Multiple choice technology performance

On a single processor system, if the CPU utilization is u% and a transaction takes a CPU time of t seconds, the overall time including wait time for the transaction to execute is

  1. t*100/(100-u)

  2. t*u/(100-u)

  3. t*100/u

  4. t*u/100
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A Correct answer
Explanation

If CPU utilization is u%, the available CPU capacity is (100-u)%. With CPU time t, the total response time including queuing/waiting is t divided by the utilization fraction: t / ((100-u)/100) = t*100/(100-u). This formula captures queueing theory where response time explodes as utilization approaches 100%. Options B, C, D incorrectly apply the percentage.

AI explanation

By definition, utilization u% is the fraction of time the CPU is busy: u/100 = (CPU busy time)/(total elapsed time). For a transaction needing t seconds of CPU time, if the CPU is only available u% of the time, the total wall-clock time T must satisfy t = T*(u/100), so T = t*100/u... but this ignores queueing — the standard 'response time under utilization' formula (used in performance/capacity planning, e.g. Amdahl/queueing-theory style problems) is T = t/(1 - u/100) = t*100/(100-u), which correctly shows response time diverging as utilization approaches 100%. The other options either omit the (100-u) denominator structure or scale incorrectly and don't exhibit this expected blow-up behavior near full utilization.

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