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 valueadded 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 $= \rho$
 $\cfrac{\text{Cycle Time}}{\text{ValueAdded Time}} = \cfrac{1}{1\rho}$

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.