This paper proposes a real-time chain and a novel embedded Markovian queueing model with variable bulk arrival (VBA) and variable bulk service (VBS) in order to establish and assure a theoretical foundation to design a blockchain-based real-time system with particular interest in Ethereum. Based on the proposed model, various performances are simulated in a numerical manner in order to validate the efficacy of the model by checking good agreements with the results against intuitive and typical expectations as a baseline. A demo of the proposed real-time chain is developed in this work by modifying the open source of Ethereum Geth 1.9.11. The work in this paper will provide both a theoretical foundation to design and optimize the performances of the proposed real-time chain, and ultimately address and resolve the performance bottleneck due to the conventional block-synchrony by employing an asynchrony by the real-time deadline to some extent.