Question

Modeling multiprogramming: (a) Assume the I/O fraction time of all processes is 20%, and assume processes are independent from each other, what’s the CPU utilization, if the number of processes, n = 1, 2, 4, and 8, respectively? (b) If the I/O fraction time is 50% for all processes, what’s the CPU utilization again, if the number of processes, n = 1, 2, 4, and 8, respectively?

Answer 1

`Hey,

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Since the processes are independent of each other, they can be run parallelly.

If there are n independent processes then, CPU utilization = 1- where P is the I/O fraction time of all processes.

a) I/O fraction time of all processes =20%=0.2

For n=1, CPU utilization = 1-0.2=0.8 or 80%

For n=2, CPU utilization = 1-=0.96 or 96%

For n=4, CPU utilization = 1-=0.9984 or 99.84%

For n=8, CPU utilization = 1-=0.99999744 or 99.999744%

For n=16, CPU utilization = 1-=0.9999999 or 99.99999%

b) I/O fraction time of all processes =50%=0.5

For n=1, CPU utilization = 1-0.5=0.5 or 50%

For n=2, CPU utilization = 1-=0.75 or 75%

For n=4, CPU utilization = 1-=0.9375 or 93.75%

For n=8, CPU utilization = 1-=0.99609 or 99.609%

For n=16, CPU utilization = 1-=0.99998 or 99.998%

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