This paper proposes a novel embedded Markovian queueing model of the M(1,n)/Mn/1 type in order to establish a theoretical foundation to design a blockchain-based system with specific interest in Ethereum. The model assumes variable bulk arrivals of transactions in Poisson distribution, i.e., M(1,n), where n the number of slots across all the mined transactions and static bulk service of transactions in exponential time, i.e., Mn, for posting in the current block, namely, VBASBP. The primary performance measurements to be taken are the average number of slots no matter how many transactions are mined under the assumption of the maximum number of slots per block as specified by n; the average waiting time per slot; and the throughput in terms of the average number of slots to be processed per time. The variable bulk arrival rate is assumed to vary linearly proportional to the size of the transactions in a multiple of per slot, and the static bulk service is assumed to take place when the number of slots in the mined transactions reaches at n, i.e., a bulk processing of multiple transactions in multiple slots for posting in a block. Numerical simulations are conducted on Matlab to demonstrate the efficacy of the model.

The slim chain is proposed in this paper in an effort to address and resolve the scalability issue of blockchain-based crypto computing by managing the volume of the blockchain itself. An adequate balancing of computation across on/off-chain is expected to relieve the spatial and temporal overhead of managing the otherwise exponentially growing size of the blockchain by making the blockchain slimmer as much as the volume migrated and kept off-chain than the conventional, as referred to as a slim chain in this paper. As an initial design, a novel theoretical model is proposed to assure the efficacy of the proposed slim chain with specific respect to the dependability from a single transaction's standpoint in a stochastic manner. It is demonstrated that the dependability can be traced with respect to whether the transaction of concern is to write off the chain or read back from off the chain to on-chain, as the transactions writing off the chain are more dependable than reading from off the chain without loss of practicality, as well as the crypto rate and the IPFS rate as IPFS (Inter-Planetary File System) is an off-chain storage considered in this research.

This paper presents ways to assure the efficacy of managing crypto links and crypto speed with respect to the dependability of blockchain. The dependability in this work is defined with reference to crypto links in a proportional manner and crypto speed in an inversely proportional manner, respectively. Also, note that dependability is proportional...

This study investigates the integration of quantum computing, classical methods, and deep learning techniques for enhanced image processing in dynamic 6G networks, while also addressing essential aspects of copyright technology and detection. Our findings indicate that quantum methods excel in rapid edge detection and feature extraction but encounter difficulties in maintaining image quality compared to classical approaches. In contrast, classical methods preserve higher image fidelity but struggle to satisfy the real-time processing requirements of 6G applications. Deep learning techniques, particularly CNNs, demonstrate potential in complex image analysis tasks but demand substantial computational resources. To promote the ethical use of AI-generated images, we introduce copyright detection mechanisms that employ advanced algorithms to identify potential infringements in generated content. This integration improves adherence to intellectual property rights and legal standards, supporting the responsible implementation of image processing technologies. We suggest that the future of image processing in 6G networks resides in hybrid systems that effectively utilize the strengths of each approach while incorporating robust copyright detection capabilities. These insights contribute to the development of efficient, high-performance image processing systems in next-generation networks, highlighting the promise of integrated quantum-classical–classical deep learning architectures within 6G environments.

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.

This paper presents a work on how to assure the dependability of a crypto system built across on and off the blockchain by using the proposed adaptive checkpoint and rollback algorithm, and a prototype is developed for demonstration purpose.The theoretical background of the proposed checkpoint and rollback algorithm is studied to characterize the variables affecting the dependability such as security, authenticity and reliability with respect to the rates of hit by any events of those issues, the rates to detect and diagnose, and then the rate to vote for a consensus whether to trigger a rollback or not. Based on the variables characterization in a stochastic manner, then steady state probabilities and state transition probabilities are derived in order to assure the ultimate effective dependability of each individual dependability variable (i.e., security, authenticity and reliability), then finally to assure the dependability in a compound manner with each variable assigned a weight depending on the nature of the systems specifications.Based on the theoretical study, a protype of a crypto system is built to demonstrated the underlying architecture and operations and to justify the need for such system to take synergistic advantages from both on- and off-chain blockchains, with an experimental result of a benefit in gas fee which is the most exigently addressed issue today in blockchain systems especially in Ethereum network of blockchains. An astonishing gas fee saving results are demonstrated. It is observed that the crypto system benefits more if more computationally intensive transactions are executed off-chain while vice versa.