Southwest Airlines is trying a new boarding procedure in the Bay Area. Will it help?

Southwest Airlines has very quietly introduced an alternative boarding procedure at a handful of markets the carrier serves on the West Coast, including San Jose.

But don’t look for the procedure to be rolled out ever at the low-fare carrier’s largest hub at Chicago’s Midway International Airport.

The boarding arrangement Southwest is using in California markets such as San Jose, Sacramento, Long Beach and Burbank involves passengers boarding not only from the traditional jetway to the plane’s…