This is the 15562nd most frequent Russian word.
прибытию
"Arrival."
In this sentence, 'прибытию' is used to refer to the concept of 'arrival' as an event or occasion, used in the dative case to express welcome towards it.
Добро пожаловать к нашему прибытию.
Welcome to our arrival.
Here, 'прибытию' is in the dative case to indicate the action towards which preparations were directed.
Мы готовились к прибытию гостей.
We were preparing for the arrival of the guests.
In this case, 'прибытию' is used in the instrumental case to describe the event of arriving.