this post was submitted on 08 Sep 2023
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Queuing theory can have some fun surprises.
Can you elaborate on the math here? (I believe you, I just want to understand the simulation parameters better).
Also, in this simulation are the customers arriving in equally spaced intervals or is random arrival time within the bounds assumed?
In the linked article they are arriving randomly. It takes 10 minutes per customer and they arrive every 10.3 minutes.
Aren't they arriving slightly slower than can be served, according to these numbers:
If one customer takes 10 minutes to serve, you can serve 6 customers in an hour
and you get 5.8 customers every hour, which is less than 6
So you serve 6 customers, meaning you have a leftover capacity of 0.2 per hour or 1 extra customer every 5 hours
Maybe the numbers are switched over or I am misunderstanding something
Edit: nevermind, read the link in the thread and realised I treated the average as the actual serving time and I'm guessing that's what makes it non intuitive. I'm still not entirely clear on how it works.
They're arriving slower than they can be processed. So the line shrinks slowly it there's a line.
Not OP, but this website should explain everything.
Thanks! This article really clears up a lot of the details that help the simulation make sense.
Assume the bank opens up to a long line and it makes sense.
Intuitive way to see why is that 6.1 customers per hour would mean infinite waiting time (when it reaches a steady state)