Is the Udhiyah obligatory for a married Muslim traveler who will arrive on the first day of Eid or on the Day of Arafah, and does its obligation recur every year with the recurrence of his travel?

The Udhiyah (sacrifice) is a confirmed Sunnah annually for the one who is able, based on the saying of the Prophet, peace and blessings be upon him: "O people, upon every household in every year is an Udhiyah." Your travel does not affect this ruling.