Carnot-Carath\'eodory Metrics in Unbounded Subdomains of ${\mathbb{C}}^2$

We introduce a new class of unbounded model subdomains of ${\mathbb{C}}^2$ for the ${\mathrm{\square }}_b$ problem. Unlike previous finite type models, these domains need not be bounded by algebraic varieties. In this paper we obtain precise global estimates for the Carnot-Carath'eodory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field.