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Help! I remember reading about a formula relating resource utilization to throughout in either The Phoenix Project or The Unicorn Project, but I'm struggling to find it. Need to convince leadership that we have a Brent problem.

tell your brent to put all the meetings they get pulled into on your kanban/sprint board and track them as work - once it's visible it's hard to ignore

They have it in Accelerate “Finally, many organizations measure utilization as a proxy for productivity. The problem with this method is that high utilization is only good up to a point. Once utilization gets above a certain level, there is no spare capacity (or “slack”) to absorb unplanned work, changes to the plan, or improvement work. This results in longer lead times to complete work. Queue theory in math tells us that as utilization approaches 100%, lead times approach infinity—in other words, once you get to very high levels of utilization, it takes teams exponentially longer to get anything done. Since lead time—a measure of how fast work can be completed—is a productivity metric that doesn’t suffer from the drawbacks of the other metrics we’ve seen, it’s essential that we manage utilization to balance it against lead time in an economically optimal way.” Excerpt From: Nicole Forsgren PhD, Jez Humble & Gene Kim. “Accelerate.” Apple Books. https://books.apple.com/us/book/accelerate/id1357261797

Ah yes that sounds familiar. I haven't read Accelerate, so I'm guessing the concept was repeated somewhere else.

@bryce It’s in the Resource Guide at the end of The Phoenix Project - ‘Why Do We Need To Visualize IT Work And Control WIP’. Pg 363 in my copy. I’ve used the same graph myself on occasion when talking to leadership! :)

Also in Sooner Safer Happier https://www.linkedin.com/posts/jonathansmart_bvssh-activity-6850751094855884800-phr3

I suspect the equation you mean is *Kingman’s* https://en.wikipedia.org/wiki/Kingman%27s_formula
The key for knowledge work is that variation (both in arrival rate and service time) has a strong impact on the steepness of the curve.

Wow, this group is so helpful! Thanks for pointing me in the right direction everyone!

@tom.ayerst This equation looks a lot more like what I was thinking of. I was confused about how to get an exponential graph with the equation from Little's Law. p / (1 - p) would do it.