In　this　paper,　we　apply　a　Markov　decision　process　to　find　the　optimal　asynchronous　dynamic　policy　of　an　energy-efficient　data　center　with　two　server　groups.　Servers　in　Group　1　always　work,　while　servers　in　Group　2　may　either　work　or　sleep,　and　a　fast　setup　process　occurs　when　the　server＇s　states　are　changed　from　sleep　to　work.　The　servers　in　Group　1　are　faster　and　cheaper　than　those　of　Group　2　so　that　Group　1　has　a　higher　service　priority.　Putting　each　server　in　Group　2　to　sleep　can　reduce　system　costs　and　energy　consumption,　but　it　must　bear　setup　costs　and　transfer　costs.　For　such　a　data　center,　an　asynchronous　dynamic　policy　is　designed　as　two　sub-policies:　The　setup　policy　and　the　sleep　policy,　both　of　which　determine　the　switch　rule　between　the　work　and　sleep　states　for　each　server　in　Group　2.　To　find　the　optimal　asynchronous　dynamic　policy,　we　apply　the　sensitivity-based　optimization　to　establish　a　block-structured　policy-based　Markov　process　and　use　a　block-structured　policy-based　Poisson　equation　to　compute　the　unique　solution　of　the　performance　potential　by　means　of　the　RG-factorization.　Based　on　this,　we　can　characterize　the　monotonicity　and　optimality　of　the　long-run　average　profit　of　the　data　center　with　respect　to　the　asynchronous　dynamic　policy　under　different　service　prices.　Furthermore,　we　prove　that　a　bang-bang　control　is　always　optimal　for　this　optimization　problem.　We　hope　that　the　methodology　and　results　developed　in　this　paper　can　shed　light　on　the　study　of　more　general　energy-efficient　data　centers.