Which is the strongest meteor shower expected in the next years in the Northern hemisphere?
Is it possible to give good predictions for this?
The Perseids in August are always good with 30+ meteors per hour. If you can get to a dark sky, you won't be disappointed. The Leonids hit their thirty-three year peak just a couple years ago so it will be a while before they peak again. The Perseids peaked in the mid-1990s (I saw 200 meteors in 1.5 hours through a hole in the clouds that just showed Perseus, Cassiopeia and Pegasus), but I don't know what the period of that shower is.
You can find lots of useful meteor shower information at the American Meteor Shower website.
There are a few meteor showers that merit mentioning:
Of course, these rate estimates are not absolute, and in rare cases some showers (for example, Leonids) can flare up, with many hundreds of meteors per hour. Also, some showers might be more liable to succumb to cloudy days than others, specifically, the ones that occur during the northern winter (Geminids, Quadrantids, etc.).
The Perseids in early August is the most reliable shower year in, year out, and the only one I bother watching. The Geminids in early December are also good, but it's too darned cold up here in Canada. I see sporadic meteors just about every night I'm out observing.