How do I calculate response time of a multiple core cpu when given certain information? On my homework the question asks:


  A program executes serially in 200 seconds. If it is parallelized, 7
  seconds of overhead are required for synchronization, locking, and
  communication. Compute the execution time, ideal speedup (if there
  were no overhead required), actual speedup, and the percentage of the
  ideal speedup that is obtained for 1, 2, 4, 8, 16, 32, 64, and 128
  processors.


How do I calculate the answer to this? It is not something that has been covered in class yet and the homework is due before the next time the class meets.

My guess is that I divide 200 seconds by the number of cores and then add 7 * # cores to get the total response time. I don't think it is that simple.

Edit:
Amdahl's law says: T(n) = T(1)[B + 1/n(1-B)] where B is the percentage of the algorithm that is not parallelized and n is the number of cores. If I assume that the 7 seconds mentioned is the part of the algorithm that is not parallelized, I can get the percentage by saying:

      7sec * n
B  =  --------
       200sec 


Then I plug the value for B into Amdahl's equation. Coencidentally, this gives me  the same answers as I got before when I did my own formula:

 200                   
 ---  +  [7 * (n - 1)] 
  n     


After doing a little bit of algebra, I discovered that my formula is a simplified version of Amdahl's formula. Of course all of this assumes I am correct when I read the question as if the 7 seconds are the part of the algorithm that is not parallelized.

Thanks for looking,

Zach
I think you don't need to add (7*number of cores) to the total response time. The overall execution time requires just 7 more seconds, because each piece of code is running in parallel with others. So just divide 200 by the number of cores and add 7 to it. Obviously in the ideal case you don't need to add anything. Also look at the Amdahl's law in the Wikipedia... It also states a law about speedup with parallelism and these problems share the same concept.