I just came across an interesting question:
- let's say we have a security waiting line at an airport which can physically provide space for 3500 passengers at the same time
- we know that the personnel at the entrance will let in 30 new passengers per minute (avg) into the waiting line but they do so in batches of 10 passengers at the same time (so 10 passengers every 20 seconds)
- the personnel at the exit will let out 15 passengers per minute but in average (processing time here is linear)
Obviously as the exit rate is slower than the entry rate at some point the physical capacity of the waiting line would get reached. The question would be at what point in time or after how many passengers will that be the case?
I find it hard to formulate the problem mathematically. Any hints to some useful theory would be appreciated :-)
Cheers!