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

Global attraction of ODE-based mean field models with hyperexponential job sizes

Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In order to prove that this unique fixed point corresponds to the limit of the stationary measures of the finite systems, the unique fixed point must be a global attractor. While global attraction was established for various systems in case of exponential job sizes, it is often unclear whether these proof techniques can be generalized to non-exponential job sizes. In this paper we show how simple monotonicity arguments can be used to prove global attraction for a broad class of ordinary differential equations that capture the evolution of mean field models with hyperexponential job sizes. This class includes both existing as well as previously unstudied load balancing schemes and can be used for systems with either finite or infinite buffers. The main novelty of the approach exists in using a Coxian representation for the hyperexponential job sizes and a partial order that is stronger than the componentwise partial order used in the exponential case.Comment: This paper was accepted at ACM Sigmetrics 201

On the Benefit of Information Centric Networks for Traffic Engineering

Current Internet performs traffic engineering (TE) by estimating traffic matrices on a regular schedule, and allocating flows based upon weights computed from these matrices. This means the allocation is based upon a guess of the traffic in the network based on its history. Information-Centric Networks on the other hand provide a finer-grained description of the traffic: a content between a client and a server is uniquely identified by its name, and the network can therefore learn the size of different content items, and perform traffic engineering and resource allocation accordingly. We claim that Information-Centric Networks can therefore provide a better handle to perform traffic engineering, resulting in significant performance gain. We present a mechanism to perform such resource allocation. We see that our traffic engineering method only requires knowledge of the flow size (which, in ICN, can be learned from previous data transfers) and outperforms a min-MLU allocation in terms of response time. We also see that our method identifies the traffic allocation patterns similar to that of min-MLU without having access to the traffic matrix ahead of time. We show a very significant gain in response time where min MLU is almost 50% slower than our ICN-based TE method