Throughput increase/decrease by how much percent

Question

I am learning computer architecture and organization. I am stuck in the following question. Can someone please help me?

The stage delays in a 5-stage pipeline are 300, 200, 100, 400 and 350 picoseconds. The second and third stages are merged into a single stage with delay 350 picoseconds. The throughput increase/decrease by ………… (percent).

This is what I tried:

Throughput of 1st case T1: 1/max delay =1/200
Throughput of 2nd case T2: 1/max delay= 1/350
%age increase/decrease in throughput: (T2-T1)/T1 * 100 = (1/350 - 1/200)/(1/200)*100
= -42.8
So the throughput decreases by 42.8%.

But the correct answer is given to be 0. I don't understand why?

Where do you get the max delay value of 200 in the first case? (Also don't forget to multiply by 100 to convert fractions to percents, though this is not your problem here). — Justin, Apr 13 '21 at 15:12
What clock rate can you drive this thing at, before and after the optimisation? — , Apr 13 '21 at 15:20
@Justin The second and third stages are merged into a single stage the delay of them is 200 and 100. So the max delay is 200. — Anshul Gupta, Apr 13 '21 at 15:24
@ANSHULGUPTA Think about what I asked. It's not IN the question, it's implied by the question. What are your answers? — , Apr 13 '21 at 15:35
Do you have to look at the throughput of the whole pipeline or the stages which are being merged? — Arsenal, Apr 13 '21 at 15:41
@Arsenal Well I guess that does not matter because we have to find the percentage increase/decrease in throughput. — Anshul Gupta, Apr 14 '21 at 12:55
OK I'll spell out a point you seem to have overlooked. All pipeline stages are clocked by the same clock. The edit changes nothing important. — , Apr 14 '21 at 12:57
@user16324 Well I have made some corrections in the question so please look at it again. — Anshul Gupta, Apr 14 '21 at 13:00
@ANSHULGUPTA Tony Stewart spelled out the answer (maybe not clear enough) for you and you have the solution right in your question. I'll rephrase my point: What is the maximum delay in the pipeline in the first case and in the second case? — Arsenal, Apr 14 '21 at 15:13

score 3 · Accepted Answer · edited Apr 23 '21 at 09:25

Improving throughput at the expense of latency

Delay: D = T + nδ
Throughput: IPS = n/(T + nδ)
Choose non-critical paths to merge in series to add latency but less than the critical path.

Now compute and see your critical path of 400 is not exceeded with 2 pipe merged in series, so the throughput is not changed, where latency δ can be different for each pipe rather than equal as shown above.

Throughput increase/decrease by how much percent

1 Answers1