What is the average length of a queue of cars? (2023)
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What is the average length of a queue of cars? (2023)
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Re: What is the average length of a queue of cars? (2023)
#2> Assume that the road has a single entry, no exits, and is infinitely long
I couldn't help but think that the author forgot to assume the road is inelastic and has no mass...
Re: What is the average length of a queue of cars? (2023)
#3> Assume that the road has a single entry, no exits, and is infinitely long I couldn't help but think that the author forgot to assume the road is inelastic and has no mass...
Spherical cars too?
Re: What is the average length of a queue of cars? (2023)
#4The conclusion looks correct for the wrong question: isn't this the formula for the number of queues?
The first car starts a queue with probability 1, the second car starts a queue if and only if it is slower (probability 1/2), the third car starts a queue if and only if it is the slowest so far (probability 1/3), and so on. Total is 1 + 1/2 + 1/3... which is the formula at the end of the blog post, with an off-by-one error.
The average queue length should be the number of cars divided by this harmonic sum. Which also diverges to infinity.
Re: What is the average length of a queue of cars? (2023)
#5[deleted]
Re: What is the average length of a queue of cars? (2023)
#6Re: What is the average length of a queue of cars? (2023)
#7[dead]
Re: What is the average length of a queue of cars? (2023)
#8> Assume that the road has a single entry, no exits, and is infinitely long I couldn't help but think that the author forgot to assume the road is inelastic and has no mass...
It's a highway, basically.
Re: What is the average length of a queue of cars? (2023)
#9> Moreover, if the reasoning above was correct, observing a queue of 22,849 cars would be essentially impossible!
One of the cars in the 100,000 cars is going to be the slowest car, and when that car appears every car behind it will join that queue
So on average wouldn't you expect there to be one large queue of 50,000 cars at the back?