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.

翻译：我们描述了一个适用于区块链排队环境的合理概率模型，在该环境中，理性且追求利润最大化的调度器对包含编码机器状态转换的有效负载的传入消息施加对抗性策略。该模型可专门应用于具有固定或可变区块时间的链、采用“诚实”调度器的传统优先级队列策略，或对抗性公共内存池。我们找到了该模型表现为具有优先级策略的批量服务队列的条件，并推导出交易相对区块序号和消息序号的实用表达式。我们以CFMM去中心化交易所的订单为背景研究这一设置——用户获得的执行价格可能对其在链中的位置高度敏感，尤其对一串计划提前执行但创建订单时不可知的交易序列敏感。我们推导了在存在和不存在MEV提取活动情况下该订单流的价格冲击统计模型。