Strategic Users in a Priority Queue with Bulk Service on Blockchains

Battle Count: 63

The paper is primarily about blockchain transaction fee economics and queueing theory rather than quantitative trading. However, it has tangential relevance to crypto trading: (1) understanding transaction fee dynamics affects execution costs for on-chain trading, (2) the queueing model could inform optimal timing of transaction submission, (3) cross-chain fee analysis is relevant for DeFi arbitrage strategies, (4) the cost structure insights could inform gas fee prediction models for trading bots. The connection to traditional quantitative trading is minimal.

High complexity due to: (1) M/GK/1 queue analysis with general service distributions requiring probability generating functions and contour integration, (2) Rouché's theorem and Residue theorem applications for finding K-1 roots of D(z) in the unit circle, (3) numerical integration over complex contours for expected queue length, (4) finite difference estimation of dW/db from empirical data, (5) cubic spline fitting for monotonicity enforcement, (6) cross-chain normalization procedures. The mathematical derivations span multiple sections with intricate proofs. K values in thousands (2922 for Bitcoin) make root-finding computationally challenging.

The paper provides detailed mathematical derivations and uses publicly available Bitcoin, Litecoin, and Dogecoin transaction data from 2023. However, no code repository is mentioned. The numerical methods (contour integration, cubic spline fitting, finite difference estimation) are described but implementation details are limited. Key parameters (K=2922, ρ̄=0.97462, µ=10 min) are explicitly stated. The Oblakova et al. (2019) root-free method is referenced for computing expected queue length.