why is the auto gearbox slow to pickup after slowing down but not stopping.

What is your question?

Once the car is at normal temp,if I slow down for a roundabout but dont stop,then drive round the junction at slow speed, when I accelerate away nothing happens for approx 3 seconds, then it picks up normally. There is no lurch or roughness, just a delay. There are no other problems. Car has done 160,000mls.