Optimal Control in Fluid Models of nxn Input-Queued Switches under Linear Fluid-Flow Costs

2021 ◽  
Vol 48 (3) ◽  
pp. 122-127
Author(s):  
Yingdong Lu ◽  
Mark S. Squillante ◽  
Tonghoon Suk
Keyword(s):  
Fluid Flow ◽  
Fluid Model ◽  
Infinite Horizon ◽  
Control Policy ◽  
Optimal Scheduling ◽  
Maximization Problem ◽  
Fluid Models ◽  
Scheduling Policy ◽  
N Input ◽  
Discounted Control Problem

We consider a fluid model of n x n input-queued switches with associated fluid-flow costs and derive an optimal scheduling control policy to an infinite horizon discounted control problem with a general linear objective function of fluid cost. Our optimal policy coincides with the cμ-rule in certain parameter domains, but more generally, takes the form of the solution to a flow maximization problem. Computational experiments demonstrate the benefits of our optimal scheduling policy over variants of max-weight scheduling and the cμ-rule.

scholarly journals Improving Energy Efficiency Fairness of Wireless Networks: A Deep Learning Approach

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4300 ◽  
Author(s):  
Hoon Lee ◽  
Han Seung Jang ◽  
Bang Chul Jung
Keyword(s):  
Energy Efficiency ◽  
Wireless Networks ◽  
Deep Learning ◽  
Power Control ◽  
Control Method ◽  
Optimal Solution ◽  
Control Policy ◽  
Maximization Problem ◽  
Optimization Approach ◽  
Conventional Optimization

Achieving energy efficiency (EE) fairness among heterogeneous mobile devices will become a crucial issue in future wireless networks. This paper investigates a deep learning (DL) approach for improving EE fairness performance in interference channels (IFCs) where multiple transmitters simultaneously convey data to their corresponding receivers. To improve the EE fairness, we aim to maximize the minimum EE among multiple transmitter–receiver pairs by optimizing the transmit power levels. Due to fractional and max-min formulation, the problem is shown to be non-convex, and, thus, it is difficult to identify the optimal power control policy. Although the EE fairness maximization problem has been recently addressed by the successive convex approximation framework, it requires intensive computations for iterative optimizations and suffers from the sub-optimality incurred by the non-convexity. To tackle these issues, we propose a deep neural network (DNN) where the procedure of optimal solution calculation, which is unknown in general, is accurately approximated by well-designed DNNs. The target of the DNN is to yield an efficient power control solution for the EE fairness maximization problem by accepting the channel state information as an input feature. An unsupervised training algorithm is presented where the DNN learns an effective mapping from the channel to the EE maximizing power control strategy by itself. Numerical results demonstrate that the proposed DNN-based power control method performs better than a conventional optimization approach with much-reduced execution time. This work opens a new possibility of using DL as an alternative optimization tool for the EE maximizing design of the next-generation wireless networks.

scholarly journals Continuity and monotonicity of solutions to a greedy maximization problem

2020 ◽  
Vol 92 (1) ◽  
pp. 33-76
Author(s):  
Łukasz Kruk
Keyword(s):  
Real Time ◽  
Network Topology ◽  
Resource Sharing ◽  
Time Parameter ◽  
Maximization Problem ◽  
Fluid Models ◽  
Admissible Set ◽  
Network Modelling ◽  
Underlying Network ◽  
Real Time Transmission

Abstract Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $${\mathbb {R}}^n$$ R n , with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.

SECOND ORDER BOUNDARY CONDITIONS FOR THE DRIFT-DIFFUSION EQUATIONS OF SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 429-455 ◽  
Author(s):  
A. YAMNAHAKKI
Keyword(s):  
Boundary Conditions ◽  
Test Problem ◽  
Fluid Model ◽  
Diffusion Equations ◽  
Robin Boundary Conditions ◽  
Fluid Models ◽  
Drift Diffusion ◽  
Dirichlet Conditions ◽  
Robin Boundary ◽  
Two Fluid

By an asymptotic analysis of the Boltzmann equation of semiconductors, we prove that Robin boundary conditions for drift-diffusion equations provide a more accurate fluid model than Dirichlet conditions. The Robin conditions involve the concept of the extrapolation length which we compute numerically. We compare the two-fluid models for a test problem. The numerical results show that the current density is correctly computed with Robin conditions. This is not the case with Dirichlet conditions.

Numerical Study of MHD Viscoelastic Fluid Flow with Binary Chemical Reaction and Arrhenius Activation Energy

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
M. Mustafa ◽  
A. Mushtaq ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Activation Energy ◽  
Fluid Flow ◽  
Chemical Reaction ◽  
Viscoelastic Fluid ◽  
Numerical Study ◽  
Fluid Model ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Large Temperature ◽  
Temperature Function

Abstract Here we address the influence of heat/mass transfer on MHD axisymmetric viscoelastic fluid flow developed by an elastic sheet stretching linearly in the radial direction. Constitutive relations of Maxwell fluid model are utilized in mathematical formulation of the problem. Non-linear radiation heat flux is factored in the model which accounts for both small and large temperature differences. Chemical reaction effects with modified Arrhenius energy function are analyzed which are not yet explored for viscoelastic fluid flows. Highly accurate numerical computations are performed. Our computations show S-shaped profiles of temperature function in case of sufficiently large temperature differences. Species concentration increases when activation energy for chemical reaction is increased. However, both chemical reaction rate and temperature gradient tend to reduce the solute concentration.

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 1. CGL description and collisionless fluid hierarchy

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
E. Khomenko ◽  
M. L. Goldstein ◽  
...  
Keyword(s):  
Heat Flux ◽  
Evolution Equations ◽  
Fluid Model ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Normal Closure ◽  
Larmor Radius ◽  
Order Moment ◽  
Fourth Moment ◽  
Fluid Models

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non-Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the fluid model of Chew–Goldberger–Low (CGL) in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the fourth-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the ‘normal’ closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the ‘normal’ closure, and beyond the fourth-order moment, Landau fluid closures are required.

MICROPOLAR FLUID MODEL FOR BLOOD FLOW THROUGH A STENOSED ARTERY

2013 ◽  
Vol 05 (04) ◽  
pp. 1350043 ◽  
Author(s):  
H. ASADI ◽  
K. JAVAHERDEH ◽  
S. RAMEZANI
Keyword(s):  
Blood Flow ◽  
Fluid Flow ◽  
Excellent Agreement ◽  
Micropolar Fluid ◽  
Degrees Of Freedom ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Element Formulation ◽  
Stenosed Artery ◽  
Circular Microchannel

Various experimental observations have demonstrated that the classical fluid theory is incapable of explaining many phenomena at micro and nano scales. On the other hand, micropolar fluid dynamics can naturally pick up the physical phenomena at these scales owing to its additional degrees of freedom caused by incorporating the effects of fluid molecules on the continuum. Therefore, one of the aims of this paper is to investigate the applicability of the theory of micropolar fluids to modeling and calculating flows in circular microchannels depending on the geometrical dimension of the flow field. Hence, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, the analytical and exact solution of the micropolar Hagen–Poiseuille flow in a circular microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is also shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow such as blood flow in a stenosed artery, having multiple kinds of stenoses, is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

Application of Number Density Transport Equation for the Recovery of Consistency in Multi-Field Model

2003 ◽  
Author(s):  
Akio Tomiyama ◽  
Naoki Shimada ◽  
Hiroyuki Asano
Keyword(s):  
Numerical Experiment ◽  
Transport Equation ◽  
Shape Factor ◽  
Field Model ◽  
Fluid Model ◽  
Fluid Models ◽  
Number Density ◽  
Two Phase ◽  
Closure Relations ◽  
Dispersed Flows

It is demonstrated through a thought numerical experiment that a conventional two- or multi-fluid model suffers from an inconsistency problem, by which it would fail in accurately predicting two-phase dispersed flows even with reliable closure relations for interfacial transfer terms. To overcome the inconsistency, a numerical method based on a number density transport equation and a shape factor for a fluid or solid particle is proposed. The (N+2)-field model (NP2 model) proposed in our previous studies [1]–[3] is adopted as the basis of the proposed method. It is confirmed that the method gives better predictions than conventional multi-fluid models and recovers the consistency.

scholarly journals Analysis of Blood Flow in Arterial Stenosis Using Casson and Power-Law Fluid Model

2013 ◽  
Vol 14 (2) ◽  
pp. 73
Author(s):  
Riri Jonuarti
Keyword(s):  
Blood Flow ◽  
Power Law ◽  
Fluid Model ◽  
Blood Flow Rate ◽  
Casson Fluid ◽  
Arterial Stenosis ◽  
Fluid Models ◽  
Power Law Fluid ◽  
Pass Through ◽  
Flow Power

Simulation of blood flow behaviour in the arteries and in arterial stenosis has been made and will be discussed in this paper. This simulation uses pulsatile flow and blood flow in artery without stenosis is considered as a dynamic fluid, compressed and condensed. Whereas, in the case of arterial stenosis has been used Casson and Power-law fluid models. In the arteries without stenosis, blood flow velocity profiles show the same pattern for each Womersley number, but with different speed value. In the case of arterial stenosis, blood flow rate decreases with increasing stenosis position away from axis of blood vessels. Resistances to flow are increases with increasing the size (height and length) of stenosis, both for the Casson and Power-law fluid models. If resistance to flow increases, it is more difficult for the blood to pass through an artery, result the flow decreases and heart has to work harder to maintain adequate circulation.Keywords : Artery, blood flow, power-law fluid, Casson fluid, stenosis  

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