A tire system comprising: a tire having a tire carcass comprising a tire cavity defined by a tire inner liner, and first and second sidewalls extending respectively from first and second tire bead regions to a tire tread region; compression actuator means mounted to the tire carcass configured for operative actuation by tire deformation during a tire revolution; and a pump assembly affixed to the tire carcass and comprising a compressor body affixed to the compression actuator means and having an internal air chamber, the internal air chamber having an inlet opening for admitting air into the internal air chamber and an outlet opening for conducting air from the internal air chamber to the tire cavity, the compressor body further comprising a flexible membrane member operationally deforming into a deformed state within the internal air chamber responsive to actuation by or contacting engagement with the compression actuator means to compress air within the internal air chamber, characterized in that the flexible membrane member is located within the internal air chamber and is operative to deform within the internal air chamber responsive to a contacting engagement with or an actuation by the compression actuator means between an open position relative to the inlet opening permitting air flow from the inlet opening into the air chamber and a closed position relative to the inlet opening obstructing air flow from the inlet opening into the air chamber; the flexible membrane member is able to compress a volume of air within the air chamber during an operational deformation between the open and closed positions; and the tire system comprises an inlet conduit extending through the tire between the inlet opening and an outward facing side of the tire. a tire having a tire carcass comprising a tire cavity defined by a tire inner liner, and first and second sidewalls extending respectively from first and second tire bead regions to a tire tread region; compression actuator means mounted to the tire carcass configured for operative actuation by tire deformation during a tire revolution; and a pump assembly affixed to the tire carcass and comprising a compressor body affixed to the compression actuator means and having an internal air chamber, the internal air chamber having an inlet opening for admitting air into the internal air chamber and an outlet opening for conducting air from the internal air chamber to the tire cavity, the compressor body further comprising a flexible membrane member operationally deforming into a deformed state within the internal air chamber responsive to actuation by or contacting engagement with the compression actuator means to compress air within the internal air chamber, characterized in that the flexible membrane member is located within the internal air chamber and is operative to deform within the internal air chamber responsive to a contacting engagement with or an actuation by the compression actuator means between an open position relative to the inlet opening permitting air flow from the inlet opening into the air chamber and a closed position relative to the inlet opening obstructing air flow from the inlet opening into the air chamber; the flexible membrane member is able to compress a volume of air within the air chamber during an operational deformation between the open and closed positions; and the tire system comprises an inlet conduit extending through the tire between the inlet opening and an outward facing side of the tire.