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From Berin Loritsch <blorit...@apache.org>
Subject Re: Adaptive Caching [was Re: initial checkin of the Scheme code]
Date Thu, 13 Dec 2001 15:34:26 GMT
Stefano Mazzocchi wrote:

> Talking about placing too many irons in the fire :)
> 


Stefano, please forgive my ignorance, as I have an Associates Degree in
Music Recording, and not a traditional CS degree.  I haven't had the
higher math classes you and many others have had here.

I understand Algebra and Trigonometry ok, so if we can simplify these
algorithms into a "pseudo-code" so I can wrap my head around them, I
will be happy to jump in the discussion.  As it is now, It's going
over my head.

I understand the Calculus ideas of functions (i.e. V(r,t)).  What throws
me are the Sigmas (I studied Ancient Greek, so I know what the letters are).
I know they are meant to represent sums, or statistical data.  I don't know
what the letter above the sigma or below the sigma is supposed to signify.

If you don't feel up to giving me a quick math lesson so I can grok the
concepts fully, can you point me to a resource where I can teach myself?

> Thus, given
> 
>  r        := resource
>  t        := time of the request
>  V(r,t)   := validity estimation cost
>  P(r,t)   := production cost when caching is not performed
>  Pc(r,t)  := production cost when caching is performed
>  l(r,t)   := lookup cost
>  s(r,t)   := storage cost
> 
> and
> 
>  I := sequence of invalid requests time [1,n]
>  V := sequence of valid request time [1,m]
> 
> we have that
> 
>                n
>                --
>  Invalid(r) =  \  (V(r,I ) + Pc(r,I ) + s(r,I ))
>                /        i          i         i 
>                --
>               i = 1
> 
> and
> 
>              m
>              --
>  Valid(r) =  \  (V(r,I ) + L(r,I ))
>              /        j         j
>              --
>            j = 1
> 
> and
> 
>             n                m
>             --               --
>  Ptot(r) =  \  P(r,I )   +   \  P(r,V )
>             /       i        /       j
>             --               --
>           i = 1             j = 1
> 




-- 

"They that give up essential liberty to obtain a little temporary safety
  deserve neither liberty nor safety."
                 - Benjamin Franklin


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