The Locator ID Separation Protocol (LISP) limits the growth of the Default-Free Zone routing tables by creating a highly aggregatable and quasi-static Internet core. However, LISP pushes the forwarding state to edge routers whose timely operation relies on caching of location to identity bindings. In this paper we develop an analytical model to study the asymptotic scalability of the LISP cache. Under the assumptions that (i) long-term popularity can be modeled as a constant Generalized Zipf distribution and (ii) temporal locality is predominantly determined by long-term popularity, we find that the scalability of the LISP cache is O(1) with respect to the amount of prefixes (Internet growth) and users (growth of the LISP site). We validate the model and discuss the accuracy of our assumptions using several one-day-long packet traces.
@cite_9 argued that empirical evidence indicates that Web requests popularity distribution is Zipf-like of exponent @math . Using this finding and the assumption that temporal locality is mainly induced through long-term popularity, they showed that the asymptotic miss rates of an LFU cache, as a function of the cache size, is a power law of exponent @math . In this paper we argue that GZipf with exponents greater than @math is a closer fit to real popularity distributions and obtain a more general LRU cache model. We further use the model to determine the scaling properties of the cache.
@cite_9
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This paper addresses two unresolved issues about Web caching. The first issue is whether Web requests from a fixed user community are distributed according to Zipf's (1929) law. The second issue relates to a number of studies on the characteristics of Web proxy traces, which have shown that the hit-ratios and temporal locality of the traces exhibit certain asymptotic properties that are uniform across the different sets of the traces. In particular, the question is whether these properties are inherent to Web accesses or whether they are simply an artifact of the traces. An answer to these unresolved issues will facilitate both Web cache resource planning and cache hierarchy design. We show that the answers to the two questions are related. We first investigate the page request distribution seen by Web proxy caches using traces from a variety of sources. We find that the distribution does not follow Zipf's law precisely, but instead follows a Zipf-like distribution with the exponent varying from trace to trace. Furthermore, we find that there is only (i) a weak correlation between the access frequency of a Web page and its size and (ii) a weak correlation between access frequency and its rate of change. We then consider a simple model where the Web accesses are independent and the reference probability of the documents follows a Zipf-like distribution. We find that the model yields asymptotic behaviour that are consistent with the experimental observations, suggesting that the various observed properties of hit-ratios and temporal locality are indeed inherent to Web accesses observed by proxies. Finally, we revisit Web cache replacement algorithms and show that the algorithm that is suggested by this simple model performs best on real trace data. The results indicate that while page requests do indeed reveal short-term correlations and other structures, a simple model for an independent request stream following a Zipf-like distribution is sufficient to capture certain asymptotic properties observed at Web proxies. The overall performance of content distribution networks as well as recently proposed information-centric networks rely on both memory and bandwidth capacities. The hit ratio is the key performance indicator which captures the bandwidth memory tradeoff for a given global performance. This paper focuses on the estimation of the hit ratio in a network of caches that employ the Random replacement policy (RND). Assuming that requests are independent and identically distributed, general expressions of miss probabilities for a single RND cache are provided as well as exact results for specific popularity distributions (such results also hold for the FIFO replacement policy). Moreover, for any Zipf popularity distribution with exponent @a>1, we obtain asymptotic equivalents for the miss probability in the case of large cache size. We extend the analysis to networks of RND caches, when the topology is either a line or a homogeneous tree. In that case, approximations for miss probabilities across the network are derived by neglecting time correlations between miss events at any node; the obtained results are compared to the same network using the Least-Recently-Used discipline, already addressed in the literature. We further analyze the case of a mixed tandem cache network where the two nodes employ either Random or Least-Recently-Used policies. In all scenarios, asymptotic formulas and approximations are extensively compared to simulation results and shown to be very accurate. Finally, our results enable us to propose recommendations for cache replacement disciplines in a network dedicated to content distribution. Computer system and network performance can be significantly improved by caching frequently used information. When the cache size is limited, the cache replacement algorithm has an important impact on the effectiveness of caching. In this paper we introduce time-to-live (TTL) approximations to determine the cache hit probability of two classes of cache replacement algorithms: the recently introduced h-LRU and LRU(m). These approximations only require the requests to be generated according to a general Markovian arrival process (MAP). This includes phase-type renewal processes and the IRM model as special cases. We provide both numerical and theoretical support for the claim that the proposed TTL approximations are asymptotically exact. In particular, we show that the transient hit probability converges to the solution of a set of ODEs (under the IRM model), where the fixed point of the set of ODEs corresponds to the TTL approximation. We further show, by using synthetic and trace-based workloads, that h-LRU and LRU(m) perform alike, while the latter requires less work when a hit miss occurs. We also show that, as opposed to LRU, h-LRU and LRU(m) are sensitive to the correlation between consecutive inter-request times. 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 approximation, notably in configurations where the intuitive arguments of clearly do not apply. The approximation is particularly useful in evaluating the performance of current proposals for an information centric network where other approaches fail due to the very large populations of cacheable objects to be taken into account and to their complex popularity law, resulting from the mix of different content types and the filtering effect induced by the lower layers in a cache hierarchy.