## Notes

Knowing queue capacity utilization ($\rho$) allows you to predict the following:

- the percent of the time that the arriving work will find the server 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 characteristics:

- 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 $= \rho$
- $\cfrac{\text{Cycle Time}}{\text{Value-Added Time}} = \cfrac{1}{1-\rho}$

This property is helpful from a practical perspective, but it's often tough to directly measure capacity utilization in product development processes. Moreover, it's problematic because the ratio of **demand** and **capacity** are individually hard to estimate.

## Questions

- What methods can measure queue capacity utilization in product development processes?