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 14th, 2022.

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

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