North Wales has no neurosurgery and no thrombectomy service. Stroke patients who need a clot removed go to the Walton Centre in Liverpool, which runs the service 24 hours a day. Critically ill children go to Alder Hey with the North West and North Wales paediatric transport service. Cardiac surgery goes to Liverpool Heart and Chest. Every one of those journeys runs down the A55, over the Dee, and across or around the Mersey, and every one of them has a clock on it: in the French ETIS registry (2024), transferred thrombectomy patients whose imaging-to-puncture time ran 120 to 180 minutes had 15% lower odds of a good outcome than those under 120, and over 180 minutes 36% lower. Adult major trauma from North Wales goes to Royal Stoke, which is outside this corridor and out of scope here.
The corridor's real road graph is baked from OpenStreetMap: the A55 from Bangor, the A494 and A550 to the M56, the M53 to the Mersey tunnels, the M56 and Mersey Gateway to the M62, the A548 coast road and the A483 from Wrexham, and the Liverpool approaches to the hospitals, draped on real elevation data. It then samples hundreds of days. Each day has weather, a time of day, a set of chokepoints that may be closed or crawling, tunnel queues, and whether the helicopter is available. For each day it answers three questions:
Which way? A crew following the nominal plan learns of a closure when it reaches it and re-routes from there. A crew with live information routes around it from the start. The gap between those two is what a control room's data is worth.
Road or air? The Wales Air Ambulance flies from Caernarfon by day; night cover comes from further away. Aintree (next to the Walton Centre) and Alder Hey have helipads, Liverpool Heart and Chest does not, so for some pathways the helicopter lands and the patient still finishes by road.
Where should the crew wait? A stand-by transfer crew has to reach the patient before it can reach Liverpool. Choosing the staging sites that meet the window most often, across the three hospitals' demand and the sampled days, is a scenario-weighted covering problem.
The crews tab opens on the base question: the one commissioned team at each of eighteen candidate bases over the same sampled year, then more crews, then the roster and a single day of the service: strokes, children, cardiac cases and patients going home, an aircraft that is busy until it is back on its pad, crews that are the wrong side of the Mersey when the next call comes. The air base tab takes the April 2024 aircraft decision apart. The critical response tab asks the narrower question of where a crew must wait to beat a clinical clock, and draws that search as the spin network it becomes.
Congestion is not a switch. Flow follows the daily profile, each class of road runs at a different fraction of its capacity, and journey time rises non-linearly as that fraction approaches one — the volume-delay curve transport planning has used for decades. Urban junctions carry their own delay, which is where city journey time actually goes. Tunnel queues scale with how busy the network is rather than with a peak flag.
An ambulance on blue lights does not sit in that queue the way general traffic does: it filters, uses the offside, and drivers pull over. So it recovers much of the congestion delay — but least of all in a tunnel or on a bridge, where there is nowhere for anyone to go. Ignoring that would make congestion look far more decisive for an ambulance than it is. The road option also carries the crew's packaging time and the handover at the far end, exactly as the helicopter option always carried its activation and handover; counting them for one and not the other quietly rigged the comparison.
The Penmaenbach headland had 25 eastbound collisions in 2023/24. The Conwy tunnel, the longest road tunnel in Wales, has three maintenance closures a year and lost a day to fire in June 2025. Those facts set the shape of the table. The closure and slow-down probabilities per hour, the tunnel queue ranges and the helicopter availability are illustrative estimates, and the modal says so because the whole point of the twin is what a calibrated version of that table would let a planner do with incident logs and traffic counts they already hold.
The routing is classical and stays that way: a shortest path on eleven thousand links is not a hard problem. Two things here are. Estimating how often a rare compound failure blows the window is a tail probability, and quantum amplitude estimation reaches a given precision with quadratically fewer sampled days than Monte Carlo. Choosing staging sites against an ensemble of days is a scenario-weighted covering problem, sparse and geometric, the same shape as the resilience twin's pre-positioning. Both are reported here in the form a quantum solver would receive, sized honestly.