Analyzing blockchain protocols is a notoriously difficult task due to the underlying large scale distributed networks. To address this problem, stochastic model-based approaches are often utilized. However, the abstract models in prior work turn out not to be adoptable to consortium blockchains as the consensus of such a blockchain often consists of multiple processes. To address the lack of efficient analysis tools, we propose a queueing network-based method for analyzing consistency properties of consortium blockchain protocols in this article. Our method provides a way to evaluate the performance of the main stages in blockchain consensus. We apply our framework to the Hyperledger Fabric system and recover key properties of the blockchain network. Using our method, we analyze the security properties of the ordering mechanism and the impact of delaying endorsement messages in consortium blockchain protocols. Then an upper bound is derived of the damage an attacker could cause who is capable of delaying the honest players' messages. Based on the proposed method, we employ analytical derivations to investigate both the security and performance features, and corroborate close agreement with measurements on a wide-Area network testbed running the Hyperledger Fabric blockchain. With the proposed method, designers of future blockchains can provide a more rigorous analysis of their consortium blockchain schemes.