The　vigorous　development　of　IoT　technology　has　spawned　a　series　of　applications　that　are　delay-sensitive　or　resource-intensive.　Mobile　edge　computing　is　an　emerging　paradigm　that　provides　services　between　end　devices　and　traditional　cloud　data　centers　to　users.　However,　with　the　continuously　increasing　investment　of　demands,　it　is　nontrivial　to　maintain　a　higher　quality-of-service　(QoS)　under　the　erratic　activities　of　mobile　users.　In　this　paper,　we　investigate　the　service　provisioning　and　updating　problem　under　the　multiple-users　scenario　by　improving　the　performance　of　services　with　long-term　cost　constraints.　We　first　decouple　the　original　long-term　optimization　problem　into　a　per-slot　deterministic　one　by　using　Lyapunov　optimization.　Then,　we　propose　two　service　updating　decision　strategies　by　considering　the　trajectory　prediction　conditions　of　users.　Based　on　that,　we　design　an　online　strategy　by　utilizing　the　committed　horizon　control　method　looking　forward　to　multiple　slots　predictions.　We　prove　the　performance　bound　of　our　online　strategy　theoretically　in　terms　of　the　trade-off　between　delay　and　cost.　Extensive　experiments　demonstrate　the　superior　performance　of　the　proposed　algorithm.