Rules

Gridlock — rules

Four parcel fleets share one city. A fleet scores one point per parcel its own vans deliver. Nobody controls the traffic lights.

The city

• 81 intersections on a 9 × 9 grid, (ix, iy) with ix, iy ∈ 0..8, origin top-left. Node (ix, iy) sits at pixel (64 + 112·ix, 64 + 112·iy), so the board is 1024 × 1024.
• 144 road segments join horizontally and vertically adjacent nodes; each carries two directed lanes, one per direction, for 288 lanes numbered 0 … 287 in a fixed order (horizontal segments first, row-major, → then ←; then vertical segments, column-major, ↓ then ↑).
• A lane is a chain of 14 cells of 8 px. Cell 0 is just downstream of the lane's tail intersection; cell 13 is the stop line. A cell holds at most one vehicle — that single rule is what produces spillback.
• A segment is an arterial if it lies on ix ∈ {2,4,6} or iy ∈ {2,4,6}. Arterials are cheaper to plan over and discharge twice as fast. They are also where everyone's greedy plan goes.
• The node grid is partitioned into a 3 × 3 district grid, NW N NE / W CENTRE E / SW S SE. A district is how a policy names a place and how the view reports congestion.
• Four depots, one per quadrant, on the mirror orbit of (1,1): D0 (1,1) Carbon, D1 (7,1) Oxygen, D2 (1,7) Germanium, D3 (7,7) Silicon. Alias and colour belong to the depot, never to the seat; the seat → depot permutation is drawn from the episode seed and re-drawn every episode.
• Signals are fixed-time and identical everywhere: a 96-tick (4.0 s) cycle, north–south green for the first 48 ticks, east–west for the rest, with a per-node offset ((ix+iy) mod 4) × 24 so diagonal green waves exist for a router to ride. phase(n,t) = ((t + offset(n)) mod 96) < 48.

Vehicles and parcels

Each seat owns 50 identical vans. A van is docked (0), loaded (1, carrying a parcel), empty (2, returning), or stalled (3, on the road and not advanced for 24 ticks). Vans never crash, never break down, and never interact except by occupying cells.

Every 24 ticks (1.0 s) each fleet receives exactly one new order into a backlog capped at 80. Demand is identical up to symmetry: one canonical destination sequence is drawn over the non-depot nodes and the fleet at depot Dj receives mirror_j of it, so all four fleets face the same pattern reflected onto their own quadrant — and all four pull through CENTRE equally.

Routing

Every van plans over the directed lane graph with Dijkstra (integer costs, ties by ascending lane id):

cost(lane) = ((laneBase + jamTerm + avoidTerm) * corridorFactor) div 100 + tieNoise
laneBase   = 48 arterial / 64 local
jamTerm    = (congestion_weight * q(lane) * 24) div 100      q = vans now in the lane, 0..14
avoidTerm  = 240 when the lane's HEAD node is in the avoided district
corridorFactor = 60 when BOTH endpoints are in the preferred district, else 100

With congestion_weight = 100 a full lane carries jamTerm = 336 against a base of 48–64: the road is effectively closed. With congestion_weight = 0 the router is pure greedy shortest path.

A van is pushed onto the pending-replan FIFO when it has no route, when its target changed, when it was served into a node whose next lane already holds replanQueue = 3 + patience·10/100 vans, or at the start of a turn. At most 24 Dijkstra runs execute per tick; a van still waiting keeps driving its old route.

The tick, in order, with no exceptions

1. Turn clock. Every 240 ticks: install the four routing plans, enqueue every on-road van for a replan (ascending global van index), roll the per-turn counters, emit turn_start, one plan per seat and one meter per seat.
2. Signals. A pure function of the tick and the node offset.
3. Orders. Every 24 ticks, one parcel per fleet, skipping any fleet at the backlog cap.
4. Loading. Every docked van without a parcel and with a non-empty backlog begins loading. It takes the order chosen by priority: near = smallest Manhattan distance from the depot (ties → oldest), far = largest (ties → oldest), fifo = oldest. Loading takes 12 ticks.
5. Dispatch (fleet metering). Every 12 ticks, per fleet: activeCap = (dispatch·50 + 50) div 100, releasePerStep = 1 + (100 − spread)·5 div 100 (spread 0 → six per step, 100 → one). While the fleet is under its cap, under its per-step allowance, has a loaded-and-waiting van, and cell 0 of that van's first lane is empty, release it. This is the only place a fleet can hold itself back, and it is the commons lever.
6. Movement. Every 3 ticks, per lane in lane order, walk the vans downstream-first (cell 12 → cell 0); a van advances one cell if that cell is empty. A van at the stop line does not move here — it is the intersection's business.
7. Intersection capacity and signal service. Every 6 ticks, per node in node order, for each green approach in the fixed order N, E, S, W: discharge up to 2 (arterial) or 1 (local) vans from the stop line, oldest first. A discharge is legal only if the receiving cell is empty. An illegal discharge is simply not made. One cell holds one van, so the stop line only ever holds one: an arterial's second discharge first pulls the van in the cell behind the stop line up into the vacated stop line, then crosses it. That promotion is part of the service step, not of movement — it is the only way two vans clear one green step — and it never puts two vans in a cell: the cell behind is emptied before the van is re-indexed.
8. Spillback. There is no step for it, and that is the point: a blocked van stays at the stop line, movement cannot enter an occupied cell, so a full receiving lane freezes its feeding approach, which fills, which freezes the approaches feeding that.
9. Pickup and delivery, resolved inside the discharge:
   • loaded van crossing into its parcel's destination → delivered += 1, a deliver event with the trip time, target becomes the depot, and it enters cell 0 of the first lane of its return route. If that cell is occupied it stays at the stop line — a delivery bay that blocks the road.
   • empty van crossing into its own depot → absorbed into the dock, which never blocks.
   • Crossing any other fleet's depot does nothing: you cannot deliver to, load at, or steal from a rival depot.
10. Replans. Pop up to 24 vans from the FIFO and run Dijkstra with the fleet's current plan and the current occupancies.
11. Statistics. Per-lane occupancy and per-van stall ticks accumulate. Every 48 ticks the 3 × 3 district digits and the city jam_index are recomputed and a heat event is emitted. A lane crossing 11 vans emits jam; falling back below 6 emits jam_clear. Four or more fully blocked lanes whose head nodes lie in one district emit one gridlock for that district (at most one per district per 240 ticks).
12. Keyframe. Every 24 ticks: the tick, all 200 vans' (lane, cell, state), the four delivered counters, the four on-road counts, the four backlog sizes, the city jam index, and the u32 state digest.
13. Seek snapshot. Every 240 ticks the runtime keeps a full state snapshot in memory so a backward seek in the viewer replays at most one turn. Snapshots are never written to the replay.
14. End check.

Scoring and endings

score[s] = float(delivered[s])       # raw count, NOT normalised. Higher is better.
win[s]   = delivered[s] == max(delivered) and that maximum is unique

winner is that slot index, or null on a tie.

No other value may appear. A seat that never connects does not end the episode: its fleet is driven by the dispatcher baseline for the whole match, the no-show is reported to COGAME_PLAYER_FAILURE_URI, and the match plays to full time.

Determinism

Same seed + same resolved plan stream ⇒ the same digest at every keyframe, in the native build and in the emscripten build. The whole step is integer: no sin, cos, tan, exp, ln, pow, sqrt, hypot, fmod or float arithmetic appears in the step path, and -ffast-math is banned. A source-grep test enforces both.