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aminer10

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09-25-2010
04:38 AM

41 Views

Finally my new scalability mathematical model is here...

Hello,

Ihave thought all the night, and finallymy new and general scalability

mathematical model, BETTER than Amadahl's law, is here:

Read my article, welcome

http://pages.videotron.com/aminer/scalability.htm

Regards,

Amine Moulay Ramdane.

http://pages.videotron.com/aminer/

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aminer10

Beginner

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09-25-2010
08:45 AM

41 Views

Hello,

Now to generalize my mathematical model and make it more clear,

if we are running n threads in parallel in a time interval and entering

n critical sections in the same time interval, my mathematical model

will be equal to:

Speed(t,N,,Sic,Soc) = 1 / (A + (P / N))

A = ((Sic_1 * ((_1-1) * (_1)) / (2 * _1)) + (Sic_2 * ((_2-1)

* (_2)) / (2 * _2)) + .... (Sic_n * ((_n-1) * (_n)) / (2 * _n)))/N

A = (Sum (i: 1 ->n ) (Sic_n * ((_n-1) * (_n)) / (2 * _n)))) / N

Sic_1...Sic_n: serial parts inside the critical regions(locked regions)

P: parallel part

n: number of threads (or processes)

N: number of cores

C_1...C_n: contention factors in percentage for each crtitical region

C = Number of contended threads (in the critical region) / n

and = C * n

I wrote in my other article:

http://pages.videotron.com/aminer/efficiency_availibility.htm

"So, as you have noticed you can simulate our enterprise

webserver with this mathematical analytical equation and

validate the data collected by fwptt stress webserrer tool

and try to keep T( the average response time of your HTTP requests)

bellow or equal to 5 seconds, and see also if your webserver

is scaling, and we call this also Quality control using OR

(operational research). "

So, if you want to keep the response time T 'low' in enterprise

websites, you have to reduce the logical and physical contention

can occur by reducing the Sic_1...Sic_n (i already explained how to do it)

and you must also control the by limiting for example the 'number'

of requests that can run at the same time and also scale out your

website etc...

My general scalability mathematical model is also applicable to physical

contention and logical contention.

Read more:

http://pages.videotron.com/aminer/scalability.htm

Regards,

Amine Moulay Ramdane.

http://pages.videotron.com/aminer/

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