Solution
= Solution
The arrival phase has a <uniform distribution> over a cycle of length $R$. The no-delay phases occupy length $R-r$, so
$$
\boxed{\mathbb P(S=0)=\frac{R-r}{R}=1-\frac rR.}
$$
Individual phase endpoints have <probability> zero. The model neglects clearance time and releases waiting vehicles together when the stop interval ends; the degenerate case $r=R$ is interpreted as release at successive cycle boundaries.