This is post that discusses Linear Networks with Feeder Lines, for a Overview of Network Types read further here.
Linear Network with Feeder Lines
Vuchic  defined two types of Linear Networks, Trunk Line with Feeders and Feeders with a Trunk Section. Below are four examples of Linear Network with Feeder Lines that differentiate from each other by what kind of Feeder Lines they incorporate.
For Linear Networks that incorporate a Trunk Section, see the Trunk Line Linear Network.
The transportation network is built around one trunk line that forms the back bone of the network. This is usually a primary transportation service (e.g. a rail line or metro line) and to increase the service area, secondary transportation services (e.g. tram lines, bus lines) are added. An example of the evolution of such a network would be a Linear Minimal Network but instead of adding detours devolving into a Maeander Minimal Network, adds feeder lines.
Linear Minimal Network
A Linear Minimal Network is often chosen as a solution to connect stations with high potential passenger volumes (town centre, population centres, schools, train station, public services, ect…) to each other. This kind of network can secure a successfully ridership at the expense of coverage by not providing service to areas with fewer potential passengers. A detour ratio close to 1:1 can be achieved by this type of network, making it very attractive for potential passengers lucky enough to be situated near a station.
Example Medellín Metro Line A
The development of the transit network of Colombia’s second largest city, Medellín, gives an excellent example for a Linear Network with Feeders. The metropolitan area around Medellín follows in the Aburrá Valley which geographically has limited its growth. Medellín did boast a rail line that followed the river and an extensive tram network that was closed in 1951. With increased traffic volume the city and the national government looked for ways to introduce a primary public transportation service in the 1970s and 1980s.
Metro of Medellín, picture by Guía de Viajes Oficial de Medellín
In 1995 the first sections of the Metro Line A were opened, which was extended further to Niquía in the north and La Estrella in the south. The 25.8km line mainly uses the old rail line route and it follows an old tram route through the city area of Medellín. Until the opening of the Metro Línea B, Línea A formed a Minimal Linear Network as the only primary transportation service in the valley.
Secantial Feeder Linear Network
A Secantial Feeder Linear Network incorporates additional services that run roughly perpendicular to the main trunk line. These type of networks are sometimes called Fish Bone Networks, the central trunk line being the vertebral column along the fish skeleton centre and rib and other bones being the feeder lines. The trunk line should have a high capacity and speed. Most of the medium and long distance trips will require passengers to use a section of it and most journeys will require two transfers.
Example Medellín Metro, Metrocable and Tranvía
The steep slopes of the Aburrá Valley have constrained the city from building a traditional metro network. However, on the wider west plain in the valley towards San Javier it was possible to build the 5.5km Metro Lineá B connecting with Lineá A by San Antonio. Instead of extending the Lineá B to the east of the station San Antonio through the older areas of the city, a rubber tired tram alternative translohr was built, the Ayacucho Tram (Tranvía).
Forced by topography, Medellín has turned to building a set of metropolitan gondolas, the Metrocables. They function as secantial feeders connecting settlements on the steep slopes of the city to the Lineá A as well as B and T-A / F.
Five Metrocables lines have been built to date with a further two currently proposed. Together with the other primary transportation services the Tranvía and metro lines they form a Secantial Feeder Linear Network.
Maeander Feeder Linear Network
Increasing the coverage of a trunk line by adding Maeander Feeder Routes can have advantages. Lines that have a route section parallel to the main line can relieve the main line which might have reached capacity in that section. Maeander Routes that first follow a route perpendicular away from to the main line before arcing back and heading to the mainline a second time can attract potential passengers wishing to transfer to the main line in both directions.
Example Medellín Metroplús and Tranvía
To further increase the coverage of the public transportation system, the Medellín and its sister cities are building a secondary transportation network of express buses and translohrs. The express bus system is called Metroplús and currently has two line, Lineá 1 and 2, which run from Aranjuez in the North of Medellín, south through the city, with two transfer possibilities to Lineá A before rejoining heading west to the University of Medellín. The Lineá 1 and Lineá 2 follow two separate parallel sections east and west of the Lineá A, which increases the North-South passenger capacity of the network in the densest parts of Medellín.
Metroplús Lineá 3 is planned to service the cities of La Estrella, Itagüí, Envigado and Sabaneta connecting to Lineá A by the station Aguacatala.
A second translohr line is planned between the Lineá A station Caribe in the north and station Aguacatala in the south. This translohr line would replace sections of the existing bus lines 300, 301, 302 and 303. Not shown in the map bellow but also an integral part of the secondary transportation network of Medellín and its sister cities, is the many smaller bus lines, the Alimentador. These bus lines usually follow a fixed meandering route with at least one transfer possibility to Lineá A or B.
Flexible Feeder Linear Network
Adding services with Flexible Routes is a low cost option of adding a large area to the network with the advantage of reducing walking distances for potential passenger. Flexible Routes originate from one point (e.g. train or metro station) leave in the direction of a destination (a particular settlement or another station). In some cases the route is predefined and merely the service interval and stops are flexible, a passenger will tell the driver when he or she wishes to disembark, and potential passenger will hand signal (or request per telephone call or mobile-app) the driver at an appropriate stopping point. In other cases the route is also flexible to an extent where the vehicle will take a small detour or an alternative route upon request of a passenger. Usually a vehicle will only leave for its destination if its capacity is full or nearly full (eg. 10 seats of 12 seats are occupied), if a enough request have been made along its route or if it is required to maintain a minimal interval (one minibus at least every 20 minutes).
Combining these type of services with a trunk line can form an efficient, adaptable and low cost transportation network. (See also Flexible Routes and Networks)
Example Medellín Micro Buses
Medellín has an extensive fleet of micro or mini buses (Colectivo). They are capable of traversing the steep slopes and narrow streets of the many settlements that developed with little city coordination. The services originate from a period of private enterprise when the tram network had closed, the city expanded rapidly and government was incapable of providing decent service. All that was needed for an entrepreneur was minibus that could carry 6 to 12 passengers from their place of lodging to work or other interest and the permission from the organisations in charge of along the routes.
Gradually these services have been standardised. A common fair per ride introduced, the routes and areas serviced defined, as well as safety standards and vehicle maintenance implemented. Some of these services have a low seat capacity and some buses approach the capacity and regularity of a regular bus service. In Medellín some are branded with Metro colours (white, yellow and green) but others can be very colourful.
On Demand Feeder Linear Network
A linear network can be complimented by an on demand service. The most common version of such a service through out the 20th century was taxi services. But this classification also applies to scooter, bicycle or car sharing systems, ride hailing systems and will also apply to autonomous vehicles tasked with serving an area.
Example Medellín Taxi and EnCicla
Medellín and its sister cities also boast an extensive taxi fleet. Only 15% of the journeys completed in Medellín are mainly completed by automobiles and a large portion of those are completed by taxi (11% of the journeys are by motorbike).
Medellín also has a bicycle sharing system. Founded by group of university students in 2011 EnCicla it originally bicycles were available at 6 staffed stations. The network has since been expanded to include 19 staffed and 32 automatic with plans to introduce service in Bello in the North and La Estrella, Itagüí, Envigado and Sabaneta in the south.
Bellow a map of the metropolitan area with existing proposed EnCicla bicycle renting stations.
The discussed models above are theoretical versions of Linear Networks with Feeders, in real life there will not be any pure version but a combination of the above. Medellín is a fascinating example of a Linear Network. It should be applauded for not only for the speed that it has been implemented but also for their ability to imagine new solutions for their difficult topography and the care taken to build passenger friendly transfer station.
Bellow a map of the Medellín metropolitan area with it’s public transportation network and proposed extensions.
-  Urban Transit – Systems and Technology (2007), Vukan R. Vuchic see also Urban Public Transportation – Systems and Technology (1981)
99% Invisible episode about transit in Medellín and it’s role in the post-drug war recovery