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I found that all say that throughput is inversely proportional to response time. But I found it's confusing that if I see their relationship by their definitions, isn't each of them a reciprocal of each other?

From my point of view, if I define them by my intuition, it then goes:

Throughput: Number of task completions per time unit = $\frac{Completion}{T}$
Response Time: time cost from task's arrival to its completion = $\frac{T}{completion}$

where $T$ is the total observation time.

What did I miss? Why can't I say that $Throughput = \frac{1}{Response Time}$?

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    $\begingroup$ Because of parallelism? A car factory may spit out a new car every minute even though the production of each car takes hours. $\endgroup$
    – Hagen von Eitzen
    Mar 1, 2021 at 6:23

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I think I've found my bug,

The mean response time should be $\frac{\text{Total Response time of all jobs}}{completion}$, and every job has a different $Response\ Time$ due to the queueing delay.

This is the main observation that it can't be the reciprocal of throughput, and especially in the parallelism case.

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