They are not interchangeable: each has it's own particular meaning.
Surrounded is quite neutral, except in the special usage "We've got you surrounded", a mostly fictional cliché said by the police when they have a criminal trapped. In this case it is rather like "beseiged". I really don't think this meaning would come across in your example: it's just a rather straightforward description of the situation.
Beseiged properly means to be surrounded and trapped (e.g. a castle being under seige: the occupants cannot get out so they will have to surrender or die when their supplies run out), however it can be used figuratively, and I think this would work in your example.
Mobbed means to be set upon my a mob: an unruly crowd of people. It's quite common to describe a celebrity as being mobbed in the sort of situation you describe.
"Surrounded" is pretty neutral. You could be surrounded by flowers or sheep or by other commuters, and it doesn't imply that whatever is surrounding you is interested in you all. It or they are just around you. "Besieged" (it is "i" before "e") implies you are being surrounded by people who are demanding something of you, like your autograph, and whose attention might be excessive or unwelcome to some extent. I think you can be "besieged" by one or two people though, so it doesn't always imply a large crowd per se, but more people that won't go away. "Mobbed" does imply a lot of people and again could be slightly negative in the sense of implying there are "too many" people vying for your intention. In the context they all mean about the same thing though.