Ubuntu Security :: Traffic To Specific Sites Throttled?

I want to check if traffic to a specific URL is being throttled by a hospital acting as an ISP. A client is having great trouble accessing a hosted web-app from inside the hospital, but access is fine from outside. The hospital IT dept are not interested as the rest of the Internet is fine. I need to trace where the latency is creeping in or where the throttling is happening, if I can do that, the hospital will remove it. Traffic is standard http to a specific URL.