Madrid's T4 at Barajas is a lovely airport, spacious and all Iberia flights arrive and depart theoretically from this terminal. However, there is the T4S which is a satellite. If the passengers arrived at T4S, which they normally would do from Chicago and then had to fly from T4, there is a shuttle train which goes directly between the terminals and takes 4 minutes. However, T4, whilst visually stunning is a big space... and the distance from the gate the train could be some distance. The shuttles run every 3 minutes.
The route Madrid to Rome is the single busiest air route from Madrid. There are loads of flights from Madrid to Rome..
It is another.. "they should have held the flight" story, and there will be loads of explanations... but you may wish to know this. The "slots" that airlines operate from in Europe are allocated in Brussels and if you miss your "slot" particularly at a busy time, it can cause delays which reverberate throughout the system for the rest of the day. I would have hoped that with that number of transfers, a decision would be made to hold the flight... but we will never know the whole circumstances in this case.
However, I can tell you this. If you have to transfer between flights in Europe... T4 Barajas is one of the airports I would choose to do it in. It is light, spacious, visually stunning and calm...
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