Exact Analysis of TTL Cache Networks: The Case of Caching Policies driven by Stopping Times

TTL caching models have recently regained significant research interest, largely due to their ability to fit popular caching policies such as LRU. This paper advances the state-of-the-art analysis of TTL-based cache networks by developing two exact methods with orthogonal generality and computational complexity. The first method generalizes existing results for line networks under renewal requests to the broad class of caching policies whereby evictions are driven by stopping times. The obtained results are further generalized, using the second method, to feedforward networks with Markov arrival processes (MAP) requests. MAPs are particularly suitable for non-line networks because they are closed not only under superposition and splitting, as known, but also under input-output caching operations as proven herein for phase-type TTL distributions. The crucial benefit of the two closure properties is that they jointly enable the first exact analysis of feedforward networks of TTL caches in great generality

Stationary Distribution of a Generalized LRU-MRU Content Cache

Many different caching mechanisms have been previously proposed, exploring different insertion and eviction policies and their performance individually and as part of caching networks. We obtain a novel closed-form stationary invariant distribution for a generalization of LRU and MRU caching nodes under a reference Markov model. Numerical comparisons are made with an "Incremental Rank Progress" (IRP a.k.a. CLIMB) and random eviction (a.k.a. random replacement) methods under a steady-state Zipf popularity distribution. The range of cache hit probabilities is smaller under MRU and larger under IRP compared to LRU. We conclude with the invariant distribution for a special case of a random-eviction caching tree-network and associated discussion

On Resource Pooling and Separation for LRU Caching

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

Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

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

A unified approach to the performance analysis of caching systems

We propose a unified methodology to analyse the performance of caches (both isolated and interconnected), by extending and generalizing a decoupling technique originally known as Che's approximation, which provides very accurate results at low computational cost. We consider several caching policies, taking into account the effects of temporal locality. In the case of interconnected caches, our approach allows us to do better than the Poisson approximation commonly adopted in prior work. Our results, validated against simulations and trace-driven experiments, provide interesting insights into the performance of caching systems.Comment: in ACM TOMPECS 20016. Preliminary version published at IEEE Infocom 201