Queueing for Performance

Find bottleneck device:

1. Convert to common time units
2. Calculate the visitation ratios $V_i$:
   1. This is the number of times a device is used in each transaction. Divide by number of transactions
3. Calculate device utilization ${\rho }_i=\lambda \times s$
4. Calculate the CPU service time $s=\frac{\rho }{\lambda }$, this is what helps us find the bottleneck device
5. Calculate the device time $V\times S$
6. Find the bottleneck device
7. Calculate the maximum transaction rate
8. Calculate the average transactions time

We can predict the maximum rate of transactions using the bottleneck device as $\frac{1}{S_i{V}_i}$ which is called the saturation. If $\lambda$ exceeds the saturation, we cannot keep up with requests.

Note

The assumption here is that we know the service times for each device which is typically not true.

We can get the average size of the device queue from perf (W). Combining W with $\lambda$ we can solve for service time (s):

• $s=\frac{-w\pm \sqrt{w^2+4w}}{2\lambda }$