Solution
= Solution
The atom at zero contributes zero to the <expected value>, while all positive delays must retain their unconditional density. Therefore
$$
\boxed{\mu=\mathbb E[S]=0\left(1-\frac rR\right)+\int_0^r\frac{s}{R}\,ds=\frac{r^2}{2R}.}
$$
This <mean> is $r/R$ times the <mean> $r/2$ conditional on encountering a stop; using $r/2$ alone would omit the vehicles passing without delay.