相关论文: On a model for the storage of files on a hardware …
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. We specify the distribution of the space of…
We consider a distributed storage system which stores several hot (popular) and cold (less popular) data files across multiple nodes or servers. Hot files are stored using repetition codes while cold files are stored using erasure codes.…
Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…
In this paper, we consider hashing with linear probing for a hashing table with m places, n items (n < m), and l = m<n empty places. For a non computer science-minded reader, we shall use the metaphore of n cars parking on m places: each…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
In this paper, a simple transient Markov process with an absorbing point is used to investigate the qualitative behavior of a large scale storage network of non reliable file servers where files can be duplicated. When the size of the…
The article presents a systematic review of the results of the development of the theoretical basis and the pilot implementation of data storage technology with automatic replenishment of data from sources belonging to different thematic…
Stochastic dynamic matching problems have recently gained attention in the stochastic-modeling community due to their diverse applications, such as supply-chain management and kidney exchange programs. In this paper, we study a matching…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
Most information storage devices write data by modifying the local state of matter, in the hope that sub-atomic local interactions stabilize the state for sufficiently long time, thereby allowing later recovery. Motivated to explore how…
Consider n items located randomly on a circle of length 1. The locations of the items are assumed to be independent and uniformly distributed on [0,1). A picker starts at point 0 and has to collect all n items by moving along the circle at…
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff introduced a model…
Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump…
High-precision modeling of systems is one of the main areas of industrial data analysis. Models of systems, their digital twins, are used to predict their behavior under various conditions. We have developed several models of a storage…
We introduce a dynamical model of node repair in distributed storage systems wherein the storage nodes are subjected to failures according to independent Poisson processes. The main parameter that we study is the time-average capacity of…
We consider a one-dimensional traffic model with a slow-to-start rule. The initial position of the cars in $\mathbb R$ is a Poisson process of parameter $\lambda$. Cars have speed 0 or 1 and travel in the same direction. At time zero the…
Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…
This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for…