Three ways to go about queue sizing

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  1. Start every limit at 1.  Add tokens 1 at a time until one person is always busy, then apply Theory of Constraints.
  2. Start every limit at an arbitrarily large value, like 10.  Subtract tokens 1 at a time until flow is observed.  Then start looking for a way to remove 1 more.
  3. Create a Value Stream Map and measure the time-on-task distribution of each activity. Use Little’s Law to calculate the corresponding queue sizes.

Notice that “match the number of people currently available” is not one of the ways.  You’re trying to discover how many people you need not how many you have.