The　clusters　in　a　blockchain　computing　system　can　be　constructed　to　be　elastic,　thus　supporting　scalable　computing　and　improving　energy　efficiency.　To　form　an　elastic　cluster,　the　service　nodes　are　dynamically　divided　into　the　working　nodes　and　the　reserved　nodes.　Specifically,　the　working　nodes　are　active　to　meet　the　computing　requirements　of　workloads,　while　the　reserved　nodes　are　switched　to　a　low-power　state　for　energy　saving.　Traditionally,　workloads　are　distributed　to　working　nodes　in　the　mode　of　N-N　service　queues.　But　in　this　mode,　the　Quality　of　Service　(QoS)　of　different　working　nodes　may　be　diverse,　because　the　requirements　are　various　for　the　accumulated　requests　in　different　working　nodes.　As　a　result,　the　overall　system　capability　is　not　sufficiently　utilized,　and　the　overall　system　QoS　is　dragged　down.　In　this　paper,　we　propose　an　N-1　queueing　and　on-demand　resource　provisioning　method　to　process　workloads　in　the　mode　of　N-1　service　queues.　Different　from　N-N　service　queues,　N-1　service　queues　prohibit　the　accumulation　of　requests　in　working　nodes.　Thereby,　once　there　are　idle　working　nodes,　waiting　requests　can　immediately　be　delivered　to　them.　As　a　result,　all　the　working　nodes　are　sufficiently　utilized,　and　the　overall　QoS　is　improved.　Accordingly,　after　using　the　N-1　service　queues,　fewer　working　nodes　are　enough　to　meet　the　same　Service　Level　Agreement　(SLA)　on　same　workloads.　In　addition,　by　using　a　resource　demand　monitor　module,　our　method　dynamically　readjusts　the　number　of　working　nodes　to　match　workload　demand.　Finally,　the　energy　efficiency　of　an　elastic　cluster　can　be　measurably　improved,　due　to　that　fewer　working　nodes　are　powered　on　while　the　same　SLA　can　be　met.