Here is an example. The function ChainOutput[] uses NDSolve to produce its result. I executed it 4 times in a row.

1) It is wrapped in a set of statements that show that it took 98 seconds cpu time within 355 second elapsed time to produce a solution. During execution Task Manager showed all 4 cores at 100%

2) This time it solved in 4.6 seconds.

3) This time 64 cpu seconds in 76 seconds elapsed time.

4) This time 41 seconds.

I've looked to see -- I'm not modifying initial conditions between runs. Unfortunately, I can't share the notebook, but I hope someone can give me a clue as to how I can remove the random number generator from this, with hopefully a solution as quick as the fastest.

In[153]:= clock0 = AbsoluteTime[];
Print[Timing[chainOutput[100, 40, 70, Ga -> Ga]]];
timeExpended = AbsoluteTime[] - clock0

During evaluation of In[153]:= {97.828227,106.69089}

Out[155]= 354.7782637

In[156]:= Timing[chainOutput[100, 40, 70, Ga -> Ga]]

Out[156]= {4.5708293, 106.69089}

In[157]:= clock0 = AbsoluteTime[];
Print[Timing[chainOutput[100, 40, 70, Ga -> Ga]]];
timeExpended = AbsoluteTime[] - clock0

During evaluation of In[157]:= {64.475213,106.69089}

Out[159]= 75.5682788

In[160]:= Timing[chainOutput[100, 40, 70, Ga -> Ga]]

Out[160]= {41.262265, 106.69089}