Little's Law Notes

[Tom]

I'm having trouble following the examples in the printed notes for
Little's Law.

The example at the end of page 3 states "Clearly, W = 0 , R = 1 , U = 1
⁄ 3 and X = 1 ."

It is clear to me that the wait time is 0 since nothing waits for
service because there is one user, and the response time is 1.

The throughput confuses me, though. X = n/L , the number of requests per
unit time. The example is 9 seconds, so L = 9, and the number of
requests is 3, so X = 1/3, right?

Well that makes sense, seeing as utilization is U = XS, where S is
defined in the question as 1, so therefore U = 1/3(1) = 1/3, the stated
answer.

However, it is "clear" that X = 1. Why is this so? Is this a mistake or
is this some different "X" that doesn't appear in the utilization
calculation?

This seems to continue for the following examples as well. The one with
4 users you define X as X = N ⁄ ( Z + S + W ), plugging in the variables
given N = 4, Z = 2, S = 1, and W = 1, X should be 1 (which follows that
U = 1, which it is), however the example says "In this case, W = 1 , R =
2 , U = 1 and X = 3"

[Kshitij Mehta]

I believe you're right. I worked with a friend and we came to the same
conclusion as you. Although, confirmation from the prof would be good.

Post by Tom
I'm having trouble following the examples in the printed notes for
Little's Law.
The example at the end of page 3 states "Clearly, W = 0 , R = 1 , U = 1
⁄ 3 and X = 1 ."
It is clear to me that the wait time is 0 since nothing waits for
service because there is one user, and the response time is 1.
The throughput confuses me, though. X = n/L , the number of requests per
unit time. The example is 9 seconds, so L = 9, and the number of
requests is 3, so X = 1/3, right?
Well that makes sense, seeing as utilization is U = XS, where S is
defined in the question as 1, so therefore U = 1/3(1) = 1/3, the stated
answer.
However, it is "clear" that X = 1. Why is this so? Is this a mistake or
is this some different "X" that doesn't appear in the utilization
calculation?
This seems to continue for the following examples as well. The one with
4 users you define X as X = N ⁄ ( Z + S + W ), plugging in the variables
given N = 4, Z = 2, S = 1, and W = 1, X should be 1 (which follows that
U = 1, which it is), however the example says "In this case, W = 1 , R =
2 , U = 1 and X = 3"