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For a realistic traffic mix, we evaluate the hit rates attained in a two-layer cache hierarchy designed to reduce Internet bandwidth requirements. The model identifies four main types of content, web, file sharing, user generated content and video on demand, distinguished in terms of their traffic shares, their population and object sizes and their(More)
—In a 2002 paper, Che and co-authors proposed a simple approach for estimating the hit rates of a cache operating the least recently used (LRU) replacement policy. The approximation proves remarkably accurate and is applicable to quite general distributions of object popularity. This paper provides a mathematical explanation for the success of the(More)
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit regime, that is, when the networks have some symmetry properties and when the number of nodes goes to infinity. An(More)
In the paper, bike sharing systems with stations having a finite capacity are studied as large stochastic networks. The inhomogeneity is modeled by clusters. We use a mean field limit to derive the limiting stationary distribution of the number of bikes at the stations. This approach is an alternative to analytical methods. It can be used even if a closed(More)
In this paper, it is shown that the coexistence of a variety of different traffics in third generation cellular networks may lead to a very undesirable behavior of the whole network: <i>a metastability property</i>. When this property holds, the state of the network fluctuates on a <i>very long time scale</i> between different set of states. These long(More)
As passive optical networks (PON) are increasingly deployed to provide high speed Internet access, it is important to understand their fundamental traffic capacity limits. The paper discusses performance models applicable to wavelength division multiplexing (WDM) EPONs and GPONs under the assumption that users access the fibre via optical network units(More)