Note that terminology in this space is very important and subtle. 7 million people are arrested each year, and > 600K are sent to prison, but the total number of people in prison (and number that are incarcerated one way or another) is much lower than those numbers suggest. The total incarcerated population is about 1.75 million.
2% of the total population arrested each year sounds like a lot!
If we believe chatgpt, then the median time in prison is a couple of months.
I'm unsure about the math: "The arrival rate $\lambda$ is the rate at which people arrive in the queue, and the service rate $\mu$ is the rate at which people are served and leave the queue. In a stable system, the service rate must be greater than the arrival rate, otherwise the queue will grow indefinitely.
Given that the total number of people in the queue $n$ is 1750000 and the arrival rate $\lambda$ is 600000 people per year, we can find the service rate $\mu$ by dividing the total number of people in the queue by the arrival rate:
$\mu = \frac{n}{\lambda} = \frac{1750000}{600000} \approx 2.92$ people per year.
This means that on average, about 2.92 people are served and leave the queue every year.
The median waiting time in the queue can be calculated using the formula for the median of an exponential distribution, which is $\frac{\ln(2)}{\mu}$.
So, the median waiting time in the queue in years is $\frac{\ln(2)}{2.92} \approx 0.237$ years."
> 2% of the total population arrested each year sounds like a lot!
It's probably mostly people getting arrested multiple times.
But yeah, there's a lot of arrests where police in other countries would have just ID'd people and sent them on their way. Arrests are simply the default operating procedure in the US, which is likely related to the fact that the lack of reliable national ID makes it harder to identify people on the spot.
https://www.prisonpolicy.org/reports/pie2023.html
Note that terminology in this space is very important and subtle. 7 million people are arrested each year, and > 600K are sent to prison, but the total number of people in prison (and number that are incarcerated one way or another) is much lower than those numbers suggest. The total incarcerated population is about 1.75 million.