Exploring Multidimensional Gas Markets on Aptos: A New Frontier for Resource Management
By Guy Goren (Aptos Labs) and Pranav Garimidi (a16z Research)
As blockchain ecosystems evolve, so too must the systems that manage their resources. The concept of Multidimensional Gas (MD-gas) markets has emerged as a research area, offering a more refined approach to allocating and pricing the diverse resources used by blockchain transactions. Unlike traditional gas models, which conflate all resources to a single dimension, typically focused on CPU consumption, MD-gas markets account for multiple dimensions such as computation, memory access, and bandwidth.
At Aptos, we are actively exploring MD-gas markets through simulations to better understand their potential benefits and trade-offs. This post provides an overview of our approach, initial findings, and why MD-gas markets could be a key factor in enhancing blockchain performance.
Why Multidimensional Gas Markets Are Important
In a high-throughput blockchain like Aptos, maximizing resource utilization is essential. Current blockchain gas models, such as Ethereum’s EIP-1559, do not differentiate between resources, as if memory-access and computation are in direct competition. In practice, however, modern blockchain transactions often consume multiple resources, each with its own constraints. For example, while computation may be in low demand, memory access and bandwidth may be in high demand, and thus require distinct management strategies. MD-gas markets enable us to price each resource separately, reflecting its unique demand and availability.
An efficient MD-gas model ensures that no transaction is left unprocessed despite available capacity in some resources. This avoids leaving valuable transactions on the “editing floor” simply because one resource dimension’s capacity is exceeded, while others remain underutilized. Achieving this balance promotes optimal resource usage, enhancing network throughput and contributing to the overall user experience.
One important distinction in our research is that we separate storage from MD-gas markets. Storage imposes non-transient costs on validators — future validators must also maintain stored data. This makes it unsuitable for the short-term, transaction-level pricing model of MD-gas markets. Instead, storage requires a different market design, one that accounts for the long-term nature of its costs, and ensures fair compensation for future validators as well as current ones.
By isolating transient resources like memory access, bandwidth and computation within MD-gas markets, we can better align resource pricing with their actual usage patterns. This helps ensure efficient resource allocation and fairness across the network.
Key Findings From Our Research
At Aptos, our research on MD-gas markets has focused on understanding how different market designs perform in a multidimensional setting. In particular, we’re comparing Vitalik’s MD EIP-1559 proposal to alternative mechanisms like First Price Auctions (FPAs).
Here are some of our initial insights from simulations:
1) First Price Auctions for MD-Gas: FPAs, where users pay the amount they bid, show promise in a multidimensional context. Specifically, FPAs can handle demand shifts more effectively by giving users the flexibility to adjust how they’re bidding based on the relative demand shifting between resources. This could lead to better overall resource usage compared to models like EIP-1559 which have a fixed way of responding to demand shifts and might not adjust prices accurately.
2) User and Validator Incentives: One of the advantages of MD-gas markets is how they reshape the dynamics between users and validators. Users can fine-tune their bids across dimensions, paying exactly for the resources they consume. Validators, on the other hand, gain more flexibility in how they prioritize transactions, leading to higher social welfare by maximizing the value extracted from each block and the overall throughput of the blockchain.
3) Price Predictability: While FPAs can sometimes introduce uncertainty in transaction costs, especially in volatile markets, we found that on-chain tools could mitigate this by providing better price signals. Users can leverage historical data to estimate future costs more accurately across resource dimensions, reducing unpredictability while maintaining flexibility.
4) EIP-1559 Pricing for MD: Ethereum’s multidimensional (MD) proposal suggests generalizing the base fee mechanism directly to multiple dimensions, meaning a transaction would only be valid if its bid meets or exceeds the base fee in every dimension.
This design, however, intensifies an inefficiency seen in EIP-1559: when demand decreases, transactions can be unnecessarily excluded even when a capacity is available. In particular, when demand drops sharply, the base fees might adjust too slowly, and viable transactions are left out despite space. This issue becomes more significant as the number of dimensions grows. Events that were rare in a single-dimension (1D) model are now exceedingly more likely, leading to underutilized capacity and a negative impact on user experience. If an EIP-1559-style base fee is preferred over a First Price Auction (FPA) for MD gas pricing, we propose an alternative generalization. Instead of the piece-wise comparison between each bid and the base fee vector, we suggest using a dot product inequality with the gas limit vector:
This approach averages out single-dimension volatility, improving transaction inclusion rates and overall resource use.
The Road Ahead
Although our initial results are encouraging, MD-gas markets are still a developing concept. More work is needed to refine these mechanisms and ensure they are both practical and efficient. Some of our future research will focus on:
- Hybrid Models: We’re exploring ways to combine the dynamic flexibility of FPAs with the predictability of models like EIP-1559 to create hybrid markets that adapt based on network conditions.
- Dynamic Gas Limits: We plan to investigate how gas limits for different resources can be adjusted in real time, ensuring that the system responds to changing demand while maintaining fairness for users and validators.
- Validator Optimization: Another key area of research is how validators can best optimize transaction packing when dealing with multidimensional resource constraints.
By continuing this research, we aim to contribute to the ongoing development of more efficient resource management systems in blockchain networks. The insights gained from MD-gas market simulations could ultimately help the broader blockchain community build more scalable, flexible, and equitable networks.