When two lines of track merge into one with high traffic trains will stop and queue up on each line, taking turns entering the merged track. This sounds like a great idea, but because the trains start from stationary each time this significantly slows down overall traffic. Your train network will often be better off giving priority to one line of track (preferably the one with more traffic) and allowing the trains on it to clear the merge at full speed before trains on the other line can access it.
Using specialized signalling you can force trains entering the merge to wait for a gap in order to reduce traffic disruption.
With two-way pre-signals and nothing extra you can force a merging train to stop if there's a train already on the main track directly in front of the combo or exit signal. The disadvantage to this construction is that you can't extend the priority further than the length of two signals.
Priority Merges Using Extra Track
Longer priority can be designated by connecting track to activate the main merging signal upstream. When a train on the prioritized track drives onto a tile connected to the unused track it tells the signal on the merging track to read red. This construction can be made with both path signals and regular block signals on your tracks. The path signal construction needs only a single block signal on the merging track, while the block signal construction requires pre-signalling on the unused track to prevent trains from signalling themselves to stop.
Be careful to construct priority merges to accommodate your shortest train's length. If you have too much space in the middle, a train can briefly occupy a section of track without activating the merge signal, allowing a train to merge and disrupt traffic. This can be prevented by splitting longer priority into segments.
Sometimes you just don't want your traffic flow to get disrupted period. Using ordinary priorities where a train can join track after braking means that if you want to prevent the joining train from causing other trains already moving at maximum speed to come near it while it's accelerating and force those trains to brake, you need to extend the length of the priority to accommodate the joining train's entire acceleration room needed to reach maximum speed from a stop. Priorities can get extremely long and they also result in long gaps between trains on the merged track, lowering its efficient traffic capacity.
Instead, you can prevent a train from accessing the merge at all (and braking) if the priority is occupied. Red two-way signals are the ultimate train pathfinding penalty in OpenTTD; a train will choose any other track option available to it in order to avoid one even if it contradicts its orders and ends up getting it lost. You can use this to your advantage by disallowing trains from even attempting to access a prioritized merge (and ending up braking) if there is currently traffic running on it. By placing a two-way signal at a merge with another track option continuing after it, trains will ignore the merge entirely when the priority signals that it is occupied and continue on their way using the other track option.
A high-speed merge also needs an extra signaling mechanism in order to totally prevent a train from ever braking at the merge point. Thus, these constructions can only be made with pre-signals. Informative images forthcoming...
Right-of-way Merging onto Dual Main Line
All signals are combo signals except at points A and B which are entry signals, and the top right, which are exit signals. Adjust the length of the signal chain according to train length and speed.
Trains joining at point A must wait for the presignal chain along the inside lane to be clear. If a train arrives at point B before train A is out of the way then it will switch to the outer lane (at no speed penalty), but only if the presignal chain for the outside lane is clear. If it is not, the presignals at point B ensure that train B will take the line which clears first.
The connection of the presignal chains at point C is optional. It allows A to continue if the presignal chain for the outside lane is clear, even if the inside lane is not, as the train on the inside will probably be able move to the outside to let A out. When the lane-change is north of Signal B, A will always wait for the inside lane to clear, regardless of the state of the outside lane.