A tire assembly includes a tire carcass body and an air tube body extending between an outward facing tire body surface and an inward tire body surface. The air tube body has an enclosed hollow enclosed outlet end at a first end and an enclosed hollow inlet end at an opposite second end. An air passageway extends through the air tube body from the inlet end to the outlet end. The outlet end is positioned to face exposed from the outward tire body surface and the inlet end is positioned to face exposed from the inward tire body surface. The air tube body is integrally formed of resilient flexible material composition and includes a hollow outer casing and one or more hollow air cables positioned within the casing for regulating the rate of air flow from the inlet end to the outlet end. The air tube body may follow a non-linear U-shaped path that surrounds a tire body bead core between the outward tire body surface and the inward tire body surface and be incorporated into the green tire build without disrupting the tire building and curing process or compromising the structural integrity or form of any of the green tire building components.