This is like the microwave problem at work though.
My food only needs 30 seconds to microwave, but Slow Joe brought thanksgiving to work and needs to use the microwave for 4 minutes. We have 2 microwaves M1-2.
With your system this is what happens:
- Slow Joe blocks M1 with a 4 minute meal
- Several 30-60 second users cycle through M2
- Another Slow Joe blocks M2
- The queue grows until M1 is free
- The feedback loop gets worse the next iteration
Basically, you need a dedicated "express lane" for quick people to use. If there are no quick people in the queue, then a slow joe can use it. Otherwise you need to increase N such that there is always at least one unblocked lane, which might not be viable.
Indeed the main problem, counter to queuing theory, is that the individuals are not pushed anymore from behind, hence they take their time, slowly without feeling any pressure.
I've seen the same in traffic simulations.
If none of the routes are optimized for tons of traffic, 1 slow driver can gridlock an entire city at rush hour.
the simplest solution is 1 entrance line and N parallel buffet rows.