The Order Book as a Markov Queuing System under a Fixed Reference Price

The queue-reactive model treats the limit order book, within periods where a reference price is constant, as a finite-dimensional Markov queuing system in which order-flow intensities depend on the current book state. It reproduces both high-frequency book stylized facts and, through reference-price moves, lower-frequency price dynamics. We read it as the tractable bridge between book-level mechanics and the price series memos actually reference.

Each queue Q_i evolves with state-dependent arrival and cancellation intensities λ_i(Q); the reference price updates via a coupled jump process, making the full system a piecewise-stationary Markov chain over book configurations.

The model's discipline is that much of what looks like pressure at the book level is queue dynamics under a constant reference price — mechanical, mean-reverting, and not a price-formation signal. Only reference-price transitions carry the lower-frequency information a directional memo cares about.

Cautions against reading book imbalance as directional conviction at horizons shorter than the reference-price dynamics; book-level features should be down-weighted relative to confirmed reference-price moves.

Assumes independence and stationarity of queues within a reference-price regime that real books violate during stress; calibration needs venue-level message data.