# Denial-of-Service Attacks on Permissioned Blockchains: A Practical Study
## 5 Experiments and Results
### Statistical Analysis of System Performance Under Attacks  
To evaluate the fundamental relationships between the attack intensity and system performance, we employed the Spearman rank-order correlation (\(\rho\)), which detects monotonic trends (consistent directional relationships where variables increase or decrease together without assuming linearity). This non-parametric method is ideal for our attack scenarios. We computed the \(\rho\) between each attack parameter (batch timeout, probability, malicious clients, tick interval) and performance metric (delay, throughput, successful transactions) to test the hypothesis that a higher attack intensity monotonically degrades system behavior. The Spearman rank correlations revealed perfect monotonic relationships across all the attack scenarios. All correlations exhibited either perfect (\(\pm 1.00\)) or near-perfect coefficients with extremely low \(p\)-values (typically \(<\)0.0 or \(<\)10\({}^{-24}\)). These values indicate highly statistically significant relationships. This analysis revealed that increases in the attack parameters clearly increased the delay and reduced the throughput and successful transactions. It confirmed that the attack intensity always degraded the performance within the tested ranges, with no exceptions or optimal operating points. Our analysis revealed clear degradation patterns across all attacks. This is shown in Table 3.  
Next, we employed regression analysis to quantify the precise functional relationships between the attack parameters and the system performance. We evaluated multiple  
Figure 13: CouchDB attack scenario where the attacker forcibly stops the CouchDB docker container on a peer to deny access to the ledger.  
regression forms: linear, quadratic, exponential, and power law, where we selected optimal fits through adjusted \(R^{2}\) maximization and residual analysis. The resulting models revealed attack-specific scaling behaviors and quantified degradation patterns with a high explanatory power(\(R^{2}\geq 0.985\)), which enabled insights for security optimization.  
The batch timeout attacks exhibited a quadratic increase in the transaction delay, where the delay grew with the square of timeout duration. The throughput decayed exponentially, where it halved every 6.36 s. This confirmed that the timeout values beyond 5 s triggered disproportionate latency penalties.  
The block discard and collusion attacks followed power-law dynamics. The throughput scaled inversely with the discard probability, where a 10% probability increase caused a 7.14% throughput loss. The collusion attacks demonstrated a 50% faster exponential decay than the block discards, indicating a more severe degradation per unit probability increase. The recorded transactions decreased linearly in both attacks, where the block discards caused 11% greater transaction losses per probability unit.  
The malicious client attacks showed a quadratic increase in delay, where the delays compounded rapidly beyond five clients. The throughput decayed exponentially, where each additional client reduced the throughput by 16.7%. This highlighted the non-linear risk of coordinated adversaries.  
The consensus protocol attacks showed near-perfect inverse relationships. The delay increased linearly with tick intervals, where 2.64 s was added per 500 ms interval. The throughput followed a reciprocal pattern, which confirmed that halving the tick interval doubled the throughput.