The servers for any Call of Duty game are usually pretty darn solid.
But users have been reporting connection problems with Call of Duty: Black Ops III and these issues haven't yet been completely fixed.
There has to be a lot of server activity this weekend, so perhaps that's tossing a wrench into the works. If you check the game's status page , the Xbox One and Xbox 360 versions are currently at "Defcon 3," which translates to: "ONLINE SERVICES ARE DEGRADED. USERS IN SOME REGIONS MAY EXPERIENCE CONNECTIVITY ISSUES." And while the PlayStation 4 and PlayStation 3 versions say the game is running at "Defcon 5," where "all online services are fully operational," many gamers – including myself – haven't been able to connect.
But it's not entirely unexpected. Like I said, there has to be a ton of traffic this weekend, so just be patient.
Related Game(s): Call of Duty: Black Ops III