What can scientific models tell us about the world?

Should you switch lanes in traffic?

Posted in Statistics, Transportation by Alexander Lobkovsky Meitiv on June 24, 2010

Switching lanes in heavy traffic can indeed increase your average speed if done right.

If you drive like me, you have no patience for bumper to bumper traffic. There is gotta be a way to beat it somehow, right? Do you sneak into an opening in a neighboring lane if it is moving faster? Do you set goals like: “when I get in front of that van, I’ll switch back?” It doesn’t always seem to work. A lane that was zooming by you comes to a dead stop when you switch into it. If the motion of each lane is random, is there a way to switch lanes and move faster than a car that stays in lane?

It turns out there is a way to beat the traffic. To show this we will use a simple model of traffic flow introduced by Nagel and Schrekenberg (see the previous post). The model consists of a circular track with consecutive slots which can be empty of occupied by cars. Cars have an integer velocity between 0 and vmax. As we saw in the previous post, simple rules for updating the positions and velocities of the cars can reproduce the traffic jam phenomenon thereby a dense region forms in which the cars are at a standstill for a few turns and then, as the jam clears in front of them, the cars accelerate and zoom around the track only to be stuck in the jam again. The jam itself moves in the direction opposite to that of the cars.

Now imagine that we put two of the circular tracks (or lanes) side by side. For starters, let’s require all cars except one to stay in their respective lanes. One rogue car can switch lanes. Can the rogue with the right lane switching strategy move faster than the rest of the cars on average? The answer is most certainly yes although finding the best lane switching strategy is a difficult computational problem. What we are going to do here is compare two lane switching strategies that at first sight seem equally good. What we will discover is that it the lane changing strategy matters. As you might have suspected, if you don’t do it right, you might actually move slower than the rest of the traffic!

Here are the two simple strategies we will compare (I suggest you read the previous post for the description of the model):

1) “Stop-switch:” if the slot directly ahead is occupied, switch if the space in the other lane directly across is not occupied.
2) “Faster-switch:” if the car directly ahead in the neighboring lane is moving faster, switch if there is space available.

The graph above compares the two strategies. It shows the percent improvement of the rogue’s average speed compared to the average speed of the rest of the cars as a function of the car density. When density is low and traffic jams are rare, switching lanes has almost no effect on your average speed for both strategies. When the density is high and traffic jams are abound, switching can make you go slower than the rest of the traffic. The reason is that when a space in the neighboring lane opens up, it is likely to be at the tail end of a jam whereas the jam in the lane you just switched out of might be already partially cleared. The final remark is that the “Stop-switch” strategy is significantly better improving the speed by as much as 35% whereas the best “Faster-switch” can do is a 15% improvement.

Finally let me mention that if all cars switch lanes and use the same strategy, nobody wins. All cars move with the same speed on average. That average speed could be smaller or larger (depending on the car density and the switching strategy) than in the case when everybody says in lane. The graph below explains why everyone is so keen on the advice “Stay in lane!” It turns out that if everyone uses the “Faster-switch” strategy, the average speed is drastically lower for everyone than if everyone stays in lane! The reason for this dramatic result is that when you change lanes, the car behind is likely to slam on the brakes which slows everyone down.

3 Responses

1. Sam said, on June 28, 2011 at 9:05 am

Very interesting post :) too bad people are generally too selfish to “stay in lane” for the good of the group!

• Alexander Lobkovsky Meitiv said, on June 28, 2011 at 9:26 am

Yes, this is a clear case of the “tragedy of the commons.” A few selfish individual benefit as long as everyone sticks to the rules. If everyone breaks the rules, then all are even worse off.

2. Quora said, on December 3, 2014 at 12:59 am

Does frequently changing lanes on a crowded highway actually shorten the amount of time it takes to arrive at your destination?

Executive Summary—it all depends. I don’t know for sure, but I used to do a lot of driving on the M1 in the UK, which makes many American roads look just empty, and I tried both strategies at different times, or would simply mentally ‘mark’ a car in…
The content of the passage is a discussion about traffic flow and lane switching strategies, including a comparison of two specific strategies: "Stop-switch" and "Faster-switch." The passage also includes a brief explanation of a traffic flow model and the results of simulations comparing the effectiveness of the two strategies.
no_question

the passage does not contain a direct mathematical question, but it does present a problem that can be analyzed mathematically. however, the analysis and results are already provided in the text, so there is no unanswered mathematical question.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
What can scientific models tell us about the world?

Should you switch lanes in traffic?

Posted in Statistics, Transportation by Alexander Lobkovsky Meitiv on June 24, 2010

Switching lanes in heavy traffic can indeed increase your average speed if done right.

If you drive like me, you have no patience for bumper to bumper traffic. There is gotta be a way to beat it somehow, right? Do you sneak into an opening in a neighboring lane if it is moving faster? Do you set goals like: “when I get in front of that van, I’ll switch back?” It doesn’t always seem to work. A lane that was zooming by you comes to a dead stop when you switch into it. If the motion of each lane is random, is there a way to switch lanes and move faster than a car that stays in lane?

It turns out there is a way to beat the traffic. To show this we will use a simple model of traffic flow introduced by Nagel and Schrekenberg (see the previous post). The model consists of a circular track with consecutive slots which can be empty of occupied by cars. Cars have an integer velocity between 0 and vmax. As we saw in the previous post, simple rules for updating the positions and velocities of the cars can reproduce the traffic jam phenomenon thereby a dense region forms in which the cars are at a standstill for a few turns and then, as the jam clears in front of them, the cars accelerate and zoom around the track only to be stuck in the jam again. The jam itself moves in the direction opposite to that of the cars.

Now imagine that we put two of the circular tracks (or lanes) side by side. For starters, let’s require all cars except one to stay in their respective lanes. One rogue car can switch lanes. Can the rogue with the right lane switching strategy move faster than the rest of the cars on average? The answer is most certainly yes although finding the best lane switching strategy is a difficult computational problem. What we are going to do here is compare two lane switching strategies that at first sight seem equally good. What we will discover is that it the lane changing strategy matters. As you might have suspected, if you don’t do it right, you might actually move slower than the rest of the traffic!

Here are the two simple strategies we will compare (I suggest you read the previous post for the description of the model):

1) “Stop-switch:” if the slot directly ahead is occupied, switch if the space in the other lane directly across is not occupied.
2) “Faster-switch:” if the car directly ahead in the neighboring lane is moving faster, switch if there is space available.

The graph above compares the two strategies. It shows the percent improvement of the rogue’s average speed compared to the average speed of the rest of the cars as a function of the car density. When density is low and traffic jams are rare, switching lanes has almost no effect on your average speed for both strategies. When the density is high and traffic jams are abound, switching can make you go slower than the rest of the traffic. The reason is that when a space in the neighboring lane opens up, it is likely to be at the tail end of a jam whereas the jam in the lane you just switched out of might be already partially cleared. The final remark is that the “Stop-switch” strategy is significantly better improving the speed by as much as 35% whereas the best “Faster-switch” can do is a 15% improvement.

Finally let me mention that if all cars switch lanes and use the same strategy, nobody wins. All cars move with the same speed on average. That average speed could be smaller or larger (depending on the car density and the switching strategy) than in the case when everybody says in lane. The graph below explains why everyone is so keen on the advice “Stay in lane!” It turns out that if everyone uses the “Faster-switch” strategy, the average speed is drastically lower for everyone than if everyone stays in lane! The reason for this dramatic result is that when you change lanes, the car behind is likely to slam on the brakes which slows everyone down.

3 Responses

1. Sam said, on June 28, 2011 at 9:05 am

Very interesting post :) too bad people are generally too selfish to “stay in lane” for the good of the group!

• Alexander Lobkovsky Meitiv said, on June 28, 2011 at 9:26 am

Yes, this is a clear case of the “tragedy of the commons.” A few selfish individual benefit as long as everyone sticks to the rules. If everyone breaks the rules, then all are even worse off.

2. Quora said, on December 3, 2014 at 12:59 am

Does frequently changing lanes on a crowded highway actually shorten the amount of time it takes to arrive at your destination?

Executive Summary—it all depends. I don’t know for sure, but I used to do a lot of driving on the M1 in the UK, which makes many American roads look just empty, and I tried both strategies at different times, or would simply mentally ‘mark’ a car in…
user
The content of the passage is a discussion about traffic flow and lane switching strategies, including a comparison of two specific strategies: "Stop-switch" and "Faster-switch." The passage also includes a brief explanation of a traffic flow model and the results of simulations comparing the effectiveness of the two strategies.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question, but it does present a problem that can be analyzed mathematically. However, the analysis and results are already provided in the text, so there is no unanswered mathematical question.