# Why isn't the throughput = (1 / response time) by their definition?

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 $$Throughput = \frac{1}{Response Time}$$?

• Because of parallelism? A car factory may spit out a new car every minute even though the production of each car takes hours. Mar 1, 2021 at 6:23

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.