The　practical　Byzantine　fault　tolerant　(PBFT)　consensus　mechanism　is　one　of　the　most　basic　consensus　algorithms　(or　protocols)　in　blockchain　technologies.　Thus　its　performance　evaluation　is　an　interesting　and　challenging　topic　due　to　the　higher　complexity　of　its　consensus　work　in　a　peer-to-peer　network.　This　study　describes　a　simple　stochastic　performance　model　of　the　PBFT　consensus　mechanism.　This　model　is　refined　not　only　as　a　queuing　system　with　complicated　service　times　but　also　as　a　level-independent　quasi-birth-and-death　(QBD)　process.　With　regard　to　the　level-independent　QBD　process,　we　apply　the　matrix-geometric　solution　to　obtain　the　necessary　and　sufficient　condition　under　which　the　PBFT　consensus　system　is　stable　and　then　numerically　compute　the　stationary　probability　vector　of　the　QBD　process.　Thus,　we　provide　four　useful　performance　measures　for　the　PBFT　consensus　mechanism,　and　we　can　numerically　calculate　these　performance　measures.　Finally,　we　use　numerical　examples　to　verify　the　validity　of　our　theoretical　results　and　demonstrate　how　the　four　performance　measures　are　influenced　by　certain　key　parameters　of　the　PBFT　consensus.　Considering　theory　of　multi-dimensional　Markov　processes,　we　are　optimistic　that　the　methodology　and　results　presented　in　this　study　are　applicable　to　a　wide　range　of　PBFT　consensus　mechanism　and　even　other　types　of　consensus　mechanisms.