Performance measure on data sizes and identical resources

Question

I have systems that have a large number of cores as well as a cluster. For a particular task for which no serial implementation is available, I can only benchmark w.r.t. time taken for tasks running on different input sizes. I see that even when data size was increased by a factor of 10 times, the time for completion is less than 10 times while using identical resources. I would like to know how to measure the performance, as this does not appear to fall under typical definitions of strong/weak scaling. This appears to be related to efficiency, but I am not certain. From what I could gather about the three:

1. Strong scaling (Amdhal's law): speedup = 1 / ( s + p / N ) = T( 1 ) / T( N )
2. Weak scaling (Gustafson’s law): scaled speedup = s + p × N
3. Efficiency: speedup / N

As I don't have speedup due to lack of serial implementation and that N a is constant, I can only think of finding ratios of efficiencies using strong scaling. Is such a parameter used in CS?

Answer 1

_{Apache Spark on workloads on 250-500 GB data. B/M was done with 100% and 10% data sets. Jobs run between 250-3000s depending on the type and size. I can force number of executors to be 1 with 1 executor core, but that would be wrong as theoretically only optimum serial job should be written.
– Quiescent 24 mins ago
( URL added )}

Thanks for this note. The problem gets ground to answer it :

Q :_{... "Is such a parameter used in CS ?"}

The answer to the questions about the observations on the above depicted problem has nothing to do with DATA-size per-se, the DATA-sizing is important, yet the core understanding is related to the internal functioning of the distributed-computing where overheads matter :

SMALL RDD-DATA 

      +-------------------E-2-E ( RDD/DAG Spark-wide distribution
      |s+------+o         |                        & recollection
      |e|      | v       s|               Turn-Around-Time )
      |t| DATA |  e     d |
      |u|1x    |   r   a  |
      |p+------+    h e   |
      +-------------------+
      |                   |
      |                   |
      |123456789.123456789|

Whereas :

LARGER RDD-DATA

      +--------:------:------:------:-------------------E-2-E ( RDD/DAG Spark-wide TAT )
      |s+------:------:------:------:------+o         + |
      |e|      :      :      :      :      | v       s v|
      |t| DATA : DATA : DATA : DATA : DATA |  e     d  a|
      |u|1x    :2x    :3x    :4x    :5x    |   r   a   r|
      |p+------:------:------:------:------+    h e    .|
      +--------:------:------:------:-------------------+
      |                                                 |
      |                   |                             |
      |123456789.123456789|                             |
      |                                                 |
      |123456789.123456789.123456789.123456789.123456789|

( not a multiple of 5x the originally observed E-2-E for "small" DATA ( Spark-wide TAT )
  yet a ( Setup & Termination overheads stay about same ~ const. )
      a ( a DATA-size variable part need-not yet may grow )
  now
      show an E-2-E of about ~ 50 TimeUNITs for 5-times more DATA,
      that is
  for obvious
      reasons not 5-times ~ 20 TimeUNITs
           as was seen
              during the E-2-E TAT from processing in "small"-DATA use-case
           as not
              all system-wide overheads accumulation
                                  scale with DATA size

For further reading on Amdahl's argument & Gustafson/Barsis promoted scaling, feel free to continue here.