Transaction Fees Optimization in the Ethereum Blockchain

Optimizing transaction fees on the Ethereum blockchain is a critical challenge for users seeking cost efficiency without compromising speed. With Ethereum's dynamic fee market, determining the ideal gas price to ensure timely transaction confirmation—while avoiding overpayment—requires advanced modeling and predictive techniques. This article explores a robust, data-driven approach to gas fee optimization, leveraging Monte Carlo simulations and binary search algorithms to help users minimize costs while meeting specific time and probability targets.

Understanding Ethereum’s Gas Mechanism

Ethereum operates on a decentralized network where transactions are grouped into blocks approximately every 15 seconds. Each transaction incurs a fee, denominated in gas, which compensates miners (or validators post-Proof-of-Stake transition) for computational resources used. The total fee is calculated as:

Transaction Fee = Gas Price × Gas Consumed

The gas price (measured in GWei) is set by the user, while gas consumed depends on the complexity of the operation—simple transfers require 21,000 gas, whereas smart contract interactions can consume significantly more.

Miners prioritize transactions with higher gas prices to maximize revenue, creating a competitive bidding environment during network congestion. This leads to fluctuating fees, making it difficult for average users to determine an optimal price.

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The Challenge of Predicting Optimal Gas Prices

Traditional fee estimation tools often fall short because they rely solely on historical block data, failing to account for pending transactions or future network behavior. Most oracles provide a single recommended gas price based on recent blocks but do not allow users to specify:

• A desired confirmation time window
• A minimum probability of success
• Current state of the transaction pool

This lack of configurability reduces reliability, especially during volatile periods.

In contrast, the method proposed by Laurent et al. introduces a probabilistic framework that enables users to define both a time limit T and a success probability α, then calculates the lowest possible gas price that meets these criteria.

Core Keywords:

• Ethereum
• Gas price optimization
• Transaction fees
• Blockchain
• Monte Carlo simulation
• Smart contracts
• Network congestion
• Fee prediction

A Two-Phase Optimization Approach

The solution combines two complementary models: a deterministic model and a stochastic Monte Carlo model, followed by a binary search algorithm to pinpoint the optimal gas price.

1. Deterministic Model: Known Transactions Only

This initial approach assumes full knowledge of all pending and future transactions—a theoretical scenario useful for establishing baseline probabilities. It ranks transactions by gas price and simulates block inclusion under Poisson-distributed block creation (average ~15 seconds).

However, since future transactions are inherently unpredictable, this model has limited real-world applicability.

2. Stochastic Model Using Monte Carlo Simulation

To reflect real-world uncertainty, the authors employ a Monte Carlo simulation that generates thousands of plausible future scenarios based on historical patterns.

Each scenario includes:

• Randomly sampled future transactions
• Estimated gas limits and consumption
• Probabilistic miner behavior (via lower gas price acceptance thresholds)
• Uniformly distributed transaction broadcast and block mining times

For each scenario, the algorithm checks whether the target transaction would be confirmed within time T. After running thousands of simulations (e.g., 2,500), the proportion of successful confirmations estimates the actual probability P(Vtr(T)).

This method accounts for:

• Transaction pool dynamics
• Block gas limits
• Precedence constraints (nonce ordering)
• Miner selection bias

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Binary Search for Optimal Gas Pricing

Once the Monte Carlo engine can estimate confirmation probability for any given gas price, a binary search algorithm efficiently finds the minimum gas price that satisfies the user-defined probability threshold α.

The process works as follows:

1. Set lower and upper bounds for gas price.
2. Compute midpoint value.
3. Use Monte Carlo simulation to estimate confirmation probability at that price.
4. If probability ≥ α, reduce upper bound; otherwise, increase lower bound.
5. Repeat until convergence.

This approach ensures users pay no more than necessary while maintaining high confidence in timely confirmation.

Data Collection and Model Calibration

Accurate predictions depend on high-quality, real-time data. The model uses:

• Historical block data (validated transactions)
• Pending transaction pool snapshots
• Miners’ historical gas price floors
• Network propagation delays

Key parameters derived from data include:

• Average block interval (λ): ~15 seconds
• Block gas limit (BL): median of recent blocks
• Distribution of transaction arrival rates
• Miners’ lower gas price acceptance (LGP): inferred per miner using hash power weighting

A critical insight from testing is that introducing a 2.5-second artificial delay between block mining and transaction receipt improves accuracy—reflecting real-world network latency and processing time.

Experimental Results and Accuracy

Tests conducted on over 5 million Ethereum transactions from November 2019 show strong predictive performance:

With a 2.5-second delay adjustment, the predicted success rates align closely with actual outcomes—deviating by less than 2% on average from the target probability.

While computation time reaches up to 2 seconds per forecast, this trade-off delivers superior configurability and accuracy compared to static or machine-learning-based predictors.

Frequently Asked Questions (FAQ)

Q: Why is gas price so volatile on Ethereum?

Gas prices fluctuate due to supply and demand dynamics. When many users submit transactions simultaneously—such as during NFT mints or DeFi launches—competition increases, driving up prices. Conversely, during low activity, fees drop significantly.

Q: How does this method differ from EIP-1559?

EIP-1559 introduced a base fee that burns and a priority fee (tip) paid to validators. While it stabilizes fees somewhat, users still need to estimate competitive tips. This optimization model can be adapted to recommend optimal tip values under EIP-1559 rules.

Q: Can this model work after Ethereum’s shift to Proof-of-Stake?

Yes. Although miner incentives have changed post-Merge, the core mechanics of transaction prioritization based on fees remain intact. The model's logic applies equally to validator behavior in PoS.

Q: Is there a way to reduce prediction time?

Yes. Precomputing common scenarios or using approximated distributions can speed up execution. For frequent users, caching results for standard time-probability combinations improves responsiveness.

Q: Does transaction size affect confirmation time?

Not directly. What matters is gas limit and gas price. A large transaction with sufficient gas and high pricing will confirm faster than a small one with low fees.

Q: How often should I update my gas price estimate?

During stable network conditions, every 10–15 minutes suffices. During high volatility (e.g., major token launches), updates every 1–2 minutes are recommended.

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Conclusion

Optimizing Ethereum transaction fees is no longer about guesswork or overpaying for speed. By combining Monte Carlo simulations with binary search algorithms, users can now determine the precise minimum gas price needed to achieve desired confirmation odds within a specified timeframe.

This method stands out by incorporating:

• Real-time pending transaction data
• Probabilistic modeling of future events
• Configurable time and success probability settings
• Validation against actual mining outcomes

As Ethereum continues evolving, such data-driven strategies will become essential for cost-effective participation in decentralized applications, trading, and smart contract interactions.

Whether you're a developer, trader, or casual user, leveraging advanced predictive models ensures you maintain control over your transaction costs—without sacrificing reliability.