Are you sure you're solving the right problem?

If you're running timing tests, in all probability what someone wants is to gather statistics on how long it takes to load the pages from different computers. But they might not understand enough about networking to further qualify their request to mean computer located in different places on the internet, reaching the website through different paths.

Gathering statistics from one computer that's pretending to be several is rather like asking the same person to take a survey three times.

You may need to have a talk with whoever is asking you to run this experiment, to explain to them a bit about how networks work, and to help them clarify what they're trying to measure.