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	<title>Comments on: The Caldecott Tunnel Problem</title>
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	<pubDate>Thu, 17 May 2012 03:38:09 +0000</pubDate>
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		<title>By: Anthony Mark Morningstar</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-159</link>
		<dc:creator>Anthony Mark Morningstar</dc:creator>
		<pubDate>Tue, 12 Aug 2008 00:26:46 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-159</guid>
		<description>The question of merging goes back to the fundamental rule of driving: Have as little interference with the other vehicles.

The math says that with merging, there are one of two options. First, all vehicles increase spead, keeping the flow rate constant at the bottleneck. But, since most forced merging is the result of construction, and there are speed limits for construction zones, that leaves the second: That all vehicles reduce speed.

Theoretically, if two lanes are merging, the total speed of the through lane is about one-half of the original speed. So, if BOTH lanes start reducing their speeds so that the spacing increases so that the merging lane can easily merge altenately (like the teeth of a zipper) then the flow should be maintained.

So, if a stretch of road is at 65MPH, and merges from two lanes to one, if the vehicles reduce speed to 30MPH, this should allow all vehicles to merge easily. All vehicles will be at 30MPH. However, if someone runs to the very end and tries to merge then, he might maintain 30MPH, but force those behind him to slow down to create a hole. His gain punishes the others.

And, if three lanes merge to one, the average speed should be around 20MPH. Simple mathematics. Again, the rude driver can cut out some amout of waiting, but will have an impact on the vehicles behind the merge.

It is just like a parking lot. If you let one car per row turn in to the main exit, everyone will progress. The person in the last space will still be last, but that is how it should work.</description>
		<content:encoded><![CDATA[<p>The question of merging goes back to the fundamental rule of driving: Have as little interference with the other vehicles.</p>
<p>The math says that with merging, there are one of two options. First, all vehicles increase spead, keeping the flow rate constant at the bottleneck. But, since most forced merging is the result of construction, and there are speed limits for construction zones, that leaves the second: That all vehicles reduce speed.</p>
<p>Theoretically, if two lanes are merging, the total speed of the through lane is about one-half of the original speed. So, if BOTH lanes start reducing their speeds so that the spacing increases so that the merging lane can easily merge altenately (like the teeth of a zipper) then the flow should be maintained.</p>
<p>So, if a stretch of road is at 65MPH, and merges from two lanes to one, if the vehicles reduce speed to 30MPH, this should allow all vehicles to merge easily. All vehicles will be at 30MPH. However, if someone runs to the very end and tries to merge then, he might maintain 30MPH, but force those behind him to slow down to create a hole. His gain punishes the others.</p>
<p>And, if three lanes merge to one, the average speed should be around 20MPH. Simple mathematics. Again, the rude driver can cut out some amout of waiting, but will have an impact on the vehicles behind the merge.</p>
<p>It is just like a parking lot. If you let one car per row turn in to the main exit, everyone will progress. The person in the last space will still be last, but that is how it should work.</p>
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		<title>By: Bill Beaty</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-151</link>
		<dc:creator>Bill Beaty</dc:creator>
		<pubDate>Sun, 10 Aug 2008 09:54:43 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-151</guid>
		<description>Note that the "side zooming" is impossible when drivers behave as suggested in the article.

The jam is created when the majority queues up early, not using the extra lane, then "side zoomers" use that lane and create a jam as they force their way in at the last second.

If their habit instead was to fill all lanes, then there is no long empty lane, and there are no "side zoomers."   Instead all lanes flow at about the same speed (and if one lane speeds up, then drivers will change lanes to fill it and slow it again.)

Those commuters seem to have no trouble zipper-merging at an early point.  If all lanes were filled, including the "extra" ones, why would they have trouble merging farther downstream?   I don't think they would.  The trouble appears because a few fast drivers are seen as "cheating," while the same lane filled with many slow drivers is "fair."</description>
		<content:encoded><![CDATA[<p>Note that the &#8220;side zooming&#8221; is impossible when drivers behave as suggested in the article.</p>
<p>The jam is created when the majority queues up early, not using the extra lane, then &#8220;side zoomers&#8221; use that lane and create a jam as they force their way in at the last second.</p>
<p>If their habit instead was to fill all lanes, then there is no long empty lane, and there are no &#8220;side zoomers.&#8221;   Instead all lanes flow at about the same speed (and if one lane speeds up, then drivers will change lanes to fill it and slow it again.)</p>
<p>Those commuters seem to have no trouble zipper-merging at an early point.  If all lanes were filled, including the &#8220;extra&#8221; ones, why would they have trouble merging farther downstream?   I don&#8217;t think they would.  The trouble appears because a few fast drivers are seen as &#8220;cheating,&#8221; while the same lane filled with many slow drivers is &#8220;fair.&#8221;</p>
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		<title>By: stine</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-143</link>
		<dc:creator>stine</dc:creator>
		<pubDate>Sat, 09 Aug 2008 04:19:45 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-143</guid>
		<description>Either we haven't discussed, or it was edited out of this version, the fact that when we are taught to drive (or at least we were during the '80s and before), we are told to leave space between vehicles.  This contributes to efficiency of 'zipper-merging', whereas the way people (at least in Atlanta) drive is to stay 1 foot off of the bumper of the car ahead, which makes 'zipper-merging' impossible.....

The real problem is that it is much to easy to get a drivers license.</description>
		<content:encoded><![CDATA[<p>Either we haven&#8217;t discussed, or it was edited out of this version, the fact that when we are taught to drive (or at least we were during the &#8217;80s and before), we are told to leave space between vehicles.  This contributes to efficiency of &#8216;zipper-merging&#8217;, whereas the way people (at least in Atlanta) drive is to stay 1 foot off of the bumper of the car ahead, which makes &#8216;zipper-merging&#8217; impossible&#8230;..</p>
<p>The real problem is that it is much to easy to get a drivers license.</p>
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		<title>By: Ken</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-139</link>
		<dc:creator>Ken</dc:creator>
		<pubDate>Fri, 08 Aug 2008 22:45:15 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-139</guid>
		<description>I've often thougth that a "merge zone" should be marked with both cross hatching on the pavement and signs indicating the start and end of the merge zone.  This would let people know where they should be zippering together.  (something along the lines of what the Brits are doing per Balraj's comment)  The vehicle whose front bumper is further forward should have right of way (rather than the person established in the lane).  This would help to optimize the flow, and hopefully calm the vigilantes down by clearly indicating that "side zooming" is acceptable and proper; and give the message that 50% of the traffic should "side zoom".

Ken</description>
		<content:encoded><![CDATA[<p>I&#8217;ve often thougth that a &#8220;merge zone&#8221; should be marked with both cross hatching on the pavement and signs indicating the start and end of the merge zone.  This would let people know where they should be zippering together.  (something along the lines of what the Brits are doing per Balraj&#8217;s comment)  The vehicle whose front bumper is further forward should have right of way (rather than the person established in the lane).  This would help to optimize the flow, and hopefully calm the vigilantes down by clearly indicating that &#8220;side zooming&#8221; is acceptable and proper; and give the message that 50% of the traffic should &#8220;side zoom&#8221;.</p>
<p>Ken</p>
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		<title>By: Rick Mitchell</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-124</link>
		<dc:creator>Rick Mitchell</dc:creator>
		<pubDate>Thu, 07 Aug 2008 00:57:56 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-124</guid>
		<description>As a retired traffic engineer, here is an unavoidable fact of life: Only so many people can pass a certain point (i.e., be in the same place) within a certain amount of time, regardless of how polite they may be. This is demonstrated on freeways every day where there is no discernible conflict or disruption, other than the normal flow of traffic. The slowdown of traffic will occur whether there is a reduction in the number of lanes or not -- given an increase in traffic beyond the physical capacity of the roadway, But it is most noticeable where a reduction in the number of lanes occurs. The three or four lanes that reduce to only two will have a higher capacity and must suffer some delay as the two-lane section discharges its continuing overload of traffic at the rate its own capacity can handle. The two-lane section, once you're in it, moves, but the lanes feeding into it are disrupted -- with the "liner-uppers" on the right, usually, and the "side-zoomers" on the left. If all of those drivers stayed in their lanes (as suggested by Ms. Gorney) they could merge comfortably as long as their combined flow rate did not exceed that of the capacity of the two-lane section (more or less) they were feeding into. With the four-to-two lane reduction at the Caldecott Tunnel, that would work (and indeed it does) when the four-lane section is running at about half of its capacity -- approximately equal to the capacity of the two-lane section -- or less than that.

Having said that, I would agree with Ms. Gorney that having everybody stay in their own lanes would be a good idea, since it would have the effect of averaging out the necessary waiting time for all drivers in all lanes, whatever the rate of flow. Much like the operation of lanes at a supermarket, where the length of the lines at all open check stands tends to equalize (and no one feels "cheated" if another shopper joins a shorter line). Drivers in California (the ones who have been here for a few years, anyway) have learned to merge in turn -- to the amazement of friends from back east, especially from Texas. However, I noticed recently while driving in Dallas and in New York that drivers in those states are also merging better as freeways (or "expressways") become more congested.

As she and Tom Vanderbilt have noted (along with many of us traffic engineers, believe it or not) traffic is "behavior" and humans do have an uncanny way of adapting theirs when it turns out to be advantageous. The supermarkets have also learned that keeping lines reasonably short is advantageous. I was in a line at a museum cafeteria recently where there were only two cashiers, and sure enough, congestion/delay! Supermarkets call additional checkers in at rush time and build an adequate number of checkout lines. The same things work with traffic -- the building just takes longer and costs a very large amount.  Sorry to break the news! Meanwhile, yes we could spread the misery evenly by using all the lanes approaching a bottleneck point. I guess the one person in a hundred with a bona-fide emergency can try to sneak by on the shoulder.

-- Rick Mitchell</description>
		<content:encoded><![CDATA[<p>As a retired traffic engineer, here is an unavoidable fact of life: Only so many people can pass a certain point (i.e., be in the same place) within a certain amount of time, regardless of how polite they may be. This is demonstrated on freeways every day where there is no discernible conflict or disruption, other than the normal flow of traffic. The slowdown of traffic will occur whether there is a reduction in the number of lanes or not &#8212; given an increase in traffic beyond the physical capacity of the roadway, But it is most noticeable where a reduction in the number of lanes occurs. The three or four lanes that reduce to only two will have a higher capacity and must suffer some delay as the two-lane section discharges its continuing overload of traffic at the rate its own capacity can handle. The two-lane section, once you&#8217;re in it, moves, but the lanes feeding into it are disrupted &#8212; with the &#8220;liner-uppers&#8221; on the right, usually, and the &#8220;side-zoomers&#8221; on the left. If all of those drivers stayed in their lanes (as suggested by Ms. Gorney) they could merge comfortably as long as their combined flow rate did not exceed that of the capacity of the two-lane section (more or less) they were feeding into. With the four-to-two lane reduction at the Caldecott Tunnel, that would work (and indeed it does) when the four-lane section is running at about half of its capacity &#8212; approximately equal to the capacity of the two-lane section &#8212; or less than that.</p>
<p>Having said that, I would agree with Ms. Gorney that having everybody stay in their own lanes would be a good idea, since it would have the effect of averaging out the necessary waiting time for all drivers in all lanes, whatever the rate of flow. Much like the operation of lanes at a supermarket, where the length of the lines at all open check stands tends to equalize (and no one feels &#8220;cheated&#8221; if another shopper joins a shorter line). Drivers in California (the ones who have been here for a few years, anyway) have learned to merge in turn &#8212; to the amazement of friends from back east, especially from Texas. However, I noticed recently while driving in Dallas and in New York that drivers in those states are also merging better as freeways (or &#8220;expressways&#8221;) become more congested.</p>
<p>As she and Tom Vanderbilt have noted (along with many of us traffic engineers, believe it or not) traffic is &#8220;behavior&#8221; and humans do have an uncanny way of adapting theirs when it turns out to be advantageous. The supermarkets have also learned that keeping lines reasonably short is advantageous. I was in a line at a museum cafeteria recently where there were only two cashiers, and sure enough, congestion/delay! Supermarkets call additional checkers in at rush time and build an adequate number of checkout lines. The same things work with traffic &#8212; the building just takes longer and costs a very large amount.  Sorry to break the news! Meanwhile, yes we could spread the misery evenly by using all the lanes approaching a bottleneck point. I guess the one person in a hundred with a bona-fide emergency can try to sneak by on the shoulder.</p>
<p>&#8211; Rick Mitchell</p>
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		<title>By: Mark Hunter</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-113</link>
		<dc:creator>Mark Hunter</dc:creator>
		<pubDate>Tue, 05 Aug 2008 16:29:14 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-113</guid>
		<description>The key to the article, for me, was the idea of allowing room between cars for the zipper to work smoothly.  The "idea," I say, because this will never happen. Drivers will always want to nestle up to the car in ahead of them rather than leave room for cars to merge in front of them.</description>
		<content:encoded><![CDATA[<p>The key to the article, for me, was the idea of allowing room between cars for the zipper to work smoothly.  The &#8220;idea,&#8221; I say, because this will never happen. Drivers will always want to nestle up to the car in ahead of them rather than leave room for cars to merge in front of them.</p>
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		<title>By: Ed Baker</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-111</link>
		<dc:creator>Ed Baker</dc:creator>
		<pubDate>Tue, 05 Aug 2008 02:40:10 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-111</guid>
		<description>Pet peeve department:
Tom, you mention in this post something that you did not, unfortunately, bring up in your wonderful book: "I think something similar may underlie the left-lane-is-for-faster-traffic dynamic on U.S. roads: It’s a good idea in practice, but someone’s always going to want to go faster, and that person’s rights are going to mash up against the guy who’s already going pretty damn fast, is exiting on the left soon anyway, and thinks he also has a right to be in the lane he’s in."

But isn't the left lane not for "faster" traffic, but for "passing" traffic? How efficient is it that a two-mile line of cars be held up for 15 minutes by someone who thinks he's got the right to drive one mile an hour faster than the five tractor trailers he's driving next to? Sheesh.</description>
		<content:encoded><![CDATA[<p>Pet peeve department:<br />
Tom, you mention in this post something that you did not, unfortunately, bring up in your wonderful book: &#8220;I think something similar may underlie the left-lane-is-for-faster-traffic dynamic on U.S. roads: It’s a good idea in practice, but someone’s always going to want to go faster, and that person’s rights are going to mash up against the guy who’s already going pretty damn fast, is exiting on the left soon anyway, and thinks he also has a right to be in the lane he’s in.&#8221;</p>
<p>But isn&#8217;t the left lane not for &#8220;faster&#8221; traffic, but for &#8220;passing&#8221; traffic? How efficient is it that a two-mile line of cars be held up for 15 minutes by someone who thinks he&#8217;s got the right to drive one mile an hour faster than the five tractor trailers he&#8217;s driving next to? Sheesh.</p>
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		<title>By: Balraj Gill</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-110</link>
		<dc:creator>Balraj Gill</dc:creator>
		<pubDate>Mon, 04 Aug 2008 11:01:10 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-110</guid>
		<description>I think a major help on the approachs to this tunnel would be 2 signs on a road near to where I live in the UK.  On this road, which leaves a mid-sized town, 2 lanes merge into 1.  The first sign, which appears whilst the road is still 2 lanes, says "Use Both Lanes".  The second sign, which appears just before one of the lanes disappears, says "Merge in Turn", and underneath has a diagram of the 2 lanes with 2 arrows over each other, like a zip pattern.  

Before, these signs, most drivers would queue up in the through lane and would do their best to block any drivers in the lane that was about to disappear.  People (especially in England!) need to be taught that queuing up in 1 lane is not the best policy for traffic flow, when another lane is still available.</description>
		<content:encoded><![CDATA[<p>I think a major help on the approachs to this tunnel would be 2 signs on a road near to where I live in the UK.  On this road, which leaves a mid-sized town, 2 lanes merge into 1.  The first sign, which appears whilst the road is still 2 lanes, says &#8220;Use Both Lanes&#8221;.  The second sign, which appears just before one of the lanes disappears, says &#8220;Merge in Turn&#8221;, and underneath has a diagram of the 2 lanes with 2 arrows over each other, like a zip pattern.  </p>
<p>Before, these signs, most drivers would queue up in the through lane and would do their best to block any drivers in the lane that was about to disappear.  People (especially in England!) need to be taught that queuing up in 1 lane is not the best policy for traffic flow, when another lane is still available.</p>
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		<title>By: Brad Templeton</title>
		<link>http://www.howwedrive.com/2008/08/03/the-caldecott-tunnel-problem/#comment-108</link>
		<dc:creator>Brad Templeton</dc:creator>
		<pubDate>Sun, 03 Aug 2008 20:21:56 +0000</pubDate>
		<guid isPermaLink="false">http://www.howwedrive.com/?p=164#comment-108</guid>
		<description>I find a contradiction between the zipper thesis (which I suspect is the correct "fastest algorithm") and the "wasted capacity" thesis which suggests that leaving the vanishing lane well before the join-point "wastes usable real estate."

In a road system like this, all that matters is the capacity of the system, in cars per hour, of the point with the slowest capacity, known as the chokepoint or bottleneck.   The capacity and width of the road before and after this chokepoint is not relevant.   One can have 100 lanes coming in or out, but the only way they matter is how they affect the chokepoint.

It's been my understanding that since "stop and go" traffic has half the cars/hour/lane capacity of modestly moving traffic, and faster traffic has even more, avoiding a stop and go collapse is the best strategy.    Of course, if more cars are coming in than can get through the chokepoint, you can't avoid that.   In that circumstance, the excess capacity argument may make sense.   You can't stay long in that circumstance or you get an immensely long jam that backs up for miles, of course.

It is the intermediate state, where we do have enough capacity (with thicker traffic) but some collapse has taken us to stop and go.   Once we collapse to stop and go we must wait for a lull in incoming traffic to get out of stop and go.

There is an argument that sidezoomers make a collapse to stop-and-go more likely.  A line of cars in the continuing lane moving at a modest pace will have to stop when a sidezoomer pushes their way into that traffic.   And thus the collapse starts, and maintains if traffic is thick.

So is it possible we have two different states for a merge, one in which use of all lanes improves total flow, and another in which it hastens collapse?

I liken this to metering lights.  Metering lights are there to avoid collapse.  While in the line for the metering lights, you want on the road, damnit.  But you could be the very additional car which collapses the traffic to stop-and-go, making your own trip slower, along with everybody else's.</description>
		<content:encoded><![CDATA[<p>I find a contradiction between the zipper thesis (which I suspect is the correct &#8220;fastest algorithm&#8221;) and the &#8220;wasted capacity&#8221; thesis which suggests that leaving the vanishing lane well before the join-point &#8220;wastes usable real estate.&#8221;</p>
<p>In a road system like this, all that matters is the capacity of the system, in cars per hour, of the point with the slowest capacity, known as the chokepoint or bottleneck.   The capacity and width of the road before and after this chokepoint is not relevant.   One can have 100 lanes coming in or out, but the only way they matter is how they affect the chokepoint.</p>
<p>It&#8217;s been my understanding that since &#8220;stop and go&#8221; traffic has half the cars/hour/lane capacity of modestly moving traffic, and faster traffic has even more, avoiding a stop and go collapse is the best strategy.    Of course, if more cars are coming in than can get through the chokepoint, you can&#8217;t avoid that.   In that circumstance, the excess capacity argument may make sense.   You can&#8217;t stay long in that circumstance or you get an immensely long jam that backs up for miles, of course.</p>
<p>It is the intermediate state, where we do have enough capacity (with thicker traffic) but some collapse has taken us to stop and go.   Once we collapse to stop and go we must wait for a lull in incoming traffic to get out of stop and go.</p>
<p>There is an argument that sidezoomers make a collapse to stop-and-go more likely.  A line of cars in the continuing lane moving at a modest pace will have to stop when a sidezoomer pushes their way into that traffic.   And thus the collapse starts, and maintains if traffic is thick.</p>
<p>So is it possible we have two different states for a merge, one in which use of all lanes improves total flow, and another in which it hastens collapse?</p>
<p>I liken this to metering lights.  Metering lights are there to avoid collapse.  While in the line for the metering lights, you want on the road, damnit.  But you could be the very additional car which collapses the traffic to stop-and-go, making your own trip slower, along with everybody else&#8217;s.</p>
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