Current　research　often　formalizes　traffic　prediction　tasks　as　spatio-temporal　graph　modeling　problems.　Despite　some　progress,　this　approach　still　has　the　following　limitations.　First,　space　can　be　divided　into　intrinsic　and　latent　spaces.　Static　graphs　in　intrinsic　space　lack　flexibility　when　facing　changing　prediction　tasks,　while　dynamic　relationships　in　latent　space　are　influenced　by　multiple　factors.　A　deep　understanding　of　specific　traffic　patterns　in　different　spaces　is　crucial　for　accurately　modeling　spatial　dependencies.　Second,　most　studies　focus　on　correlations　in　sequential　time　periods,　neglecting　both　reverse　and　global　temporal　correlations.　This　oversight　leads　to　incomplete　temporal　representations　in　models.　In　this　work,　we　propose　a　Space-Specific　Graph　Convolutional　Recurrent　Transformer　Network　(SSGCRTN)　to　address　these　limitations　simultaneously.　For　the　spatial　aspect,　we　propose　a　space-specific　graph　convolution　operation　to　identify　patterns　unique　to　each　space.　For　the　temporal　aspect,　we　introduce　a　spatio-temporal　interaction　module　that　integrates　spatial　and　temporal　domain　knowledge　of　nodes　at　multiple　granularities.　This　module　learns　and　utilizes　parallel　spatio-temporal　relationships　between　different　time　points　from　both　forward　and　backward　perspectives,　revealing　latent　patterns　in　spatio-temporal　associations.　Additionally,　we　use　a　transformer-based　global　temporal　fusion　module　to　capture　global　spatio-temporal　correlations.　We　conduct　experiments　on　four　real-world　traffic　flow　datasets　(PeMS03/04/07/08)　and　two　traffic　speed　datasets　(PeMSD7(M)/(L)),　achieving　better　performance　than　existing　technologies.　Notably,　on　the　PeMS08　dataset,　our　model　improves　the　MAE　by　6.41%　compared　to　DGCRN.　The　code　of　SSGCRTN　is　available　at　https://github.com/OvOYu/SSGCRTN.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2024.