As I mentioned in reply to Malika I've been thinking further about Tarvenhive and, certainly in terms of transportation, it is starting to come together quite nicely I think.
I decided the number of stations/length of metro routes in the outer regions of the hive (which I've christened the 'Skirt') should be at the upper end of my previous estimate with 5300 stations and just over 10,000 km of routes. Another thought that occured to me though is that it isn't just the shear size of the network itself that is an issue, but also the load that would be placed on the busiest routes. In New York the busiest stations already have 4 platforms for each line, two for each direction, so that is definitely going to be necessary here. I also think the trains are going to have to be double-deck and rather lengthy on the busiest lines.
An interesting thought that occurred to me about the metro lines in the Skirt region is that is they are mostly underground then eventually as they travel inwards toward the centre of the Hive they will meet the Underhive. As I am going with a gradual growth model for Tarvenhive this also means that the Underhive will have been expanding over time so there must be old disused metro lines that now lie within the Underhive and have probably been blocked off from the rest of the network. In fact the area covered by the Underhive is about the same size as Moscow, so, partly as a homage to Metro 2033 which I have been playing recently, I decided that the Underhive will contain an old disused version of what is essentially the Moscow Metro. I was also thinking that the current extent of the Underhive might in some places be constrained by the path of an orbital line into which, being rather important, a considerable effort is being put into keeping it out of the Underhive.
Within the central regions of the Hive there will also be metro lines but there will have to be multiple layers at different heights throughout the Hive. Providing vertical connections would be a system of elevator-like capsules running on vertical rails. At the moment I'm thinking that the capsules would be triple deck and about 10m in diameter. One advantage for the vertical lines is that you can have almost as many individual tracks around a big central platform as you like so the small relative size of the individual capsules can be offset by having lots of them.
Connecting Tarvenhive to the other Hives there would be high-speed monorails, a big spaceport and several airports as well as other smaller landing sites. I was toying the idea of a space elevator, but I decided that although there will be space elevators on Tian, Tarvenhive will be too far from the equator.