MELBOURNE, Australia -- A comfortable first-round victory complete at the Australian Open, Canada's Milos Raonic will next meet a player who has given him trouble in the past and is brimming with confidence.

Gilles Muller won his first ATP World Tour title last week in Sydney to jump six spots to No. 28 in the world rankings. He has also won both of his previous meetings against the third-ranked Raonic.

"I've got to take care of my own end of the court, serve well, and try to create some opportunities on his (serve)," Raonic said Tuesday after a 6-3, 6-4, 6-2 win over Germany's Dustin Brown. "Obviously it's going to be a bit more of a predictable match than today but it's still going to be one where I'm going to have to step up and take it from him rather than expect him to give it to me."

Muller beat Raonic at Wimbledon in 2011 when the Canadian retired due to injury. His other victory was a 7-5, 7-6 (1) decision a year later on an indoor hardcourt in Valencia.

The unseeded Luxembourger opened the first Grand Slam of the 2017 season with a 7-6 (6), 7-6 (5), 6-3 win over American Taylor Fritz.

Raonic, meanwhile, played Brown for the first time since their initial meeting in the first round of last year's U.S. Open, where the Canadian also won in straight sets.

"I did what I needed to do," said Raonic. "I took care of my serve, I broke quite early in all the sets. It just dropped off a little bit when I faced a few dangers on my service games in the beginning of the third, end of the second.

"Obviously you want to get in, get out and play as well as you can starting off. Obviously it's not easy. I played solid and I was efficient out there, which I'm happy with."

Last year as the No. 13 seed, Raonic had his best performance at Melbourne Park. He advanced to the semifinals before losing to Andy Murray.

The 26-year-old Raonic is playing in his seventh Australian Open and in his 24th major. His best result so far has been a run to the Wimbledon final last year.

Also Tuesday, Toronto native Peter Polansky dropped a 6-0, 3-6, 3-6, 6-2, 3-0 decision to Spain's Pablo Carreno Busta. Polansky had to retire in the fifth and decisive set.

"Unfortunately I had to withdraw from my match today. My back is fine, but the heat definitely got 2 me. The good news is I am still alive lol," Polansky tweeted.