The　dockless　bike　sharing　system　(DBSS)　has　been　globally　adopted　as　a　sustainable　transportation　system.　Due　to　the　robustness　and　tractability　of　the　closed　queuing　network　(CQN),　it　is　a　well-behaved　method　to　model　DBSSs.　In　this　paper,　we　view　DBSSs　as　CQNs　and　use　the　mean　value　analysis　(MVA)　algorithm　to　calculate　a　small　size　DBSS　and　the　flow　equivalent　server　(FES)　algorithm　to　calculate　the　larger　size　DBSS.　This　is　the　first　time　that　the　FES　algorithm　is　used　to　study　the　DBSS,　by　which　the　CQN　can　be　divided　into　different　subnetworks.　A　parking　region　and　its　downlink　roads　are　viewed　as　a　subnetwork,　so　the　computation　of　CQN　is　reduced　greatly.　Based　on　the　computation　results　of　the　two　algorithms,　we　propose　two　optimization　functions　for　determining　the　optimal　fleet　size　and　repositioning　flow,　respectively.　At　last,　we　provide　numerical　experiments　to　verify　the　two　algorithms　and　illustrate　the　optimal　fleet　size　and　repositioning　flow.　This　computation　framework　can　also　be　used　to　analyze　other　on-demand　transportation　networks.