Suppose we now have a Erlang distribution $b(x;2,1) = x e^{-x}$. According to the definition of Erlang distribution we know that the variance of such a distribution is 2 and we want to reduce the variance of this model. So we hope that the modified time $\tilde{b}$ would fall faster than the original $b$. We're trying to use:
$\tilde{b} = \begin{cases} \frac{1}{c} x e^{-x} & 0 < x < t \\ \frac{1}{c} t e^{-x} & x \geq t\end{cases}$.
Integration tells us $c = 1 - e^{-t}$. And after we choose $c$, how should we generate such a random variable?