The private railways are the icing on the cake of an 18xx game. They add flavour, but are not the main part of the game. Their main role is actually to give the players different starting positions, with slightly different cash holdings and initial income. They may also have significant other effects, especially if they can be bought into a company.
On the other hand, the private railways are the first things that the players have to buy. Therefore the designer has to get them right. This is a lesson I learnt from my first test game. Until then, I had only a hazy idea of how the privates would work, and I had to decide on various rules in a hurry at the start of the game. In fact, I began that game with two different models for how private railways might influence the rest of the game.
The first was a minor enhancement of the 1825 rules. In this approach, privates would be owned by players, but interact with track-building. In phase 2, companies would be forbidden to lay track in a hex occupied by a private (possibly unless the owner agrees). In later phases, whenever a company does lay track in a private railway's hex, this closes the private. So some private railways occupy valuable hexes and influence early track lays; other will stay open longer and give more income over the course of the game.
The second was an 1830-like approach. Companies may buy private railways and this may give the companies special abilities. The most obvious ability is the laying of a tile in the private's hex – although for hexes in the thick of things this might be too unbalancing.
Another might be extra income for a certain town or city. Another might be a share in a particular company. This last ability probably wouldn’t work so well in 18GB, as it would be a 20% holding in the early game.
My current plan is a combination of these approaches. As in 1830, companies may buy private railways from phase 3 onwards and most privates give an extra ability to their owning railway. No company may lay a tile in a private railway's hex until the private is owned by a company (not necessarily the one laying the tile). However, in phase 4, companies may forcibly buy a private railway from a player (at face value) if they lay a tile in the private's hex. This prevents players from continuing to block important hexes. All private railways close at the start of phase 5.
As an extra thought, I’m wondering whether it would be possible/sensible to represent one or two companies as privates that give the ability to teleport a token. E.g. the SWR might become a private with the ability to lay a token in Swansea. (Although this would affect the optional grouping rules). Currently, the optional companies are the GNR in York and the GSWR in Ayr/Glasgow. The GNR could give a bonus to York and a free tile lay in any plain hex. The GSWR could give a bonus for Ayr and perhaps a free upgrade for Glasgow.