Paper: arXiv 2302.01663

Authors: Andrew W. Macpherson

Abstract

We describe a plausible probabilistic model for a blockchain queueing environment in which rational, profit-maximising schedulers impose adversarial disciplines on incoming messages containing a payload that encodes a state transition in a machine. The model can be specialised to apply to chains with fixed or variable block times, traditional priority queue disciplines with `honest’ schedulers, or adversarial public mempools. We find conditions under which the model behaves as a bulk-service queue with priority discipline and derive practical expressions for the relative block and message number of a transaction. We study this setup in the context of orders to a CFMM DEX where the execution price a user receives may be quite sensitive to its positioning in the chain – in particular, to a string of transactions scheduled for prior execution which is not knowable at the time of order creation. We derive statistical models for the price impact of this order flow both in the presence and absence of MEV extraction activity.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and mathematical framework modeling blockchain queueing environments, MEV extraction, and CFMM price impact using bulk-service queues. However, it leans heavily theoretical with limited empirical backtesting or real-world transaction data validation, impacting its empirical rigor and reproducibility scores.

Research Flowchart

  flowchart TD
    A["Research Question: Model Blockchain Queues & Order Flow Price Impact in CFMMs"] --> B["Inputs: Blockchain Rules, CFMM State, Rational Scheduler Actions"]
    B --> C["Develop Probabilistic Queueing Model<br/>(Adversarial Mempool vs. Honest Priority)"]
    C --> D["Derive Block & Position Distribution for Transactions"]
    D --> E["Model Price Impact Dynamics<br/>(With & Without MEV Extraction)"]
    E --> F["Outcomes: Conditions for Bulk-Service Queueing & Price Sensitivity Metrics"]