Abstract Cloud services and other shared third-party infrastructures allow individual content providers to easily scale their services based on current resource demands. In this paper, we consider an individual content provider that wants to minimize its delivery costs under the assumptions that the storage and bandwidth resources it requires are elastic, the content provider only pays for the resources that it consumes, and costs are proportional to the resource usage. Within this context, we (i) derive worst-case bounds for the optimal cost and competitive cost ratios of different classes of cache on M th request cache insertion policies, (ii) derive explicit average cost expressions and bounds under arbitrary inter-request distributions, (iii) derive explicit average cost expressions and bounds for short-tailed (deterministic, Erlang, and exponential) and heavy-tailed (Pareto) inter-request distributions, and (iv) present numeric and trace-based evaluations that reveal insights into the relative cost performance of the policies. Our results show that a window-based cache on 2nd request policy using a single threshold optimized to minimize worst-case costs provides good average performance across the different distributions and the full parameter ranges of each considered distribution, making it an attractive choice for a wide range of practical conditions where request rates of individual file objects typically are not known and can change quickly.
Finally, it is important to note that TTL-based replacement eviction policies @cite_7 @cite_2 (and variations thereof @cite_4 ) (considered in this paper) have have been found useful for approximating the performance of capacity-driven replacement policies such as LRU @cite_26 @cite_3 @cite_28 @cite_14 @cite_24 . For an individual content provider, our results may therefore also be applicable to the case in which the provider use Our results may therefore also be applicable to provide insight for the case in which a content provider uses a fixed-sized cache. Generalizations of the TTL-based Che-approximation @cite_26 and TTL-based caches in general have proven useful to analyze individual caches @cite_26 @cite_3 @cite_28 @cite_14 @cite_24 , networks of caches @cite_6 @cite_16 @cite_13 @cite_14 @cite_24 , and to optimize different system designs @cite_27 @cite_23 @cite_19 @cite_10 .
@cite_26 @cite_4 @cite_14 @cite_7 @cite_28 @cite_10 @cite_3 @cite_6 @cite_24 @cite_19 @cite_27 @cite_23 @cite_2 @cite_16 @cite_13
1549860141 2524013375 2168282297 2156068340
Many researchers have been working on the performance analysis of caching in Information-Centric Networks (ICNs) under various replacement policies like Least Recently Used (LRU), FIFO or Random (RND). However, no exact results are provided, and many approximate models do not scale even for the simple network of two caches connected in tandem. In this paper, we introduce a Time-To-Live based policy (TTL), that assigns a timer to each content stored in the cache and redraws the timer each time the content is requested (at each hit miss). We show that our TTL policy is more general than LRU, FIFO or RND, since it is able to mimic their behavior under an appropriate choice of its parameters. Moreover, the analysis of networks of TTL-based caches appears simpler not only under the Independent Reference Model (IRM, on which many existing results rely) but also with the Renewal Model for requests. In particular, we determine exact formulas for the performance metrics of interest for a linear network and a tree network with one root cache and N leaf caches. For more general networks, we propose an approximate solution with the relative errors smaller than 10−3 and 10−2 for exponentially distributed and constant TTLs respectively. 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. This paper presents a way of modeling the hit rates of caches that use a time-to-live (TTL)-based consistency policy. TTL-based consistency, as exemplified by DNS and Web caches, is a policy in which a data item, once retrieved, remains valid for a period known as the "time-to-live". Cache systems using large TTL periods are known to have high hit rates and scale well, but the effects of using shorter TTL periods are not well understood. We model hit rate as a function of request arrival times and the choice of TTL, enabling us to better understand cache behavior for shorter TTL periods. Our formula for the hit rate is closed form and relies upon a simplifying assumption about the interarrival times of requests for the data item in question: that these requests can be modeled as a sequence of independent and identically distributed random variables. Analyzing extensive DNS traces, we find that the results of the formula match observed statistics surprisingly well; in particular, the analysis is able to adequately explain the somewhat counterintuitive empirical finding of that the cache hit rate for DNS accesses rapidly increases as a function of TTL, exceeding 80 for a TTL of 15 minutes. TTL caching models have recently regained significant research interest due to their connection to 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; in addition to classical policies used in DNS and web caching, our stopping time model captures an emerging new policy implemented in SDN switches and Amazon web services. The second method further generalizes these results to feedforward networks with Markov arrival process (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 caching operations with phase-type (PH) TTL distributions. The crucial benefit of the two closure properties is that they jointly enable the first exact analysis of TTL feedforward cache networks in great generality. Moreover, numerical results highlight that existing Poisson approximations in binary-tree topologies are subject to relative errors as large as 30 , depending on the tree depth.