As　an　innovative　approach,Direct　Acyclic　Graph(DAG)-based　blockchain　is　designed　to　overcome　the　scalability　and　performance　limitations　of　traditional　blockchain　systems,which　rely　on　sequential　structures.The　graph-based　architecture　of　DAG　allows　for　faster　transactions　and　parallel　processing,making　it　a　compelling　option　across　various　industries.To　enhance　the　analytical　understanding　of　DAG-based　blockchains,this　paper　begins　by　introducing　a　Markov　model　tailored　for　a　DAG-based　blockchain　system,specifically　focusing　on　the　Tangle　structure　and　the　interaction　between　tips　and　newly　arrived　transactions.We　then　establish　a　continuous-time　Markov　process　to　analyze　the　DAG-based　blockchain,demonstrating　that　this　process　is　a　level-dependent　quasi-birth-and-death(QBD)process.We　further　prove　that　the　QBD　process　is　both　irreducible　and　positively　recurrent.Building　on　this　foundation,we　conduct　a　performance　analysis　of　the　DAG-based　blockchain　system　by　deriving　the　stationary　probability　vector　of　the　QBD　process.Notably,we　introduce　a　novel　method　to　calculate　the　average　sojourn　time　of　any　arriving　internal　tip　within　the　system　using　first　passage　times　and　Phase-type(PH)distributions.Finally,numerical　examples　are　provided　to　validate　our　theoretical　findings　and　to　illustrate　the　influence　of　system　parameters　on　the　performance　metrics.