Min-cost live webcast under joint pricing of data, congestion and virtualized servers

Live video webcast streams the same live content from its source to a large number of Internet clients through CDN networks, and may consume large volumes of traffic and contribute significantly to Internet congestion during popular events such as the FIFA World Cup. A fair pricing scheme to charge webcast operators should take into account the total amount of data transferred in the network, the cost of running virtualized server instances on the selected CDN edge locations, as well as the potential congestion level the webcast may impose on the underlying Internet. In this paper, we propose a comprehensive pricing model for video webcast operators based on all of the above factors. In particular, we model the congestion level of the webcast as the sum of bandwidth-delay products on all links in the formed video distribution overlay, which indicates the total number of “waiting packets” occupying the Internet. Under such a pricing model, we formulate the min-cost webcasting via at least k CDN servers as a problem we call “k-Node-Weighted Steiner Tree”, for which we give the first polynomial-time approximation scheme with an approximation ratio of O(ln n), where n is the number of participating clients. By relaxing the pricing and cost model, we point out the relationship of the special cases of problem with a number of famous problems including Uncapacitated Facility Location problem(UFL) and Node-Weighted Steiner Tree problem(NWST). We verify the effectiveness of our algorithm at reducing the cost of live webcast based on real delay traces collected from PlanetLab and the Seattle project with pricing parameters synthesized from Amazon Web Service.