Under　the　service-time-limited　scheduling　policy　(STLSP),　any　solution　to　the　switched　server　system　asymptotically　converges　to　a　unique　periodic　solution.　Though,　the　STLSP　restricts　the　service　time　for　each　buffer,　it　does　not　consider　the　constraints　on　the　buffer　capacity.　However,　the　buffer　capacity　is　finite　for　most　of　real-world　problems.　Motivated　by　this　problem,　this　paper　generalizes　the　STLSP,　and　considers　the　execution　of　the　STLSP　with　the　constraints　on　the　buffer　capacity.　We　give　the　checking　condition　of　feasible　initial　states,　which　guarantees　that　the　solution　to　the　switched　server　system　under　the　STLSP　asymptotically　converges　to　the　periodic　solution　while　satisfying　the　constraints　on　the　buffer　capacity.　Furthermore,　for　the　switched　server　system　with　two　buffers　under　the　STLSP,　we　give　the　expression　of　the　set　of　all　feasible　initial　states.　The　simulation　analysis　validates　our　methods.