Bitcoin is currently subject to a significant pay-for-speed trade-off. This is caused by lengthy and highly variable transaction confirmation times, especially during times of congestion. Users can reduce their transaction confirmation times by increasing their transaction fee. In this paper, based on the inner workings of Bitcoin, we propose a model-based approach (based on the Cram\'er-Lundberg model) that can be used to determine the optimal fee, via, for example, the mean or quantiles, and models accurately the confirmation time distribution for a given fee. The proposed model is highly suitable as it arises as the limiting model for the mempool process (that tracks the unconfirmed transactions), which we rigorously show via a fluid limit and we extend this to the diffusion limit (an approximation of the Cram\'er-Lundberg model for fast computations in highly congested instances). We also propose methods (incorporating the real-time data) to estimate the model parameters, thereby combining model and data-driven approaches. The model-based approach is validated on real-world data and the resulting transaction fees outperform, in most instances, the data-driven ones.

翻译：比特币当前面临显著的“按速度付费”权衡问题，这是由于交易确认时间过长且高度可变（尤其在网络拥堵时期）所致。用户可通过提高交易手续费来缩短确认时间。本文基于比特币内部运作机制，提出一种基于模型的方法（以Cramér-Lundberg模型为基础），通过均值或分位数等指标确定最优手续费，并精准刻画给定手续费下的确认时间分布。该模型具有高度适用性，因为它自然成为内存池过程（追踪未确认交易）的极限模型——我们通过流体极限严格证明这一结论，并将其推广至扩散极限（针对高拥堵场景下快速计算的Cramér-Lundberg近似模型）。同时，我们提出了结合实时数据的参数估计方法，实现了模型驱动与数据驱动方法的融合。基于真实数据的验证表明，在多数场景下，该模型方法得出的交易手续费优于纯数据驱动方案。