First, the issue: Currently, there is no way to prevent transit vehicles on the roads (buses, trams) from getting stuck in traffic, making your public transit much worse with no remedy.
Now you might think, just add bus lanes. Unfortunately, bus lanes in the current version of the game are so broken as to be essentially useless in the most important situations. In a dense area with many intersections, cars will use bus lanes as turn lanes since the other lanes will never allow a right turn. You can also build a bus-only road, but cars will use it anyway. Any bus line will be used by taxis.
Here are the needed solutions to make it possible to give transit priority in traffic:
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Option to allow inner (non-transit lanes) for right turns. This would prevent the bus lane being open as a turn lane. Regular cars will have a traffic light control right turns, transit vehicles can already turn right.
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Transit priority traffic lights. A policy that modifies the function of traffic lights, or a new traffic light option. When a bus or tram reaches an intersection with a red light (or is waiting behind traffic for one), the light will interrupt and go to a phase that allows the vehicle to pass. Trams prioritized over buses if multiple vehicles are waiting, other than that, first transit vehicle to arrive gets priority first. Traffic light returns to normal cycle after all transit has passed.
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Disable taxis able to use bus lanes. As a city or district policy. I build my bus lanes for transit, not one-person vehicles.