In many systems the completion of an activity takes an amount of time that is not perfectly predictable. In statistics we would consider these to be random variables.

For two measurements of time $t_1$ and $t_2$ I can readily evaluate $\mathbb{1} [t_1 \leq t_2]$. When I consider the ensemble of measurement outcomes I have to consider $\mathbb{1} [T_1 \leq T_2]$ which compares random variables.

Considering ordering on random quantities like this is termed stochastic ordering, with particular notions of stochastic dominance coming to mind.

In ToC we would like to identity which activities in a sequence is the slowest step, termed a "bottleneck". But knowing that different notions of stochastic ordering raises a question of what form of stochastic dominance is the most relevant in order to make ToC work?



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