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

Understanding (Un)Written Contracts of NVMe ZNS Devices with zns-tools

Operational and performance characteristics of flash SSDs have long been associated with a set of Unwritten Contracts due to their hidden, complex internals and lack of control from the host software stack. These unwritten contracts govern how data should be stored, accessed, and garbage collected. The emergence of Zoned Namespace (ZNS) flash devices with their open and standardized interface allows us to write these unwritten contracts for the storage stack. However, even with a standardized storage-host interface, due to the lack of appropriate end-to-end operational data collection tools, the quantification and reasoning of such contracts remain a challenge. In this paper, we propose zns.tools, an open-source framework for end-to-end event and metadata collection, analysis, and visualization for the ZNS SSDs contract analysis. We showcase how zns.tools can be used to understand how the combination of RocksDB with the F2FS file system interacts with the underlying storage. Our tools are available openly at \url{https://github.com/stonet-research/zns-tools}

Understanding (Un)Written Contracts of NVMe ZNS Devices with zns-tools

Operational and performance characteristics of flash SSDs have long been associated with a set of Unwritten Contracts due to their hidden, complex internals and lack of control from the host software stack. These unwritten contracts govern how data should be stored, accessed, and garbage collected. The emergence of Zoned Namespace (ZNS) flash devices with their open and standardized interface allows us to write these unwritten contracts for the storage stack. However, even with a standardized storage-host interface, due to the lack of appropriate end-to-end operational data collection tools, the quantification and reasoning of such contracts remain a challenge. In this paper, we propose zns.tools, an open-source framework for end-to-end event and metadata collection, analysis, and visualization for the ZNS SSDs contract analysis. We showcase how zns.tools can be used to understand how the combination of RocksDB with the F2FS file system interacts with the underlying storage. Our tools are available openly at \url{https://github.com/stonet-research/zns-tools}

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

A New Stable Peer-to-Peer Protocol with Non-persistent Peers

Recent studies have suggested that the stability of peer-to-peer networks may rely on persistent peers, who dwell on the network after they obtain the entire file. In the absence of such peers, one piece becomes extremely rare in the network, which leads to instability. Technological developments, however, are poised to reduce the incidence of persistent peers, giving rise to a need for a protocol that guarantees stability with non-persistent peers. We propose a novel peer-to-peer protocol, the group suppression protocol, to ensure the stability of peer-to-peer networks under the scenario that all the peers adopt non-persistent behavior. Using a suitable Lyapunov potential function, the group suppression protocol is proven to be stable when the file is broken into two pieces, and detailed experiments demonstrate the stability of the protocol for arbitrary number of pieces. We define and simulate a decentralized version of this protocol for practical applications. Straightforward incorporation of the group suppression protocol into BitTorrent while retaining most of BitTorrent's core mechanisms is also presented. Subsequent simulations show that under certain assumptions, BitTorrent with the official protocol cannot escape from the missing piece syndrome, but BitTorrent with group suppression does.Comment: There are only a couple of minor changes in this version. Simulation tool is specified this time. Some repetitive figures are remove