Sitcoms with plot/subplot structure

[Alan Brady's Hair]

Sitcoms have always made use of subplots that would crash into the main plot at the last minute. For instance, Ollie Douglas is taking his apples to town, the truck breaks down, and somehow the day is saved because Lisa has been experimenting with her hotscake making process.

What, though, was the first show that routinely used multiple plots in an episode, even if they didn't eventually tie together? Was it Barney Miller? It seems like they nearly always had multiple people in the squad room, sometimes tying together, sometimes not.