PBS isn't a network. It's a program provider, and most of its programs are not market-exclusive.
As PBS evolved out of the old National Educational Television (NET), it inherited a patchwork of member stations. Some were statewide educational networks like New Hampshire, Connecticut, Maine and Vermont. Some were individual local outlets operated by colleges and universities. Some were individual local outlets operated by community nonprofits like WGBH. Because PBS's mission was to spread its programming as widely as possible, it was happy to link up with as many stations as it could - especially because in those early years, there was no network schedule per se, with most shows being distributed on tape/film from station to station by bus or mail. It was only in the eighties that PBS began moving toward a national prime-time schedule, and it was at that point that we ended up with one primary PBS station per market.
There were once many markets with "duopoly" PBS signals like WGBH/WGBX. Albany, Buffalo, Philadelphia, Washington, Chicago, San Francisco, Pittsburgh, Minneapolis, Milwaukee and Dallas all had two stations operated by a common owner. Often, as with WGBH/WGBX, one station showed the main PBS programming while the other was used for classroom programming, reruns, or even the kind of specialty stuff (statehouse coverage, for instance) that wouldn't have made sense on the main channel. Most of those duopolies went away in the 80s and 90s, especially as the advent of DTV multicasting gave every station the opportunity to run multiple program streams. Today only Boston, Milwaukee and Minneapolis remain from that list, and all 3 are using their dual signals in much the same way - HD with full bandwidth on one channel, multiple SD streams on the other.
In many other markets, multiple separately-owned PBS stations evolved for various reasons. Sometimes there was a college or school district station that grew up parallel to a community-owned station (WLRN/WPBT Miami, WUSF/WEDU Tampa). Sometimes there was both a statewide network and a separate local station (WGTV/WPBA Atlanta), or two overlapping statewide networks (Nebraska and Iowa, both viewable in Omaha/Council Bluffs). Sometimes there were just multiple community groups - KQED San Francisco/KTEH San Jose, or WNET New York/WLIW Long Island. And in some cases, you had all of the above; the Los Angeles market ended up with a community station (KCET), a school district station (KLCS) and two university-owned stations (KOCE and KVCR).
Over the years, some of those competitive situations have shaken out: stations have merged operations (WNET/WLIW, KQED/KTEH), or some of the "second" stations have left the PBS orbit to do other noncommercial programming. WNYE New York ended up under city ownership with a combination of ethnic and community programming; WYBE Philadelphia does community TV aimed at minority communities; KMTP San Francisco shows a lot of international programs. Or the "second" station ends up with a lineup of PBS (and other) shows that's different from the main station in the market. In a way, RIPBS/WSBE has taken that role, since most of its market already gets WGBH or CPTV for the main PBS network schedule.
The point is, there's no way to generalize: all of these situations have developed in response to local circumstances, which is exactly what the system was meant to do.