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Considering seek time (Rs=5ms) as given above and I/O request arrives at a rate 100 I/Os per second.

Calculate Utilization of I/O controller (U), Total Response time (R), Average Queue size and Total time spent by request in a queue.

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Given :

Rs = 5 ms

I/O request rate (a) = 100 IOPS, i.e. $R_a = \frac{1}{a} = \frac{1}{100}$

i.e. = $\frac{1}{100} \times 10^3 ms$

= 10 ms

(a) Utilization = % $ U = \frac{Rs}{Ra}$

= $\frac{5}{10} = 0.5$

= 50%

(b) Total Response time = R = $\frac{Rs}{1-U}$

= $\frac{5}{1-0.5} = 10 ms$

(C) Average Queue size = $\frac{u^2}{1-u}$

= $\frac{(0.5)^2}{1-0.5} = 0.5$

(d) Time spent by request in queue = U x R

= 0.5 x 10 = 5 ms.

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