A Bivariate Performance Model across On- and Off-Chain in A NFT (Non-Fungible Token) Chain

This paper proposes a quantitative model to assess the performance of a NFT (Non-Fungible Token)-centered chain as referred to as a NFT Chain in this paper. NFT chain in general stores its data distributed across on chain (e.g. NFT registration data and an address pointing at the data located off chain such as meta data table and ultimate digital asset's data) due to the high cost to store the potentially high volume of data for digital assets. Therefore, it is expected that the overall performance of NFT chain is primarily to be dominated and bound by the off-chain performance. The proposed performance model employing an embedded Markovian queueing process model, tracks a bivariate state of the NFT chain such that
$(i,j)$
where
$i$
stochastically tracks the number of slots of the transactions executed on chain and
$j$
stochastically tracks the number of transactions off chain as well, and the states transition as determined by
$\lambda_{on}, \lambda_{off}, \mu$
, and the number of slots in the current block. Extensive numerical simulations are performed to validate the efficacy of the model. The primary set of variables used in the simulations consists of
$\lambda_{on}, \lambda_{off}, \mu$
and the average number of slots of the transactions during a block posting,
$L$
, is simulated based on both
$L_{on}$
and
$L_{off}$
; and the average waiting time
$W$
based on both
$W_{on}$
and
$W_{off}$
, in an intermingled manner in order to take into account of the nature of NFT transactions executed across on- and off-chain without loss of generality. The simulation results demonstrate a good agreement with the expected and intuitive trends and the proposed NFT chain performance model serves as a sound theoretical foundation for the design of an NFT chain from the system's perspective.