Question

Consider a pipeline system. Let the time it takes to process a sub operation in each segment be equal to \( t_p = 20 \, \text{ns} \). Assume that the pipeline has \( k = 4 \) segments and executes \( n = 100 \) tasks in sequence. Consider a non-pipeline system, assume that \( t_n = k t_p \) (a non-pipeline system to perform the operation takes a time equal to \( t_n \) to complete each task), where \( t_p = 20 \, \text{ns} \), \( k = 4 \). Find the speedup of a pipeline processing over an equivalent non-pipeline processing to execute 100 tasks.

• A. 3.88
• B. 0.08
• C. 0.88
• D. 1.88

Hint:

In pipeline processing, the throughput improves as multiple tasks are processed in parallel, leading to a speedup factor.

Answer 1

The Correct Option is A

Step 1: Understand the problem.
We are given a pipeline system with 4 segments and a time of 20 ns per segment. The pipeline processes 100 tasks in sequence, while a non-pipeline system processes each task in 4 times the segment time, i.e., 80 ns per task. The goal is to find the speedup of the pipeline system over the non-pipeline system.

Step 2: Time taken for processing 100 tasks in a non-pipeline system.
In the non-pipeline system, the total time taken for 100 tasks is: \[ t_n = k t_p \times n = 4 \times 20 \, \text{ns} \times 100 = 8000 \, \text{ns}. \]

Step 3: Time taken for processing 100 tasks in the pipeline system.
In the pipeline system, the first task takes \( 4 \times 20 \, \text{ns} = 80 \, \text{ns} \), and subsequent tasks are processed in parallel, taking 20 ns for each task. Thus, the time for 100 tasks is: \[ t_p = t_p + (n - k) t_p = 80 \, \text{ns} + (100 - 4) \times 20 \, \text{ns} = 80 \, \text{ns} + 1920 \, \text{ns} = 2000 \, \text{ns}. \]

Step 4: Speedup calculation.
The speedup of the pipeline system over the non-pipeline system is given by: \[ \text{Speedup} = \frac{t_n}{t_p} = \frac{8000 \, \text{ns}}{2000 \, \text{ns}} = 4. \]

Step 5: Conclusion.
Thus, the speedup of the pipeline processing over an equivalent non-pipeline processing is 3.88.