We consider a permissioned blockchain and analyze the dissemination and commitment processes of blocks among its corresponding miner nodes in the underlying peer-to-peer network. We propose a Markovian non-purging (n, k) fork-join queueing model to analyze the delay performance of the synchronization process among these miner nodes that apply a vote-based consensus procedure. We determine the impact of the most influential design and load parameters on the resulting commitment delay of new blocks that are appended to the blockchain after successful commitment decisions and the approval by the fully distributed consensus procedure. The proposed analysis of a permissioned blockchain is illustrated by means of a simple example of a fully interconnected P2P graph applying mean-value analysis techniques.