$6\mathrm{.}6$ Little's Law for Mean Slowdown

Recall that Little's Law relates the mean response time to the mean number of

jobs in any ergodic system. It is interesting to ask whether a similar law can be

proven that relates mean slowdown to the mean number of jobs in the system.

We do not have an answer. However, you should be able to derive the following

bound in the case of a single FCFS queue:

$E[$ Slowdown $]\frac{E[N]}{}*E[\frac{1}{S}]$

where $S$ represents job size, $N$ represents the number of jobs in the system, and

$$ is the average arrival rate into the queue.