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What is the average length of a queue of cars? (2023)
Some time ago I was driving on a twisty mountain road, stuck in a slow-moving queue of cars as it was impossible to overtake safely. Out of boredom, I was wondering how many cars were in the queue, and, more generally, what would be the average length of queues in this road. Let’s find out!
Some time ago I was driving on a twisty mountain road, stuck in a slow-moving queue of cars as it was impossible to overtake safely. With a little bit more insight, one could realize that, assuming the velocities to be i.i.d., the number of vehicles in a queue is a random variable with Geometric distribution. Each Bernoulli trial corresponds to a new vehicle entering the road and checking whether it is not faster than the queue of cars in front of it.
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