Algorithm 12 Time to end of lane.

Input:tmin, tmax, time to reach TLS ut, actual speed us, distance to next TLS d max speed allowed vM Result: $v_{\min },v_{\max }$ in case a speed change is necessary or ∅ otherwise 1:if not $t_{\min }\le u_t\le t_{\max }$ then 2:    $v_{\min }\leftarrow [\frac{d}{t_{\min }}\ast 3.6]$ 3:    if $u_t>t_{\max }$ and $v_{\min }\le v_M$ then 4:        $a_{\mathrm{needed}}=2\ast (d-\frac{u_s\ast t_{\max }}{3.6}/t_{\max }^2)$ 5:        $a_{\max }\leftarrow$ MaxAccel$\left(u\right)$ 6:        if $a_{\mathrm{needed}}<a_{\max }$ then 7:           $v_{\max }\leftarrow argmin([\frac{d}{t_{\min }}\ast 3.6],v_M)$ 8:        else 9:           $v_{\min }\leftarrow v_{\max }\leftarrow 0$ 10:        end if 11:    else 12:        $v_{\max }\leftarrow v_{\min }$ 13:    end if 14:    return $(v_{\min },v_{\max })$ 15:elsereturn None 16:end if