  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.
