An A320 Captain reported multiple transgressions of the gate parking safety zone by ground vehicles while being electronically marshalled by an apparently oblivious ground crewperson. Stated such transgressions are frequent in his experience.

Narrative

I was required to make three separate full stops while parking. While the Marshaller stood oblivious to his surroundings; no less that three different vehicles drove through the safety zone while I was moving in it. A tug pulled several carts in my blind spot forward of the left wing. Another tug actually pulled a wheelie and drove straight at the aircraft from directly in front of me. A third tug pulling a small white trailer drove across the nose of the box as I approached the stop point. None of this seemed to have any effect on the parking system green light. 'What's the problem' was the expression on his face. The ramp is out of control. There is absolutely NO DISCIPLINE on the part of the rampers. Actually; I don't think that they are violating the safety procedures; it seems that they are completely unaware of them. This is not an exceptional occurrence. I have vehicles move through the parking safety zone AT LEAST several times a week. These vehicles include the RAMP SAFETY Supervisor's van.