The narrow ramp at the outside edge of these stairs allows a cyclist to roll a bike up the incline while walking on the stairs.
Where the terrain is too steep for a walkable ramp, this treatment has several advantages for both cyclists and pedestrians.
For cyclists, it makes climbing the stairs easier, especially if the bike is heavily loaded. It allows stopping on the stairs without having to set down a bike. And it gets the bike off to the side where it does not create conflicts with other stair users.
For pedestrians, the ramp leads cyclists to self-segregate to the outside edge of the stairs, leaving the center of the stairs and the handrail available for pedestrians.
This staircase connects two major cycling routes in Seattle, Lakeside Avenue and Interstate 90. I-90 crosses over Lake Washington here on an elevated bridge several stories above Lakeside Ave.
I've seen this concept retrofitted onto existing staircases as simply as laying a length of worn railroad rail along the edge of the stairs, providing a channel (sometimes called a "runnel") that guides the wheels and stays put by its own weight.