Limit Order Book Queue Position Fill Simulation

In price-time priority electronic order matching at Optiver and Tower Research, limit orders resting at the Best Bid or Best Ask queue up in strict First-In-First-Out (FIFO) sequence.

Suppose your trading algorithm posts a limit order of size $Q_{own}$ at price $P$. Ahead of your order in the queue rests an initial volume $V_{ahead}$. Subsequently, an event stream of external executions and cancellations occurs at price $P$:

• Trade Event: (timestamp, 'trade', volume): Consumes resting liquidity in FIFO order.
• Cancellation Event: (timestamp, 'cancel', volume): Volume canceled ahead of your position reduces $V_{ahead}$ (up to $V_{ahead} = 0$). Cancellations do not affect your own resting shares.

Your Task

Implement simulate_queue_fills(initial_ahead: int, own_qty: int, events: list[tuple[float, str, int]]) -> dict that simulates the queue and returns a dictionary with:

• 'first_fill_time': float timestamp when your order begins executing (or None if no shares were executed).
• 'full_fill_time': float timestamp when your order is completely filled (or None if unfulfilled).
• 'filled_volume': int total number of shares filled.
• 'remaining_volume': int shares remaining unfilled.

Constraints

• $0 \le initial\_ahead \le 10^9$
• $1 \le own\_qty \le 10^9$
• Events are sorted chronologically by timestamp ($t_1 \le t_2 \le \dots$).
• $1 \le \text{len}(events) \le 10^5$

Examples

events = [
    (1.0, 'trade', 30),
    (2.0, 'cancel', 20),
    (3.0, 'trade', 60)
]
# initial_ahead = 50, own_qty = 40
# t=1.0: trade 30 -> ahead = 20, own = 40
# t=2.0: cancel 20 -> ahead = 0, own = 40
# t=3.0: trade 60 -> ahead=0, fills all 40 of own! first_fill=3.0, full_fill=3.0