Outside a city core with very high frequency of transit, say 8 minutes or better, bus and train services must be timetabled to meet each other with short connections as far as possible. Normally, this is done through setting up nodes at major suburban centers where trains and buses can all interchange. For example, see this post from six months ago about the TransitMatters proposal for trains between Boston and Worcester: on the hour every half hour, trains in both directions serve Framingham, which is the center for a small suburban bus system, and the buses should likewise run every half hour and meet with the trains in both directions.
This is a dendritic system, in which there is a clear hierarchy not just of buses and trains, but also of bus stops and train stations. Under the above system, every part of the Framingham area is connected by bus to the Framingham train station, and Framingham is then connected to the rest of Eastern New England via Downtown Boston. This is the easiest way to set up timed rail-bus connections: each individual rail line is planned around takt and symmetry such that the most important nodes can have easy timed bus connections, and then the buses are planned around the distinguished nodes.
However, there’s another way of doing this: a bus can connect two distinct nodes, on two different lines. The map I drew for a New England high- and low-speed rail has an orbital railroad doing this, connecting Providence, Worcester, and Fitchburg. Providence, as the second largest city center in New England, supplies such rail connections, including also a line going east toward Fall River and New Bedford, not depicted on the map as it requires extensive new construction in Downtown Providence, East Providence, and points east. But more commonly, a connection between two smaller nodes than Providence would be by bus.
The orbital bus is not easy to plan. It has to have timed connections at both ends, which imposes operational constraints on two distinct regional rail lines. To constrain planning even further, the bus itself has to work with its own takt – if it runs every half hour, it had better take an integer multiple of 15 minutes minus a short turnaround time to connect the two nodes.
It is also not common for two suburban stations on two distinct lines to lie on the same arterial road, at the correct distance from each other. For example, South Attleboro and Valley Falls are at a decent distance, if on the short side, but the route between them is circuitous and it would be far easier to try to set up a reverse-direction timed transfer at Central Falls for an all-rail route. The ideal distance for a 15-minute route is around 5-6 km; bus speeds in suburbia are fairly high when the buses run in straight lines, and if the density is so high that 5-6 km is too long for 15 minutes, then there’s probably enough density for much higher frequency than every half hour.
The upshot is that connections between two nodes are valuable, especially for people in the middle who then get easy service to two different rail lines, but uncommon. Brockton supplies a few, going west to Stoughton and east to Whitman and Abington. But the route to Stoughton is at 8.5 km a bit too long for 15 minutes – perhaps turning it into a 30-minute route, either with slightly longer connections or with a detour to Westgate (which the buses already take today), would be the most efficient. The routes to Whitman and Abington are 7 km long, which is feasible at the low density in between, but then timetabling the trains to set up knots at both Brockton and Abington/Whitman is not easy; Brockton is an easy node, but then since the Plymouth and Middleborough Lines are branches of the same system, their schedules are intertwined, and if Abington and Whitman are served 15 minutes away from Brockton then schedule constraints elsewhere lengthen turnaround times and require one additional trainset than if they are not nodes and buses can’t have timed connections at both ends.
Planners then have to keep looking for such orbital bus opportunities. There aren’t many, and there are many near-misses, but when they exist, they’re useful at creating an everywhere-to-everywhere network. It is even valuable to plan the trains accordingly provided other constraints are not violated, such as the above issue of the turnaround times on the Old Colony Lines.