With M equals 1, we simply get 4 divided by 5 equals to 80%.

Now how does it look down here?

If I pool two such systems, I have no impact

on the processing time, however, I have now a shorter inter-arrival time.

I here had 12 customers arrive per hour.

If I pool, I have to have 24 customers per hour showing up.

So pooling at least two similar systems, I move from 12 to 24 customers per hour,

meaning an inter-arrival time from five minutes to 2.5.

And notice oftentimes students get confused on this point.

A shorter inter-arrival time means more demand.

Finally I have an M=2,

M =2, P= 4, A = 2.5.

If I plot this into the formula, P divided by A times M,

I'm going to get a utilization of 4 divided by 2 times 2.5.

And voila, it's the same 80% as I had before.

So pooling in and by itself actually does not change the utilization,

but it will impact the waiting time.

Let's try this out in our Excel spreadsheet.