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.