xfinity router & modem connection problems

Just "upgraded" to an Xfinity router/modem combo unit.

One of three Macbook Airs is having great problems across the 'net.

No problem getting full signal on the router.

Whether using Safari, Firefox, trying to connect to the Apple store, the first request across the 'net is "fine." But then the 'net connection just dies. The router strength is still high. But accessing any URL, accessing the Mac store, anything, the Mac comes to a dead crawl.

Xfinity tried some things on their side and said that everything was fine from their side and I should thus call Apple.

This particular Macbook Air - all running Yosemite and no problems with the other two Macbook Airs or any of the iPads or iPhones in the house - had trying at someone else's house as well with the Xfinity combo router/modem. It had no trouble on the old Comcast modem and Netgear router replaced last week.

Any insight would be helpful.