The stretched exponential distribution of internet media access patterns

The commonly agreed Zipf-like access pattern of Web workloads is mainly based on Internet measurements when text-based content dominated the Web traffic. However, with dramatic increase of media traffic on the Internet, the inconsistency between the access patterns of media objects and the Zipf model has been observed in a number of studies. An insightful understanding of media access patterns is essential to guide Internet system design and management, including resource provisioning and performance optimizations. In this paper, we have studied a large variety of media workloads collected from both client and server sides in different media systems with different delivery methods. Through extensive analysis and modeling, we find: (1) the object reference ranks of all these workloads follow the stretched exponential (SE) distribution despite their different media systems and delivery methods; (2) one parameter of this distribution well characterizes the media file sizes, the other well characterizes the aging of media accesses; (3) some biased measurements may lead to Zipf-like observations on media access patterns; and (4) the deviation of media access pattern from the Zipf model in these workloads increases along with the workload duration. We have further analyzed the effectiveness of media caching with a mathematical model. Compared with Web caching under the Zipf model, media caching under the SE model is far less effective unless the cache size is enormously large. This indicates that many previous studies based on a Zipf-like assumption have potentially overestimated the media caching benefit, while an effective media caching system must be able to scale its storage size to accommodate the increase of media content over a long time. Our study provides an analytical basis for applying a P2P model rather than a client-server model to build large scale Internet media delivery systems.

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