Comcast, the country’s largest cable and broadband provider, and Netflix, the giant television and movie streaming service, announced an agreement Sunday in which Netflix will pay Comcast for faster and more reliable access to Comcast’s subscribers. The deal is a milestone in the history of the Internet, where content providers like Netflix generally have not had to pay for access to the customers of a broadband provider. But the growing power of broadband companies like Comcast, Verizon and AT&T has given those companies increased leverage over sites whose traffic gobbles up chunks of a network’s capacity. Netflix is one of those sites, accounting for nearly 30 percent of all Internet traffic at peak hours. The agreement comes just 10 days after Comcast agreed to buy Time Warner Cable for $45 billion, an acquisition that would make Comcast the cable provider to nearly one-third of American homes and the high-speed Internet company for close to 40 percent.