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.
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.