Masalah penjadualan kerja ialah satu masalah pengoptimuman kombinatorik yang diketahui mempunyai darjah kebebasan berinteraksi yang besar. Oleh itu, masalah ini selalunya dikategorikan sebagai NP-lengkap. Kebanyakan penyelesaian bagi masalah ini menggunakan heuristik. Penyelesaiannya termasuk pendekatan berasaskan penjadualan tersenarai, teori giliran, teori graf dan pencaraian berenumerasi. Dalam kertas ini, satu kaedah penjadualan dinamik dicadangkan bagi memeta satu set kerja kepada satu set pemproses dalam rangkaian jaring boleh-konfigurasi. Model kami dipanggil Dynamic Scheduler on Reconfigurable Mesh (DSRM). Model ini berasaskan sistem giliran m/m/c di mana kerja-kerja yang tiba menunggu giliran masing-masing mengikut taburan Poisson, dan diservis mengikut taburan eksponen. Objektif utama dalam kajian ini ialah untuk menghasilkan jadual yang mempunyai taburan kerja seimbang pada pemproses-pemproses. Objektif kedua ialah untuk mempertingkat kadar pengagihan kerja ke tahap maksimum untuk memastikan kejayaan. Kedua-dua objektif ini merupakan satu masalah dikenali sebagai maksimum-minimum, di mana kejayaan dalam satu objektif boleh menyebabkan kemerosotan dalam objektif yang satu lagi. Keberkesanan pendekatan ini dikaji melalui model simulasi DSRM. Kata kunci: Jaring boleh-konfigurasi; penjadualan kerja; pengseimbangan beban dan perkomputeran selari Task scheduling is a combinatorial optimisation problem that is known to have large interacting degrees of freedom and is gerally classified as NP-complete. Most solutions to the problem have been proposed in the form of heuristics. These include approaches using list scheduling, queueing theory, graph theoretic and enumerated search. In this paper, we present a dynamic scheduling method for mapping tasks onto a set of processing elements (PEs) on the reconfigurable mesh parallel computing model. Our model called the Dynamic Scheduler on Reconfigurable Mesh (DSRM) is based on the Markovian m/m/c queueing system, where tasks arrive and form a queue according to Poisson distribution, and are serviced according to the exponential distribution. The main objective in our strudy is to produce a schedule that distributes the tasks fairly by balancing the load on all PEs. The second objective is to produce a high rate of sucessfully assigned tasks on the PEs. These two requirements tend to conflict and they constitute the maximum-minimum problem in optimisation, where the maximum of one causes the other to be minimum. We study the effectiveness of our approach in dealing with these two requirements in DSRM. Key words: Reconfigurable mesh; task scheduling; load balancing; and parallel computing
Ordinal regression is used to model the ordinal response variable as functions of several explanatory variables. The most commonly used model for ordinal regression is the proportional odds model (POM). The classical technique for estimating the unknown parameters of this model is the maximum likelihood (ML) estimator. However, this method is not suitable for solving problems with extreme observations. A robust regression method is needed to handle the problem of extreme points in the data. This study proposes Huber M-estimator as a robust method to estimate the parameters of the POM with a logistic link function and polytomous explanatory variables. This study assesses ML estimator performance and the robust method proposed through an extensive Monte Carlo simulation study conducted using statistical software, R. Measurement for comparisons are bias, RMSE, and Lipsitzs' goodness of fit test. Various sample sizes, percentages of contamination, and residual standard deviations are considered in the simulation study. Preliminary results show that Huber estimates provide the best results for parameter estimation and overall model fitting. Huber's estimator has reached a 50% breakdown point for data containing extreme points that are quite far from most points. In addition, the presence of extreme points that have only a distance of two times far from most points has no major impact on ML estimates. This means that the estimates for ML and Huber may yield the same results if the model's residual values are between -2 and 2. This situation may also occur for data with a percentage of contamination below 5%.
The concept of assurance in the two-arm non-inferiority trials has been explored, expressing the noninferiority margin as a clinically meaningful treatment difference. This short paper focuses on developing an assurance formula in the three-arm non-inferiority trial, based on the ratio of means. The discussion starts with the simple case of known variances and then extends to the case of unknown but equal variances. To avoid complicated integration, assurance for the latter case was studied using Bayesian Clinical Trial Simulation (BCTS). The findings indicate that assurance allows the experimenter to formally take into account the uncertainty surrounding the parameter estimates by using the prior distributions. Furthermore, BCTS can be easily implemented to find the required sample size without having to resort to complex integration.Keywords: Assurance; power; non-inferiority trial; three-arm design; BCTS AbstrakKajian kaedah jaminan di dalam ujian tidak-inferior dua-kumpulan telah pun dibuat dengan mewakilkan margin tidak-inferior sebagai perbezaan rawatan yang bermakna (dalam konteks klinikal). Fokus kertas ini pula adalah terhadap pembentukan formula jaminan di dalam ujian tidak-inferior tiga-kumpulan, yang mewakilkan margin tidak-inferior sebagai nisbah min. Perbincangan dimulakan dengan kes asas di mana varians populasi dianggap diketahui dan dilanjutkan pada kes varians populasi tidak diketahui. Oleh kerana kes yang kedua ini melibatkan kamiran kompleks, kaedah jaminan telah diaplikasikan dengan bantuan Bayesian Clinical Trial Simulation (BCTS). Hasil kajian mendapati bahawa kaedah jaminan membolehkan penyelidik mengambil kira secara formal ketidakpastian berkenaan anggaran parameter yang terlibat di dalam pencarian saiz sample, iaitu dengan mewakilkan ketidakpastian tersebut menggunakan taburan prior yang bersesuaian. Selain itu, BCTS boleh diaplikasikan dengan mudah untuk mencari saiz sampel yang diperlukan tanpa perlu menyelesaikan masalah kamiran yang kompleks.Kata kunci: Jaminan; kuasa; ujian tidak-inferior; rekabentuk 3-kumpulan, BCTS
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.