Stable Blockchain Sharding under Adversarial Transaction Generation

TL;DR

This work analyzes the stability of blockchain sharding under adversarial transaction generation, establishing a fundamental upper bound on the stable injection rate and proposing two scalable schedulers for uniform and non-uniform shard networks. The Basic Distributed Scheduler operates with a central leader and graph coloring to serialize conflicting transactions, achieving provable stability bounds in the uniform setting. The Fully Distributed Scheduler removes central control via hierarchical shard clustering, providing stability guarantees in non-uniform networks and associated latency bounds. Through simulations, the authors validate bounded queues and latency within the proposed bounds and demonstrate the relative performance under different network topologies and burstiness. Overall, this is the first adversarial stability analysis of sharded blockchains and lays groundwork for scalable, attack-resilient scheduling in distributed ledger systems.

Abstract

Sharding is used to improve the scalability and performance of blockchain systems. We investigate the stability of blockchain sharding, where transactions are continuously generated by an adversarial model. The system consists of $n$ processing nodes that are divided into $s$ shards. Following the paradigm of classical adversarial queuing theory, transactions are continuously received at injection rate $ρ\leq 1$ and burstiness $b > 0$. We give an absolute upper bound $\max\{ \frac{2}{k+1}, \frac{2}{ \left\lfloor\sqrt{2s}\right\rfloor}\}$ on the maximum injection rate for which any scheduler could guarantee bounded queues and latency of transactions, where $k$ is the number of shards that each transaction accesses. We next give a basic distributed scheduling algorithm for uniform systems where shards are equally close to each other. To guarantee stability, the injection rate is limited to $ρ\leq \max\{ \frac{1}{18k}, \frac{1}{\lceil 18 \sqrt{s} \rceil} \}$. We then provide a fully distributed scheduling algorithm for non-uniform systems where shards are arbitrarily far from each other. By using a hierarchical clustering of the shards, stability is guaranteed with injection rate $ρ\leq \frac{1}{c_1d \log^2 s} \cdot \max\{ \frac{1}{k}, \frac{1}{\sqrt{s}} \}$, where $d$ is the worst distance of any transaction to the shards it will access, and $c_1$ is some positive constant. We also conduct simulations to evaluate the algorithms and measure the average queue sizes and latency throughout the system. To our knowledge, this is the first adversarial stability analysis of sharded blockchain systems.

Figures (3)

• Figure 1: Representation of time slots division in Algorithm \ref{['alg:basic-distributed-scheduler']}
• Figure 2: Simulation results for Algorithm \ref{['alg:basic-distributed-scheduler']}: On the left, the average number of pending transactions in the pending queue of each home shard is shown versus $\rho$. On the right, the average transaction latency measured in rounds is plotted against $\rho$.
• Figure 3: Simulation results for Algorithm \ref{['alg:fully-distributed-scheduler']}: On the left, the average number of pending scheduled transactions in the queue (scheduled but not committed) of cluster leader shard is shown versus varying values of $\rho$. The average transaction latency measured in rounds is plotted against $\rho$ on the right.

Theorems & Definitions (13)

• Example 1
• Theorem 1: Stability Upper Bound
• proof
• Lemma 1
• proof
• Theorem 2: BDS stability
• proof
• Lemma 2
• proof
• Lemma 3