In　this　paper,　we　study　a　stock-rationing　queue　with　two　demand　classes　by　means　of　the　sensitivity-based　optimization,　and　develop　a　complete　algebraic　solution　for　the　optimal　dynamic　rationing　policy.　To　do　this,　we　establish　a　policy-based　birth-death　process　to　show　that　the　optimal　dynamic　rationing　policy　must　be　of　transformational　threshold　type.　Based　on　this　finding,　we　can　refine　three　sufficient　conditions　under　each　of　which　the　optimal　dynamic　rationing　policy　is　of　threshold　type　(i.e.,　critical　rationing　level).　Crucially,　we　characterize　the　monotonicity　and　optimality　of　the　long-run　average　profit　of　this　system,　and　establish　some　new　structural　properties　of　the　optimal　dynamic　rationing　policy　by　observing　any　given　reference　policy.　Finally,　we　use　numerical　examples　to　verify　computability　of　our　theoretical　results.　We　believe　that　the　methodology　and　results　developed　in　this　paper　can　shed　light　on　the　study　of　stock-rationing　queue　and　open　a　series　of　potentially　promising　research.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.