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# Queue Capacity Utilization

Queue capacity utilization is the amount of time the service process is working (not idle).
#queues
Zettelkasten, August 04, 2021
## Notes - Queue capacity utilization is the amount of time the [service process](/zettel/queueing-theory) is working (not idle). - Knowing capacity utilization allows you to predict: - the percent of time arriving work will find the resource busy; - the average number of items in the queue; - the average number of items in the system; - the percent of overall cycle time is queue time; - the ratio of cycle time to value-added time. - For $M/M/1/\infty$ Queue, you can predict these characteristcs: - Percent Capacity Utilization $= \rho$ - Percent Unblocked Time $= 1 - \rho$ - Number of Items in Queue $= \cfrac{\rho^2}{1-\rho}$ - Numbers of Items in System $= \cfrac{\rho}{1-\rho}$ - Percent Queue Time $= \rho$ - $\cfrac{\text{Cycle Time}}{\text{Value-Added Time}} = \cfrac{1}{1-\rho}$ - Percent capacity utilization and percent queue time are identical for a random queue. - If you operate an $M/M/1/\infty$ queue at $X$ percent utilization, you're choosing to use $X$ percent queue time. - Queues grow when you approach 100 percent utilization, they become exponentially large. - It's hard to measure capacity utilization directly. ## References - [The Principles of Product Development Flow](/books/the-principles-of-product-development-flow) - [Tero Parviainen. A Dash of Queueing Theory](https://teropa.info/blog/2016/04/02/a-dash-of-queueing-theory.html)
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