Question

Consider a system with the main memory size of 32MB and each process size 4MB, if each process spends 80% of its time in doing I/O, what is the CPU utilization percentage? (Assuming there is no virtual memory and the space required for OS is negligible)

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should'nt the answer be 20% since for,80% of time,process uses I/0.

it is given tht main memory size if 32MB and process size if 4MB,so at max 8 processes can perform I/0 in parallel.so at that CPU will be free and therefore its utilisation will be only 20%.

Comments

Akriti, P1 excutes for some time $(0-t_1)$ goes to I/O, P2 executes (t_1 - t_2) goes to I/0, P_3 executes (t_2 - t_3) goes to I/0 and so on for all processes and at some time all processes are doing I/O and CPU is free.

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but when P1 has gone for I/O then CPU can take other process,like P2 or P3

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@mcjoshi. SO, when all processes are doing IO, CPU isnt forcefully idle. Its part is completed and its idle because there is no work for CPU to be done.

Answer 1

The CPU utilization can be modeled by the formula
    CPU utilization = 1 - pⁿ 
    where there are n processes in memory and each process spends a fraction p of its time waiting for I/O

So, here number of processes= 32 MB / 4 MB = 8

Answer= 1 - (0.8)⁸ =0.8322 = 83.22%

Note: Here, CPU utilization is a function of n, which is called the degree of multiprogramming.

Source: 

http://www.cs.wichita.edu/~chang/lecture/cs540/lecture/ch4.ppt

Comments

@smartmeet,

i have some doubt here.8 proccesses can do I/O at the same time,so when THESE 8  are perfroming i/o ,what will CPU be doing??what is the point of giving 8 processes in the question?