Systems and methods for controlling the flow of vitrified material. In at least some embodiments, a vitrified material control system comprises a melt chamber (8) configured to contain a molten material (27) during operation of the control system; a siphon valve (11) configured to facilitate a flow of the molten material from the melt chamber; and a vacuum-generation system (26, 15, 16) configured to controllably deliver a vacuum to the molten material in the melt chamber and to thereby regulate a flow of the molten material from the melt chamber. In other embodiments, methods of controlling a flow of molten vitrified material from a heating device are disclosed. The methods may include, for example, applying a vacuum to the molten material to control a dwell time of the molten material in a vessel of the heating device and regulating the vacuum based on a measured temperature of the molten material.