Performance Modeling and Assurance for Cross Chain

Abstract

Since the invention of Bitcoin in 2008, there has been a surge in the number of blockchain networks with a variety of heterogeneous designs and functionalities. With the increasing number of blockchain applications and users, it becomes necessary to allow interoperability across isomorphic/heterogeneous blockchains, and further the interoperability is highly demanded in NFT (Non-Fungible Token)-to-NFT trading. This paper proposes a communication model across the blockchains, and an M/Cox/1 queueing model-based model. The cross chain model considers two distinct types of the communication such as atomic swaps and inter-ledger asset transfer. There are two types of communication controls in consideration, namely, Hashed TimeLock Contract (HTLC) for crossing isomorphic chains and Interledger Asset Transfer Protocol (IATP) for crossing heterogeneous chains. In the proposed performance model, a Poisson arrival process is assumed at a rate of λ, and two service rates are assumed to be exponentially distributed at a rate of µ1(asset swap / transfer Pre - Commit and verify) and µ2(transfer commit/rollback), respectively. Lastly, the selection ratio of a communication protocols between IATP and HTLC is assumed to be at a rate of$p$and ($1 -p$), respectively. Extensive numerical simulations are performed to study the impact of communication request arrival rates, communication service rate, communication traffic rates and proportion of the communication protocols on$L$(number of transactions in the system) and W(average waiting time in the system of transaction). This paper will establish a sound theoretical foundation to identify the interrelation and impacts between various design variables on the performance, and ultimately will reveal an optimal solution to a high performance design of cross chain across isomorphic /heterogeneous chains.