On a model for the storage of files on a hardware I : Statistics at a fixed time and asymptotics

On a model for the storage of files on a hardware II : Evolution of a typical data block

We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, at the right of their arrival point. We study here the evolution of the extremities of the data block straddling 0, which is empty at time 0 and is equal to $\RRR$ at a deterministic time.

关于有限容量的存储网络

On a loss storage network with finite capacity

本文研究了有限容量非可靠文件服务器存储网络的流体图景，利用有界凸域中带斜反射的Skorokhod问题识别流体极限，分析了欠载、临界和过载三种状态，并通过新鞅和平均性质求解过载状态。

Steady-State Behavior of Some Load Balancing Mechanisms in Cloud Storage Systems

In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We consider a system of $n$ servers storing files using a Maximum Distance Separable code (cf. \cite{li2016mean}). Specifically, each file is stored in equally sized pieces across $L$ servers such that any $k$ pieces can reconstruct the original file. File requests are routed using the Batch Sampling routing scheme. I.e. when a request for a file is received, a centralized dispatcher routes the job into the $k$-shortest queues among the $L$ for which the corresponding server conta…

Diffusion Approximations for Load Balancing Mechanisms in Cloud Storage Systems

In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the Maximum Distance Separable (MDS) code (cf. Li, Ramamoorthy, and Srikant (2016)). Specifically, each file is stored in equally sized pieces across $L$ servers such that any $k$ pieces can reconstruct the original file. When a request for a file is received, the dispatcher routes the job into the $k$-shortest queues among the $L$ for which the corresponding s…