Dieter Maurer wrote:
Jens Vagelpohl wrote at 2006-1-31 15:07 +0000:
On 31 Jan 2006, at 15:01, Jake wrote:
That article contains little information to back up the conclusions, and some of it is patently wrong. Another case of hearsay and half- thruths being propagated by well-meaning but uninformed parties.

There is a convincing example (I think from Matt Kromer) what
happens to "mean response time" when the number of threads
is increased from 1 to 2:

  Assume you have 2 units of work. If you have a single
  thread, 1 unit is done, then the second. The
  mean response time is (1 + 2) / 2 = 1.5.

  Now assume you have two threads (but a single processor).
  Both threads work (quasi) parallel but have only half of the
  processor power. Both will take 2 time units to perform
  their unit of work. The mean response time is (2 + 2) / 2 = 2.

This is specious reasoning from a statistical point of view. You never have only two requests. To have a proper statistical evaluation, you need a theoretical model of the distribution of requests over time. This can be as simple as "a request every t". Then you have a continuous flow of requests, and the two means become equal.

Just try it with 4 units of work and equivalent time distribution as in the original example:
- Case 1: (1+2+3+4)/4 = 2.5
- Case 2: (2+2+4+4)/4 = 3

If you generalize to n units of work, you'll get (the math is simple):
- Case 1: n(n+1)/2n = n/2+0.5
- Case 2: 4((n/2)(n/2+1)/2)/n = n/2+1

Which are equivalent to n/2 when n grows.


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