Please Explain a simple Formula, calculating time in-between a call queue I have a simple algebra formula, proven to work. But I need help in understanding why it works.
The Scenario: I work at a call center, and am trying to calculate the time free in-between calls. I have the 3 variables, provided by Live data:


*

*Staff Available (not on calls)

*Staff Busy (on calls)

*Average call length of 5 minutes


So once I end a call, I go to the back of the line of available staff before I get the next call.
This is the formula, tested to work:
: (Staff Available / Staff Busy) * 5 minutes call length = Time in-between calls
Example: 100 staff. 80 busy, 20 available. [20/80 * 5 = 1.25 minutes]
Example: 100 staff. 50 busy, 50 available. [50/50 * 5 = 5 minutes] (Which is expected, as we are double staffed.)
Example: 100 staff. 20 busy, 80 available. [80/20 * 5 = 20 minutes]

Question - Why does this equation work? I must be taking shortcuts. Why do we divide Available/Busy instead of Available/Total? 
I'd greatly appreciate any explanation. Thank you very much.
-Brennan
 A: There are different ways of looking at it. One way is this: $${\mathrm{Average \ Gap} } = {{\mathrm{Idle \ Time}} \over {\mathrm{Number \ of \ Calls}}}$$
Now take your 80% busy, 20% available case. In an hour, your idle time will be 20% of the time, or 12 minutes. The average number of calls will be the remaining time (48 minutes) divided by the average length of a call (5 minutes.) 
This results in 1.25 minutes. If you clean it up by removing the artifice of using one hour, you will get your shortcut version. 
A: Let's suppose any particular staff's workload can be represented by the busy staff and the available staff. Then, the staff spends $\frac{\text{Busy}}{\text{Total}}$ of the time taking calls and $\frac{\text{Available}}{\text{Total}}$ free. Since the calls are on average $5$ minutes long, if he take $5$ minutes taking calls, it follows that the amount of time free he has on average is $t$, where:
$$\frac{5}{\frac{\text{Busy}}{\text{Total}}}=\frac{t}{\frac{\text{Available}}{\text{Total}}}$$
Simplifying, we get the formula you stated:
$$t=\frac{\text{Available}}{\text{Busy}}\times5$$
