This　paper　discusses　a　large-scale　dockless　bike-sharing　system　(DBSS)　with　unusable　bikes,　which　can　be　removed,　repaired,　redistributed　and　reused　under　two　batch　policies:　one　for　removing　the　unusable　bikes　from　each　parking　region　to　a　maintenance　shop,　and　the　other　for　redistributing　the　repaired　bikes　from　the　maintenance　shop　to　some　suitable　parking　regions.　For　such　a　bike-sharing　system,　this　paper　proposes　and　develops　a　new　computational　method　by　applying　the　RG-factorizations　of　block-structured　Markov　processes　to　the　closed　queueing　networks.　Different　from　previous　works　in　the　literature　of　queueing　networks,　a　key　contribution　of　our　computational　method　is　to　set　up　a　new　nonlinear　matrix　equation　to　determine　the　relative　arrival　rates,　and　to　show　that　the　nonlinearity　comes　from　two　different　groups　of　processes:　The　failure　and　removing　processes,　and　the　repair　and　redistribution　processes.　Once　the　relative　arrival　rate　is　introduced　to　each　node,　these　nodes　are　isolated　from　each　other　so　that　the　Markov　processes　of　all　the　nodes　are　independent　of　each　other,　and　thus　the　Markov　system　of　each　node　is　described　as　an　elegant　block-structured　Markov　process　whose　stationary　probabilities　can　be　easily　computed　by　the　RG-factorizations.　Based　on　this,　the　paper　establishes　a　more　general　product-form　solution　of　the　closed　queueing　network,　and　provides　performance　analysis　of　the　DBSS　through　a　comprehensive　discussion　of　the　bikes＇　failure,　removing,　repair,　redistribution　and　reuse　processes　under　two　batch　policies.　We　hope　that　our　method　opens　a　new　avenue　for　quantitative　evaluation　of　more　general　DBSSs　with　unusable　bikes.