to disk. This behaviour can be observed from Figure \[genericmodels\], a spike in the amount of time taken is at 80% $M_{sel}$. The model for the collect phase in our test environment is illustrated as below: $$T_{collect} = 0.01 \times M_{sel} + 0.97
\label{eq:genericcm}$$ Again, the $RMSE$ value of $3.036$ and the Collect plot in Figure \[crossvalidation\] supports our model.

**Spill Model**
---------------

As shown in Figure \[genericmodels\], our linearity assumption between data size and processing time is confirmed. The model obtained after the cross-validation is presented in Equation . The model has $RMSE$ value is $2.522$ which would be considered a good model in this case. $$T_{spill} = 0.02 \times M_{sel} + 0.98
\label{eq:genericsm}$$

**Merge Model**
---------------

Spill files are merged together to form bigger files. From the plot, we can see a close relation between the actual and the predicted values with an $RMSE$ of $9.36$. The parameters of the model are shown in Equation \[eq:genericmmodel\] $$T_{merge} = 0.002 \times M_{sel}logM_{sel} + 4.80
\label{eq:genericmmodel}$$

**Shuffle Model**
-----------------

This phase is the most expensive of all because it involves inter-node communication. The model main parameters are the amount of data being shuffled and the number of Mappers task. The 