xhoster_at_gmail.com wrote:
> "VC" <boston103_at_hotmail.com> wrote:
>
>>Hi,
>>
>><xhoster_at_gmail.com> wrote in message
>>news:20050609141630.752$66_at_newsreader.com...
>>
>>>Frank van Bortel <frank.van.bortel_at_gmail.com> wrote:
>>
>>[... skipped ...]
>>
>>
>>>>Why would a mirrored write be slower for writes? OK, as slow
>>>>as the slowest disk, but those differences can (should!) only
>>>>be marginal.
>>>
>>>If each write takes a random amount of time uniformly distributed
>>>between 0 and 1 (in whatever units of time would make sense), then the
>>>average wait for one write is 0.5, while the average wait for slower of
>>>two
>>>writes is 0.6667.
>>
>>I wonder how you arrived at the number (0.6667)...
>
>
> Probability and calculus. By definition of uniform 0 to 1,
> Pr(rand<=x)=x. since they are independent Pr(max(rand1,rand2)<=x) = x^2.
> Convert cdf to pdf by differentiation gives pdf(max=x)=2x.
> The average is integration x*dx*pdf(x) over 0 to 1
> which is integration 2x^2 which is 2/3x^3|0to1, which gives 2/3.
>
> And then I simulated it in Excel, just to be sure.
>
>
>
>>Let's assume that track seeks are distributed uniformly (each track,
>>from a given position, is accessed with the same probability).
>
>
> I had thought rotational waits were dominant over head-seek waits
> these days.
>
>
>>Further,
>>let's assume we have two *identical* disks. Then, the seek distance is
>>a random variable Xr = min(X1, X2) for reads and Xw=max(X1,X2) for
>>writes. Then, with another huge assumption of X1 and X2 being
>>independent, it can be shown that the expected seek distance would be
>>approx. 0.2*n for reads and 0.46*n where n is the number of tracks. For
>>a single disk, both values are n/3. So, for reads we would have about
>>39% gain in performance and for writes about 38% loss.
>
>
> You could be more explicit in the "it can be shown" part, but that's
> good enough for me.
>
>
> Xho
How do your extrapolations compare to the real numbers contained here?
http://www.netapp.com/tech_library/3145.html
See Section 4
--
Daniel A. Morgan
http://www.psoug.org
damorgan_at_x.washington.edu
(replace x with u to respond)
Received on Sun Jun 12 2005 - 15:09:51 CDT
