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As numerous machine learning and other algorithms increase in complexity and data requirements, distributed computing becomes necessary to satisfy the growing computational and storage demands, because it enables parallel execution of…
The main goal of parallel processing is to provide users with performance that is much better than that of single processor systems. The execution of jobs is scheduled, which requires certain resources in order to meet certain criteria.…
In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the…
In a post-prognostics decision context, this paper addresses the problem of maximizing the useful life of a platform composed of several parallel machines under service constraint. Application on multi-stack fuel cell systems is considered.…
We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…
The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for…
We first present a probabilistic version of ACP that rests on the principle that probabilistic choices are always resolved before choices involved in alternative composition and parallel composition are resolved and then extend this…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…
In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We consider a physical asset consisting of complex systems, where the systems may require upgrades during the lifetime of the asset. In practice, the asset owner and system supplier can make the upgrade decisions together, requiring a…
We consider the optimal allocation of generic resources among multiple generic entities of interest over a finite planning horizon, where each entity generates stochastic returns as a function of its resource allocation during each period.…
This paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. \ The motivation for this work stems from the important problem in reliability analysis, to estimate the number of…
Purpose: The model allocates the system components orders to the suppliers to minimize the parts price and the system construction delay penalties and maximize the system availability during its use. It considers the quantity-based discount…
Recently, Chowdhury and Kundu [6] compared two parallel systems of heterogeneous independent log-Lindley distributed components using the concept of vector majorization and related orders. Under the same set-up, this paper derives some…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
Optimal maintenance policies play an important role in the reliability analysis of repairable systems. This paper examines a two-unit priority standby system with a repair facility, where the priority unit is subject to preventive…
Relative ageing describes how a system ages with respect to another one. The ageing faster orders are the ones which compare the relative ageings of two systems. Here, we study ageing faster orders in the hazard and the reversed hazard…