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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

• Queue capacity utilization is the amount of time the service process 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

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