Fog　computing　is　an　emerging　paradigm　that　brings　computing　capabilities　closer　to　distributed　IoT　devices,　which　provides　networking　services　between　end　devices　and　traditional　cloud　data　centers.　One　important　mission　is　to　further　reduce　the　monetary　cost　of　fog　resources　while　meeting　the　ever-growing　demands　of　multiple　users.　In　this　paper,　we　focus　on　minimizing　the　total　cost　for　multiple　mobile　users　to　provide　an　efficient　resource　provisioning　scheme　in　fog　computing.　The　total　cost　includes　two　aspects:　the　replication　cost　and　the　transmission　cost.　We　consider　three　cases　for　the　resource　provision　problem　by　focusing　on　different　cost　models.　First,　one　simple　case　where　users　can　only　upload　one　replication　is　discussed,　and　an　optimal　solution　is　proposed　by　converting　the　original　problem　into　a　bipartite　graph　matching.　Then　we　consider　a　more　complicated　case　in　which　each　user　can　upload　multiple　replications　on　fog　nodes　in　the　resource　provisioning.　Specifically,　two　models　are　discussed:　the　0-1　transmission　cost　model　and　the　different　transmission　cost　model.　For　the　0-1　transmission　cost　model,　each　user　can　upload　multiple　replications　with　a　constant　transmission　cost,　and　one　optimal　greedy　solution　is　proposed.　For　the　different　transmission　cost　model,　the　transmission　cost　is　related　to　the　distance　of　each　pair　of　fog　nodes.　This　problem　is　proven　to　be　NP-hard.　We　first　propose　a　non-adaptive　algorithm　which　is　proved　to　be　bounded　by2/3W　+　1/3OPT.　Another　3　+　is　an　element　of-approximation　algorithm　is　proposed　based　on　local　search,　which　has　better　performance　with　higher　complexity.　Extensive　simulations　also　prove　the　efficiency　of　our　schemes.　(C)　2020　Elsevier　Inc.　All　rights　reserved.