • @boomzilla said:

    I might also be misremembering.

    I'm with @ChrisH on this. Two seconds is what I remember, too.


  • BINNED

    @Kian said:

    every car should be, on average, two minimum safe distances behind the car ahead.

    What color is the sky in your world?

    @boomzilla said:

    I learned that you were supposed to leave a 3 second gap.

    The fact that you even remember that automatically qualifies you for a :belt_onion:.

    The modern way to :doing_it_wrong: is to only remember traffic rules long enough to pass the test.



  • @antiquarian said:

    What color is the sky in your world?

    Read the sentence before that: "In the case of a two lane road being limited to a one lane road, that means the road has to be at most at half capacity. Meaning every car should be, on average, two minimum safe distances behind the car ahead."

    Every car being two minimum safe distances from each other on average is the definition of a road being at half capacity. Nothing more. It's a descriptive comment. And a road being at half capacity is simply what is needed for a constriction from two lanes to one lane on that road to not create a congestion.

    You can replace "minimum safe distance" with "comfort distance" as @HardwareGeek used, which is probably a better term.


  • BINNED

    @Kian said:

    Every car being two minimum safe distances from each other on average is the definition of a road being at half capacity.

    :whoosh:

    In that case no road is ever at half capacity unless there's only one car on it. πŸ›‚

    @Kian said:

    You can replace "minimum safe distance" with "comfort distance" as @HardwareGeek used, which is probably a better term.

    Half of the drivers have a "comfort distance" of a car length or less, so that would be more accurate.



  • @boomzilla said:

    I learned that you were supposed to leave a 3 second gap.

    @ChrisH said:

    Really? It's 2 seconds here in Germany. Guess our brakes are better.

    I seem to remember 3 from years ago also. But now everyone says 2. (I'm guessing the recommendation changed some years ago) Doesn't matter, you leave that much space here and a minimum of 2 cars are going to move into it...



  • @dcon said:

    you leave that much space here and a minimum of 2 cars are going to move into it...

    QFT



  • @Kian said:

    I don't know if you misunderstood what I said, or the wiki article you linked. From your own link:

    Neither. You misunderstood @asdf's post. The wiki article was posted in response to you saying this:

    @Kian said:

    An interesting fact I realized while writing is that a road's capacity is actually a constant, independent of the posted speed limit.

    According to the wiki article that @asdf linked, and your interpretation of that article, road capacity is not constant, so your original statement was incorrect, and @asdf successfully refuted your claim.



  • @HardwareGeek said:

    @dcon said:
    you leave that much space here and a minimum of 2 cars are going to move into it...

    QFT

    And as my luck has it, I'll be in lane 2 and drivers from lanes 1 and 3 will try to move into the same space one car length in front of me. (which is not what I was implying above)



  • @dcon said:

    you leave that much space here and a minimum of 2 cars are going to move into it...

    yep


  • Winner of the 2016 Presidential Election

    @abarker said:

    road capacity is not constant

    Actually, given a fixed speed limit, it's a constant. He started being wrong at "independent of the posted speed limit". And some of the rest was wrong as well.



  • So our solution to highway traffic is to reduce the speed limit?

    🚎🚎🚎🚎🚎🚎🚎🚎🚎🚎🚎


  • Winner of the 2016 Presidential Election

    @xaade said:

    So our solution to highway traffic is to reduce the speed limit?

    Erm... I know you're joking, but I think you're also still misunderstanding the relationship between capacity, mean speed and actual flow under certain conditions (density).



  • @asdf said:

    Actually, given a fixed speed limit, it's a constant. He started being wrong at "independent of the posted speed limit". And some of the rest was wrong as well.

    FTFY


  • Winner of the 2016 Presidential Election

    Nope, the capacity is defined as the maximum flow (cars/hour).



  • @xaade said:

    If I want to merge and there's not enough proper following distance in the lane next to me, but enough distance to just fit inbetween two cars.

    I merge, and then all the cars have to suddenly and unexpectedly slow down to accommodate the merge, this slows traffic.

    Think this through.

    Start with a hypothetical scenario where two lanes are zipper-merging as far downstream as possible, and traffic is flowing smoothly. Now slowly increase the traffic density until traffic speed upstream of the merge point has just started to be constrained by the need to maintain a proper following distance.

    Downstream of the merge, that critical lane density is doubled. There is simply no longer enough room on the road for everybody to maintain a safe following distance. That condition causes the formation of shockwave jams, and these will repeatedly propagate upstream into the pre-merge traffic and force all those nice regular pre-merge following distances to clump up.

    That means drivers merging in now have a choice between (a) maintaining zipper discipline as far downstream as they can, varying their speed as necessary to achieve this, perhaps even to the point of stopping briefly as a jam propagates backward through the merge point or (b) merging into gaps in the destination lane as soon as those become available.

    Choosing (b) will certainly result in a smoother individual merge manoeuvre, but it also moves the effective merge point upstream. That means that there is now a longer train of post-merge traffic, which means more opportunities for shockwave jams to form; also, such of them as do form will propagate further upstream before damping out.

    Choosing (a) maximizes traffic throughput, by minimizing the amount of road surface not belonging to cars and their following distances. But it's fairly marginal; early merging would typically create a bubble of unused road surface worth maybe ten cars (including following distances) at most.

    The only case where any of this stuff is going to make a real and significant difference is where the road downstream of the merge point widens out again very quickly, because that might well make the difference between a post-merge over-density that's not long enough to create many shockwave jams, and a density that is.



  • @Kian said:

    the length of the constriction is irrelevant to the flow of traffic.

    Almost, but not quite.

    Shockwave jams form in constricted regions and propagate upstream. If the constricted region is very short, it is sometimes the case that shockwave jams don't form in it at all; drivers simply choose to spend that small amount of time travelling way too close to the car in front, knowing that they will only need to be doing so for a few seconds.



  • @xaade said:

    it's a pointless conversation as well because people don't even follow minimum safety distance either, which is why most of these constrictions end up congesting traffic.

    So, the real reason we're having this late/early discussion is because people are bad drivers, which was the whole thing I was going for.

    Your just-world viewpoint continues to make it hard for you to understand things.

    All drivers who are not actually engaged in rear-ending the car in front of them are maintaining a minimum safety distance with which they feel comfortable. It might not be the best or recommended minimum safety distance, and it might not be your preferred minimum distance, but that doesn't make it Not A Thing.

    When a road is below capacity, most of the drivers on it have the opportunity to maintain their own preferred minimum safety distance and more without being constricted by the speed of the car immediately in front of them. Under those conditions, you can merge in front of another driver and the worst that will happen is that they might need to slow briefly to re-establish their preferred distance back from you.

    But as soon as a road is at capacity, any such slowing-down is going to propagate upstream until it damps out.

    A road is at capacity when there is no space between cars, if you figure the length of a car as including its driver's idea of their minimum safety distance. That's a real-world physical effect that applies regardless of speed and regardless of driver skill.

    In fact if there were fewer dangerous tailgaters, cars would be spaced further apart on average and road capacities would decrease. Those shitty drivers you see all around you are doing you a favour, at least until they cause a crash.



  • @abarker said:

    According to the wiki article that @asdf linked, and your interpretation of that article, road capacity is not constant, so your original statement was incorrect, and @asdf successfully refuted your claim.

    In an ideal world where everyone drives safely, cars would keep a distance measured as two seconds between each other. This is defined not only by physical limits in the car and road, but by how long it takes a person to react to something sudden happening in front of them. Even if your car could stop on a dime at any speed, if you're too close to the car in front when it stops or slows down significantly, you're going to ram them because you couldn't move your foot from the gas to the brake pedal in time.

    Since ideally everyone would keep a minimum distance of two seconds between cars, regardless of the speed they're driving at, then if you stand at one spot in a fully loaded road with no congestion, you should be able to measure one car every two seconds (a bit less to account for the length of the car itself, but it's not appreciable at high speeds). That's the maximum capacity any road can have. 0.5 cars/second per lane, or 1800 car/hour per lane. If you go above that, then your cars have to by necessity be keeping less than 2 seconds of distance between each other.

    As was pointed out, drivers have varying "comfort distances", and will keep that distance rather than a strict two seconds. So to be more realistic, make an average of the comfort distance of varying drivers at different speeds, which from experience I would say that drivers over estimate their ability at higher speeds, and add a slight correction factor as speed increases to account for humans being shit drivers.

    You're not going to end up too far from the 1800 cars/hour per lane limit. Notice how the speed only plays a part because humans suck. If you actually enforced the rule (by switching over to driverless cars, for instance), you'd find that regardless of the speed, the optimal capacity of any road in good conditions (safe distance would have to increase in rain, etc) is essentially constant.

    You can't increase the capacity of a road by increasing the speed limit, because to keep drivers safe you need to increase the distance between them proportionally. The only ways to increase the capacity are to expect drivers to drive less safely (fixing the distance between them when increasing the speed), or add lanes.



  • @Kian said:

    when it comes to capacity (cars/hour), you need to add lanes to increase it

    Decreasing safe following distances works too. Marking a lane as robots-only could easily increase capacity as much as creating about two extra lanes.



  • @flabdablet said:

    Decreasing safe following distances works too.

    Which I just pointed out in the post right above this :P :hanzo:'d your pendatry!


  • β™Ώ (Parody)

    @flabdablet said:

    understand things.

    LOL. this made my night. Thank you for that.



  • @flabdablet said:

    Decreasing safe following distances works too. Marking a lane as robots-only could easily increase capacity as much as creating about two extra lanes.

    It still wouldn't prevent congestion at the merge, though, if the road is operating at more that 50% of that increased capacity. To illustrate, consider an extreme example:

    Suppose robotic cars that are in continuous communication with all the nearby cars. You could theoretically reduce the following distance to zero, because each car knows what the cars around it are going to do, and can brake or accelerate in perfect unison with the cars ahead and behind; cars could travel bumper-to-bumper at the speed limit.

    Now you reach a merge point. If the road is at more than 50% of capacity, there simply physically isn't room to fit a car between the others. The cars must slow down to open gaps for the cars in the other lane to merge into.



  • @HardwareGeek said:

    It still wouldn't prevent congestion at the merge, though, if the road is operating at more that 50% of that increased capacity.

    Of course.

    In fact, a highway operating near capacity with a mixture of robots-only and humans-allowed lanes would be a complete fucking nightmare for merging, and end up with massive tailbacks in the robot lane upstream of the merge point. The only sane way to design it would be to ensure that each such point was merging either two robots-only or two humans-allowed lanes.



    1. All merges are bad.
    2. The only way you improve a merge is by minimizing the slow down of the car behind you.
    3. The only thing that makes a late forced merge better than an early forced merge is that it uses up more of the constricting lane.

    So, steps to merging:

    1. Use up any ample gaps first. IFF you can merge at optimal speed.
    2. Remaining cars wait until the cones to late merge so that they use up more of the lane.
      If you cannot merge at speed, this makes you fall into this category, not the above.

    By skipping step 1, you've made it worse.
    But I have never argued against step 2. I've never gotten close to arguing that forcing an early merge is good.

    @flabdablet said:

    Your just-world viewpoint continues to make it hard for you to understand things.

    No, I understand it perfectly well.

    @flabdablet said:

    When a road is below capacity, most

    Yes.

    @flabdablet said:

    But as soon as a road is at capacity, any such slowing-down is going to propagate upstream until it damps out.

    Yes, and at this point there is no longer any gaps so you use up the road until the merge point.

    The way I've demonstrated is that forced merging at any point is bad, which is why when there must be forced merging, physical road space becomes a premium, and at that point late-merging is better than early merging.

    Before that point, early merging is better, unless it's forced. You want to limit the slowdown from a merge as much as possible.

    In fact, it's the varying comfort distances that cause early merging to be better giving specific circumstances.

    If you've sat there besides a gap the entire time, and there are no cars ahead of you, you gain nothing from waiting until the cones.

    The road above you can't magically accept a car in the constricted lane. And accelerating to allow more cars in the constricted lane is also stupid.

    That's why the optimal requires an intelligent decision. Neither hard-fast rule is superior.

    @flabdablet said:

    In fact if there were fewer dangerous tailgaters, cars would be spaced further apart on average and road capacities would decrease.

    They would decrease but move at optimum speed.

    @flabdablet said:

    Those shitty drivers you see all around you are doing you a favour, at least until they cause a crash.

    No, because even when there is a zero merge scenario, tailgaters typically alternate tapping their breaks, which is demonstrated to cause traffic.



  • @flabdablet said:

    Of course.

    You say "of course," but not everybody commenting in the topic seems to get it.



  • @xaade said:

    All merges are bad.

    See, you're wrong straight out of the starting gate.

    Merges are bad only under traffic conditions that put the roadway downstream from the merge point at or near capacity. If the road downstream is at or over capacity, then the merge will be bad regardless of driver strategy. Driver strategy can shove the thing around a bit between temporarily bad and temporarily very bad, but the only thing that can ever make it sustainably not bad is an increase in road capacity - either from making more lanes, or using assorted kinds of in-car technology to enable significant reductions in mean safe following time.



  • @xaade said:

    If you've sat there besides a gap the entire time, and there are no cars ahead of you, you gain nothing from waiting until the cones.

    In the time it takes that gap to move down the destination lane and arrive at the cones, it might have damped the upstream propagation of a jam wave. And if that happens, it might well be that the best gap available to you when you're nearly at the cones is further downstream than the one you picked initially.



  • William Beaty has spent far too long thinking through all this stuff. Recommended reading.

    Edit: after spending a little time looking over his stuff again (it's been a few years) I've just been struck by something: there's a comment in one of the emails about dealing emotionally with the irritation you provoke in drivers behind you when you slow down in order to open a large jam-busting gap ahead of you.

    That irritation is real and natural, and one frequent consequence of it is to induce in the irritated drivers a strong tendency to tailgate. If you're jam-busting by opening a large gap ahead of you, you're probably also causing a fairly large region of irritated tailgating behind you. And that means you're actually packing the cars behind you closer together in time: by inducing drivers behind you to tailgate, you're actually increasing the capacity of the roadway.

    Of course, by inducing tailgating that might not otherwise happen, you might also be making those cars more likely to collide. On the other hand, the fact that you're doing this in order to maintain a constant speed is also going to reduce the unpredictability that converts an unsafe following distance into a rear-ender in the first place.

    Interesting.



  • Btw, funny noone mentioned "how much gap is enough?".

    By driving with gap fits a normal sized car, the gap won't fit a bus, truck or maybe a 18-wheeler. If you don't leave enough gap, you'll have to slow down for they to merge, which eventally means the gaps between you and the vehicles behind will be narrower. If you drive with gap the allowed them to fit in the beginning, the road usage is inefficient.

    And after they merge, do you need to slow down to make more room for gap between you and whatever vehicle just merged to the line?

    Since long vehicles should use slow lane, if it's merger into slow lane than maybe it's alright. If it's merger into fast lane, do matter how you plan, you'll go back to the original problem.



  • Funny how the page you lifted your merge animations from makes the very same argument as all those you've chosen to oppose here.


  • area_deu

    QFT:

    The "zipper flow" is counterintuitive. It's created by proper late-merging at the last minute. It's destroyed by early merging. For this reason, the Fed Highway Admin has specific recommendations for proper driver behavior. They (and the various state highway groups) also have found the best road signage for smoothing the flow: "STAY IN LANE UNTIL MERGE POINT." Then at the last minute, another sign: "MERGE HERE, TAKE TURNS." Early merging ruins everything.


  • Discourse touched me in a no-no place

    @asdf said:

    arrows are state transitions

    There appear to be a few missing arrows...


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