I have been living this for days. Watching the blue line creep. I didn't change anything so obviously, it came about as a by product of updating something! Hello Apple! Are you listening?
I am running the latest versions of Yosemite and Safari on my late 2013 MBP w/ 16GB RAM. I do a lot of internet searching and Safari is crawling. I use Safari for personal web research, and Firefox and Chrome for work activity. They are not as deeply affected, although they are slower. I have deleted cache and history. I have cleared my desktop, emptied trash, and rebooted (more than once). Still, the thin blue bar is crawling. Oh, I also removed the extensions.
What it seems like is something is filling up, and once filled, it cannot go faster until something moves out of the way. It feels like a MB out allows a MB in. It feels like something needs to be flushed. I cannot work at the slow pace Safari is running; I download very little in the way of bandwidth hogs like music and video, so that is not causing the clog. I accumulate cookies but as I said, I have deleted those several times a day at this point. I am going to have to move over to FF and Chrome and leave Safari for another day as this is going to drive me mad.
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The comment about resetting the router reminded me of something I had observed. I have a Time Capsule connected to my service provider's Arris modem. Somehow, my connection reverts to the Arris connection, not the TC connection. The Arris one is the network I am on when it is slow. When I change it to my TC network, the speed issue is resolved.
So now the question is, what causes it to change the network to which it is pointed....