Conjectures about Traffic Light Queues

In discrete time, $\mathrm{\ell }$-blocks of red lights are separated by $\mathrm{\ell }$-blocks of green lights. Cars arrive at random. The maximum line length of idle cars is fully understood for $\mathrm{\ell }=1$, but only partially for $2\le \mathrm{\ell }\le 3$.