Be Excellent To Each Other

Hiya!
I've been thinking on this overnight but not certain how to do it and wondered if any of my clever pals could help me.

I have three machines, we'll call them A, B and Z. A and B feed Z. If A has a cycle time of 228 seconds, B has a cycle time of 120 seconds and Z has a cycle time of 65 seconds, what is the easiest way to build a calculation that shows how quickly Z can empty a queue of 20 items from A and B, considering A and B are still running and therefore topping up the queue?

How do I chart that, to show the point where the queue is taken care of?

Do you need to chart it?

Take a time period divisible by both of the A/B machines, such as 43,320 seconds.

In that time Machine A has added 190 items (43320/228)
In that time Machine B has added 361 items (43320/120)

A total of 551 items. How long does that take Z to remove?

65*551 = 35,815.

So it can easily keep them clear.

For 20 items I guess you could chart them, to show on which seconds the two machines feed it. So the first sequence would be:

A - 228, 456, 684, 912, 1140, 1368 etc
B - 120, 240, 360, 480, 600, 720, 840, 960, etc

Mark the seconds they hit the queue, and if Z is 'busy' at that time.

I need to go to work now though.

Thanks for taking time to answer

Now-assume the queue started with 20 items in it. How long would it take Z to empty the queue, with A and B continuing to fill it?

It might help to understand why you want to know since there are a number of different ways to do it

One way to look at it would be just to run 3 timelines for each machine which would show the numbers handled at each point (with possibly a 4th row for current queue) and then just look at specific times - so at 4550 , machine Z will have handled 50 over the initial 20 that it started with , and machine A will have added 37 and machine B will have added 20 - total queue remaining is 7 - go another jump ahead and see what the numbers look like for that point.

Jumping ahead to 6175 Z has handled 75 over the original 20 , A has added 51 , B has added 27 , total queue is 3
And then jumping to 7150 Z has handled 90 over the original 20 , A has added 59 , B has added 31 so the queue is zero at that point.

FYI given your job is there not an extra variable going to be dropped in here which is times machines are out for maintenance ?

The scenario I'm concentrating on is a breakdown at Z allowing a queue to built up from A and B. There is space in the system for this but at some point, say 20, the system is full and A and B stop. Once Z restarts, I want an easy way to figure out how long Z will take to get the system empty again, or at least back under control (say a queue of 3 at most).
To complicate matters, A and B have various products they run and so cycle time can vary wildly at both of them. Therefore, I would like to build a spreadsheet where you can select the product and therefore cycle time at A and then at B, figure out if Z can keep up and figure out at what point a build back should begin worrying you.
Then, I can introduce X, Z's counterpart.

Okay so that should be do-able in Excel , I did a very simplistic set with 3 sets of rows , set 1 is time in 65 second chunks and a number incrementing below (total handled) , set 2 is time in 120 second chunks and a number below (total added by machine A) and set 3 is time in 228 second chunks and a number below (total added by machine B) and just looked at the state at different points , you can do a bit more programmatically to automate all of that (beyond me but not beyond some other people on here i'm sure)