Pedro Arantes
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Most of the Damage Done by a Queue Is Caused by High-Queues States

Low-queue states are more probable than high-queue states, but high-queue states are more important because they delay more jobs.
#cycle-time
Zettelkasten, November 14, 2022.

Notes

The probability of finding a queue in a specific quantitative state (low or high-queue state) is a function of capacity utilization. Low-queue states are more probable than high-queue states, but high-queue states are more important because they delay more jobs. As a result, they strongly influence cycle time and can cause more economic damage and waste to the project.

The State Probability\text{State Probability} of an M/M/1/M/M/1/\infty queue to have nn jobs in the system is:

State Probability=1ρρn\text{State Probability} = \frac{1-\rho}{\rho^n}
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