Características de las ondas sonoras

Video Popularity Decay has been discussed about in a range of research [16, 35–37], however it appears to rarely be quantified or analysed beyond the effects of the specific tests performed by the researchers in question. Additional to the lack of analysis of video decay, is the frequent omission of growth of popularity of video objects.

The subject of decay is discussed by Gummadi et al. [16] in the context of a peer- to-peer system called “Kazaa” in a rather poor manner as items larger than 100 MB are declared to experience a larger amount of request for items older than one month by 72% and items smaller than 10 MB are declared to experience a larger amount of requests towards items older than one month but by only 52% with the omission of medium sized items. The decay here is for multimedia items, not exclusively VoD, which causes some doubt as to how much this data resembles exclusively VoD data. It may well be possible that the majority of items observed are not video, dictating the decay-rate experienced by items in the system.

The subject of decay is also discussed by Li et al. [36] and Chen at al. [38] appear to agree that within their observed datasets that the initial day of observations see the videos decrease in popularity by 20%, and again decrease by 20% 9 days later. This observation is based in video request data that is explicitly not UGC on both Peer-to- Peer (P2P) based systems, as well as CDN run systems, such as Hulu and PPLive. Li et al. [36] appear to consider items once they are stored on the cloud device and then observed the decreasing popularity. This comes after a video is identified as popular enough to be submitted to the cloud, which may see a large part of the item’s lifetime

be omitted (an hour minimum due to design), as the time before the item became pop- ular it was not yet considered for measurement of popularity, especially considering the initial surge in popularity.

Chen et al. [39] follow the lifetime of video items in a system which includes the decay. The observation is made in a VoD service run by Tencent, which is one of the largest VoD services in China. It provides video to an active user base of over 50 million people. For the purpose of measuring video decay, videos are separated into categories, easily distinguishable by key characteristics (Movies, Music Videos, TV content, News and Sports), for which each category has a total decay rate measured over the duration of 7 days. The observations made suggest that most categories appear to see a great quantity of requests on the day of release, as well as the day following. After this period all categories see a drastic decrease in popularity, with the exception of the “Movies” category which appears to see a peak in interest on the third day the item is in the system. It is unclear if items on day 0 (the initial day of release) were in the system for the entirety of it, or just the later section of the day. This additional bit of missing information would point out if the items, almost immediately after release, start seeing a decreasing request rate or if this happens, as suggested by Chen et al., on the second day in the system. The conclusive statement by Chen et al. [39] is that video items in their infancy receive a great amount of promotion, mainly on the front-page of the VoD application, which may be the primary reason for the popularity received by these newly introduced video items.

Avramova et al. [37] provide a close look at the decay of video popularity of primarily video items which have already achieved a great deal of popularity by their submission to the top 50, list on their respective platforms, such as YouTube (US and JP platforms), IMDB rental records, and “Uitzending Gemist(.nl)” which is a Dutch TV catch-up service. Once submitted to the top 50 the items were observed for a minimum of 30 days. The observations concluded that it is primarily the UGC that sees a thick tail in the observed decay curve which can be described as a power-law distribution. All other

VoD System Nr. of Observed Entries τ α β

YouTube (Japan & USA) ≤ 160 ≤ 20 ≈ 0 0.5

UitZending Gemist ≤ 42 ≥ 10 ≈ 106 _0.5

IMDB ≤ 18 ≥ 10 ≈ 106 _0.5

Table 2.1: Results gathered by Avramova et al. The results are approximated from the graphs in the publication which can be factored in to the simulator

traces, described as TV catch-up services, appear to follow a more drastic decrease over time described as following exponential decay. The formula used by Avramova et al. [37] to plot the decay in the form of a Cumulative Distribution Function (CDF) experienced by video items in all systems is as shown in Equation 2.3

Ik(t) = ρk   1 −   1 +  β −1 αk _{− 1}_{(t − Θk)} τk    −αk   (2.3)

In Equation 2.3 [37] τ describes the time it takes for a fraction 1 − β of the total view count to accumulate. ∆t describes the time at which the item is observed and Θ describes the time of entry in the system. α is the important variable to consider as it is the variables that is form-determining in the function. If α is large, the function produces an exponential curve which would see the item gain the majority of its requests in the beginning of its existence. If α is small, the function produces a power-law curve which would see the item remain relevant for an extended period of time, with a small amount of popularity remaining throughout the item’s existence.