Delay-Oriented Transaction Packaging Ordering in Sharded Blockchains

In blockchain, miners make profits by packaging transactions. There are a large number of pending transactions in the blockchain, and users often assign high transaction fees to reduce the delay in transaction packaging. However, in sharded blockchains, it requires more computational and communication resources to process cross-shard transactions than intra-shard transactions. As a result, miners are inclined to package intra-shard transactions to maximize their profits when packaging transactions, and cross-shard transactions with higher transaction fees are unable to be processed in time, which degrades the quality of service (QoS) of users. That is, the existing transaction packaging methods lack a clear mechanism to ensure that the QoS of users is directly related to the transaction fees they pay. In this paper, we design a new incentive mechanism, such that the block reward is not a fixed value but is related to the transaction processing delay and the number of cross-shard communications involved. The block reward can encourage miners to process transactions in time. We then study how to maximize the total miners' profit by determining the appropriate transaction packaging order to provide QoS to users. Specifically, we model the problem of transaction packaging ordering in each shard as a delay-oriented transaction processing problem and propose a Transaction Delay Optimization algorithm (TDO). Theoretical analysis proves that TDO is an approximation algorithm for the transaction packaging ordering problem with the approximation ratio of $\frac{eC}{({e - 1})C - 2eS_{\text{max}}}$, given block capacity $C$ and maximum transaction size $S_{\text{max}}$. We conduct experiments through simulations. Simulation results show that TDO can effectively provide QoS to users and maximize the profits of miners.