In this work we investigate the power of power law in the VoD service over IP network. Especially, we show that the power of power law is strong in the location of the contents storage for the VoD service and its impact on the link dimensioning. This work first shows the instance of the power law in the popularity of the video contents from the real data for the IPTV service. After that we propose an analytic model that characterizes the behavior of customers in accessing the video servers as well as the power law in the viewing pattern. Finally, we show the impact of the power law by proposing a model for the cost as well as link dimensioning. Via numerical experiment we show the implication of the proposition.
Ⅰ. IntroductionRecently, the IPTV (Internet Protocol TV) service is very popular and it is the most important killer application and source of cash to the Internet service providers (ISPs). VoD (Video on Demand) became a companion service to the IPTV service. It is envisioned that VoD is popular due to merits such as time-disjoint property of viewing, abundant choice of contents, and diverse applications such as stock market, music video, sports games, dramas, etc.One of the most important problems in providing the VoD service to mass customers is the determination for the location of the video program.Video programs are located at servers in various ways: centralized or distributed, the operation of which is described in detail later. This work promotes the distributed architecture for the location of video servers, because it is much efficient.On the other hand, it is usually known that one can find the phenomenon of power law from measurements in the Internet such as a growth model, caching, and networking [1] . The definition of power law is as follows: the probability mass function (pmf) of a random event to occur is represented by a power function, a detailed definition of which is given at Section 2. Breslau et al. argue that the frequency of the web-object follows power law [2] . Mitzenmacher shows the instance of power law in the size of the web-object [3] . It is known that the number of online friends in the SNS (Social Network Service) follows the power law [4] . When it comes to the video streaming service, lots of works argue the existence of the power law in the viewing pattern of the video. Gill et al. show that the popularity of the YouTube video follows a Zipf-like distribution, where power law is synonymous with Zipf's law [5] . Cha et al. show that the popularity of the TV channel in the IP network follows the Zipf-like property, too [6] .When it comes to the link dimensioning, there exists a few literature that deals with the power law. Won et al. assume that the popularity of the IPTV program follows a Zipf's law with a binary exponential function where the number of customers for (i-1)-th popular program is twice greater than 608 that of i-th popular program [7] . However, in reality, the popularity of the IPTV program does not follow the binary exponential function...
