Question

Why stage delay maximum is cosidered for pipilines with non uniform delay?

Answer 1

Computer Organization and Architecture | Pipelining | Set 3 (Types and Stalling)

Please see Set 1 for Execution, Stages and Performance (Throughput) and Set 2 for Dependencies and Data Hazard.
 
Types of pipeline

Uniform delay pipeline
In this type of pipeline, all the stages will take same time to complete an operation.
In uniform delay pipeline, Cycle Time (Tp) = Stage Delay

If buffers are included between the stages then, Cycle Time (Tp) = Stage Delay + Buffer Delay

Non-Uniform delay pipeline
In this type of pipeline, different stages take different time to complete an operation.
In this type of pipeline, Cycle Time (Tp) = Maximum(Stage Delay)

For example, if there are 4 stages with delays, 1 ns, 2 ns, 3 ns, and 4 ns, then

Tp = Maximum(1 ns, 2 ns, 3 ns, 4 ns) = 4 ns

If buffers are included between the stages,

Tp = Maximum(Stage delay + Buffer delay)

Example : Consider a 4 segment pipeline with stage delays (2 ns, 8 ns, 3 ns, 10 ns). Find the time taken to execute 100 tasks in the above pipeline.
Solution : As the above pipeline is a non-linear pipeline,
Tp = max(2, 8, 3, 10) = 10 ns
We know that ETpipeline = (k + n – 1) Tp = (4 + 100 – 1) 10 ns = 1030 ns

NOTE: MIPS = Million instructions per second

 

Performance of pipeline with stalls

Speed Up (S) = Performancepipeline / Performancenon-pipeline
=> S = Average Execution Timenon-pipeline / Average Execution Timepipeline
=> S = CPInon-pipeline * Cycle Timenon-pipeline / CPIpipeline * Cycle Timepipeline

Ideal CPI of the pipelined processor is ‘1’. But due to stalls, it becomes greater than ‘1’.
=> S = CPInon-pipeline * Cycle Timenon-pipeline / (1 + Number of stalls per Instruction) * Cycle Timepipeline

As Cycle Timenon-pipeline = Cycle Timepipeline,