1.15 [5] When a execution time on each processor is comprised of its fair share

Question

1.15 [5] When a execution time on each processor is comprised of its fair share of the computing time and the additional overhead time required to "lock" critical shared sections of memory and/or to send data from one processor to another. program is adapted to run in a multiprocessor system, the Assume a program requires 200 sec of execution time on one processor. When run on p processors in a multi-processing system, each processor requires t/p sec, as well as an additional 3 sec of overhead, irrespective of the number of processors. Some definitions: e exec time/proc- how long each processor spends executing your program (do not include overhead) time w/overhead-the prior calculation but with overhead added ideal speedup-the ratio of the original execution time to the execution time per processor without overhead (should be a positive integer) · actual speedup-the ratio of the original uniprocessor execution time to your time with overhead (should be always 21.0) actual to ideal speedup-this is the "tax" you pay. (Should always be $1.0) (10 pts) Compute the per-processor execution time for each of the multi-processor arrangements shown by completing the following table. a. exee time time w actual actual / procs proc overhead speedup speedup 200 200 8 16 32 64 128 in Hint: You can copy the table into Excel or Google Sheets, and paste the result back here if you like. You 'll have to add the etc. to calculate your formulas answers b. (1 pts) Which number of multiprocessors results in the greatest speedup? Which number of multiprocessors results in the highest actual/ideal ratio, c. (1 pts closest to the 1.00 of the single processor?

Explanation / Answer

Solution (a):

Here, on single processor:

but on multi processor :

For no. of processors = p = 2 :

For no. of processors = p = 4 :

For no. of processors = p = 8 :

For no. of processors = p = 16 :

For no. of processors = p = 32 :

For no. of processors = p = 64 :

For no. of processors = p = 128 :

Solution (b): 128 processors will give greatest speedup.

Solution (c): Highest actual to ideal speedup ratio will be 0.9708737864 in case 2 processors.

procs exec time/proc time w/overhead ideal speedup actual speedup actual/ideal 1 200 200 1 1 1 2 100 103 2 1.941747573 0.9708737864 4 50 53 4 3.773584906 0.9433962264 8 25 28 8 7.142857143 0.8928571429 16 12.5 15.5 16 12.90322581 0.8064516129 32 6.25 9.25 32 21.62162162 0.6756756757 64 3.125 6.125 64 32.65306122 0.5102040816 128 1.5625 4.5625 128 43.83561644 0.3424657534

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