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Hi My car is a BMW 318i with an automatic transmission. When I stop for a traffic light the car start to vibrate quite badly and if I change the gear from D to N the vibrate stops? Is there something wrong with my transmission/ clutch ? Further more I can feel that there is a delay in gear change. When the engine is not warm enough the gear doesn't change up until 3000rpm. When the engine is warm enough the gear change occurs at 2500rpm. When I'm going down hill, if I apply breaks the engine revs go up and applies engine breaks automatically. Are all there related to a major transmission issue? A small help would much appreciated.
Thank you.

From your description, this doesn't sound like an automatic transmission fault. The trans is designed to hold gears longer when cold in order to warm the engins up quicker and the transmission is adaptive, so it knows to shift down when you are braking going down hill. These are all normal characteristics.
It would pay to have a BMW specialist take a look at the vibration at idle, but a very common cause of this in the 318 would be a faulty coil pack.

Thank you very much for the help. You saved me lot of trouble. =)