A Mathematical Framework for Performance Multi-Objective Optimization of Blockchain Sharding with MongoDB Distributed Storage

Source abstract

Blockchain sharding partitions network state and transaction load across multiple parallel subchains (shards) in order to overcome the throughput ceiling of monolithic consensus protocols. In this study, we develop a mathematical performance model for blockchain sharding in which the underlying persistence layer is realized as a MongoDB distributed cluster, so that shard placement, chunk migration, and query routing are governed by MongoDB’s own sharding sub-system, namely the mongos routers, the config servers, and the balancer. Closed form expressions are formulated for aggregate throughput, transaction latency, load-balance fairness, and scalability performance as functions of the shard count n, and a multi-objective optimization criterion is derived for selecting a practical operating point. A numerical analysis over n = 1 to 64 shards quantifies the trade-off between raw throughput growth and cross-shard coordination overhead. The analysis shows that the marginal throughput gain per doubling of shard count falls from 90.5% (for n = 1 to 2) to 22.9% (for n = 32 to 64), while scalability performance drops below 75% once n exceeds 8. The results indicate a practical operating range of 8 to 16 shards for MongoDB backed sharded blockchain deployments under the assumed workload parameters, beyond which coordination and rebalancing costs dominate any additional throughput gains.