Pedro Arantes
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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 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/M/M/1/\infty Queue, you can predict these characteristcs:

    • Percent Capacity Utilization =ρ= \rho
    • Percent Unblocked Time =1ρ= 1 - \rho
    • Number of Items in Queue =ρ21ρ= \cfrac{\rho^2}{1-\rho}
    • Numbers of Items in System =ρ1ρ= \cfrac{\rho}{1-\rho}
    • Percent Queue Time =ρ= \rho
    • Cycle TimeValue-Added Time=11ρ\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/M/M/1/\infty queue at XX percent utilization, you're choosing to use XX 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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