4,468 research outputs found

    On Resource Pooling and Separation for LRU Caching

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    Caching systems using the Least Recently Used (LRU) principle have now become ubiquitous. A fundamental question for these systems is whether the cache space should be pooled together or divided to serve multiple flows of data item requests in order to minimize the miss probabilities. In this paper, we show that there is no straight yes or no answer to this question, depending on complex combinations of critical factors, including, e.g., request rates, overlapped data items across different request flows, data item popularities and their sizes. Specifically, we characterize the asymptotic miss probabilities for multiple competing request flows under resource pooling and separation for LRU caching when the cache size is large. Analytically, we show that it is asymptotically optimal to jointly serve multiple flows if their data item sizes and popularity distributions are similar and their arrival rates do not differ significantly; the self-organizing property of LRU caching automatically optimizes the resource allocation among them asymptotically. Otherwise, separating these flows could be better, e.g., when data sizes vary significantly. We also quantify critical points beyond which resource pooling is better than separation for each of the flows when the overlapped data items exceed certain levels. Technically, we generalize existing results on the asymptotic miss probability of LRU caching for a broad class of heavy-tailed distributions and extend them to multiple competing flows with varying data item sizes, which also validates the Che approximation under certain conditions. These results provide new insights on improving the performance of caching systems

    The Role of Chaos in One-Dimensional Heat Conductivity

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    We investigate the heat conduction in a quasi 1-D gas model with various degree of chaos. Our calculations indicate that the heat conductivity κ\kappa is independent of system size when the chaos of the channel is strong enough. The different diffusion behaviors for the cases of chaotic and non-chaotic channels are also studied. The numerical results of divergent exponent α\alpha of heat conduction and diffusion exponent β\beta are in consistent with the formula α=22/β\alpha=2-2/\beta. We explore the temperature profiles numerically and analytically, which show that the temperature jump is primarily attributed to superdiffusion for both non-chaotic and chaotic cases, and for the latter case of superdiffusion the finite-size affects the value of β\beta remarkably.Comment: 6 pages, 7 figure

    Multifunctional Bracts in the Dove Tree Davidia involucrata (Nyssaceae:Cornales)

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    Although there has been much experimental work on floral traits that are under selection from mutualists and antagonists, selection by abiotic environmental factors on flowers has been largely ignored. Here we test whether pollen susceptibility to rain damage could have played a role in the evolution of the reproductive architecture of Davidia involucrata, an endemic in the mountains of western China. Flowers in this tree species lack a perianth and are arranged in capitula surrounded by large (up to 10 cm#5 cm) bracts that at anthesis turn from green to white, losing their photosynthetic capability. Flowers are nectarless, and pollen grains are presented on the recurved anther walls for 5–7 days. Flower visitors, and likely pollinators, were mainly pollen-collecting bees from the genera Apis, Xylocopa, Halictus, and Lasioglossum. Capitula with natural or white paper bracts attracted significantly more bees per hour than capitula that had their bracts removed or replaced by green paper. Experimental immersion of pollen grains in water resulted in rapid loss of viability, and capitula with bracts lost less pollen to rain than did capitula that had their bracts removed, suggesting that the bracts protect the pollen from rain damage as well as attracting pollinators

    Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

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    To efficiently scale data caching infrastructure to support emerging big data applications, many caching systems rely on consistent hashing to group a large number of servers to form a cooperative cluster. These servers are organized together according to a random hash function. They jointly provide a unified but distributed hash table to serve swift and voluminous data item requests. Different from the single least-recently-used (LRU) server that has already been extensively studied, theoretically characterizing a cluster that consists of multiple LRU servers remains yet to be explored. These servers are not simply added together; the random hashing complicates the behavior. To this end, we derive the asymptotic miss ratio of data item requests on a LRU cluster with consistent hashing. We show that these individual cache spaces on different servers can be effectively viewed as if they could be pooled together to form a single virtual LRU cache space parametrized by an appropriate cache size. This equivalence can be established rigorously under the condition that the cache sizes of the individual servers are large. For typical data caching systems this condition is common. Our theoretical framework provides a convenient abstraction that can directly apply the results from the simpler single LRU cache to the more complex LRU cluster with consistent hashing.Comment: 11 pages, 4 figure
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