Saturation Assumption Research Articles

A novel Effective Capacity-based framework for providing statistical QoS guarantees in IEEE 802.11 WLANs

This article proposes a performance model of the IEEE 802.11 MAC layer that employs the notion of Effective Capacity. In particular, the paper establishes that an IEEE 802.11 mobile station can be regarded as a Semi-Markovian bursty server of the On/Off type, with known distributions for the On and Off periods, and subsequently applies known results for Semi-Markovian models to derive the Effective Capacity function of this On/Off server. The general Effective Bandwidth/Capacity theory can then be used for computing buffer overflow probabilities and for employing simple traffic control policies to enforce related QoS guarantees. The policies guarantee a soft bound on the buffer overflow probability and are suitable for real-time traffic control over WLANs. The Effective Capacity model of IEEE 802.11 stations is originally developed by assuming that the other competing stations are saturated. This is a conservative assumption that becomes very accurate in a highly loaded network. Subsequently, the model is adapted to encompass lightly loaded networks as well. In the adapted model, each mobile station directly measures a few model parameters, instead of calculating them on the basis of the saturation assumption, and uses these measurements in the computation of its Effective Capacity function. The theoretical results are checked against simulations, validating the appropriateness of the model.

Comparing slotted and continuous CSMA

Carrier-Sense Multiple-Access (CSMA) protocols form a popular class of random-access schemes for regulating node activity in wireless networks. We compare the continuous and the time-slotted versions of this protocol in the saturated regime, and show that continuous CSMA has higher aggregate throughput than the slotted protocol, but this comes at the cost of fairness, i.e., the throughput is not evenly distributed across all nodes. We then release the saturation assumption and consider a multi-hop scenario where packets are forwarded through the network and nodes may occasionally empty. We study end-to-end throughput of both continuous and slotted CSMA, and show that slotted CSMA has a higher throughput than the continuous protocol.

Some new residual-based a posteriori error estimators for the mortar finite element methods

In this paper, we propose some new residual-based a posteriori error estimators for the mortar finite element discretization of the second order elliptic equations with discontinuous coefficients. Reliability and efficiency of the estimators are given. Our analysis does not require any saturation assumptions and the mesh restrictions on the interface which are often needed in the literature. Numerical experiments are presented to confirm our theoretical analysis.

On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations

AbstractThis work combines two complementary strategies for solving the steady incompressible Navier–Stokes model with a zeroth‐order term, namely, a stabilized finite element method and a mesh–refinement approach based on an error estimator. First, equal order interpolation spaces are adopted to approximate both the velocity and the pressure while stability is recovered within the stabilization approach. Also designed to handle advection dominated flows under zeroth‐order term influence, the stabilized method incorporates a new parameter with a threefold asymptotic behavior. Mesh adaptivity driven by a new hierarchical error estimator and built on the stabilized method is the second ingredient. The estimator construction process circumvents the saturation assumption by using an enhancing space strategy which is shown to be equivalent to the error. Several numerical tests validate the methodology. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

Convergence of adaptive BEM for some mixed boundary value problem

For a boundary integral formulation of the 2D Laplace equation with mixed boundary conditions, we consider an adaptive Galerkin BEM based on an (h−h/2)-type error estimator. We include the resolution of the Dirichlet, Neumann, and volume data into the adaptive algorithm. In particular, an implementation of the developed algorithm has only to deal with discrete integral operators. We prove that the proposed adaptive scheme leads to a sequence of discrete solutions, for which the corresponding error estimators tend to zero. Under a saturation assumption for the non-perturbed problem which is observed empirically, the sequence of discrete solutions thus converges to the exact solution in the energy norm.

Coarse-scale resistivity for saturation estimation in heterogeneous reservoirs based on Archie’s formula

Relations between porosity, saturation, and resistivity are essential when estimating in-place hydrocarbon volumes. The most common relation is the Archie formula. During the last decade, several new coarse-scale electromagnetic techniques for resistivity measurements have been developed. Applications of coarse-scale resistivity must consider the underlying geologic variability of porosity and saturation to be used in such relations. I have investigated the effect of small-scale (logging-scale) variability in porosity and water saturation on coarse-scale resistivity for Archie relations. An analytical expression for coarse-scale resistivity is derived based on the assumption of lognormal distributed porosity and saturation. Similarly, coarse-scale water saturation is derived assuming lognormal distributed porosity and resistivity. The results suggest that the coarse-scale equivalent Archie resistivity is normally less than the geometric average and larger than the harmonic average of the heterogeneous resistivity distribution. An important aspect of the analytical derived relations is the quantification of the effect of the variability (variance and covariance) on the coarse-scale results. Another coarse-scale average resistivity based on macroscopic anisotropy could be a practical approximation of the coarse-scale equivalent Archie resistivity in many cases.

Hierarchical error estimates for the energy functional in obstacle problems

We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations.

Queuing Analysis in a Multiuser Diversity System With Adaptive Modulation and Coding Scheme

In wireless packet networks, the performance of multiuser diversity schedulers has been analyzed with the saturation assumption; however, the finite queue length effect should be taken into account. We propose a new scheduling scheme exploiting multiuser diversity that considers not only channel information but queue information as well. Considering the finite queue length effect and adaptive modulation and coding scheme (AMCS), we analyze the performance of the proposed scheduler.

Efficient and reliable hierarchical error estimates for an elliptic obstacle problem

We present and analyze novel hierarchical a posteriori error estimates for a self-adjoint elliptic obstacle problem. Under a suitable saturation assumption, we prove the efficiency and reliability of our hierarchical estimates. The proof is based upon some new observations on the efficiency of some hierarchical error indicators. These new observations allow us to remove an additional regularity condition on the underlying grid required in the previous analysis. Numerical computations confirm our theoretical findings.

Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems

We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.

COSMIC GPS Radio Occultation Temperature Profiles in Clouds

AbstractThermodynamic states in clouds are closely related to physical processes such as phase changes of water and longwave and shortwave radiation. Global Positioning System (GPS) radio occultation (RO) data are not affected by clouds and have high vertical resolution, making them ideally suited to cloud profiling on a global basis. By comparing the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) RO refractivity data with those of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis and ECMWF analysis for soundings in clouds and clear air separately, a systematic bias of opposite sign was found between large-scale global analyses and the GPS RO observations under cloudy and clear-sky conditions. As a modification to the standard GPS RO wet temperature retrieval that does not distinguish between cloudy- and clear-sky conditions, a new cloudy retrieval algorithm is proposed to incorporate the knowledge that in-cloud specific humidity (which affects the GPS refractivities) should be close to saturation. To implement this new algorithm, a linear regression model for a sounding-dependent relative humidity parameter α is first developed based on a high correlation between relative humidity and ice water content. In the absence of ice water content information, α takes an empirical value of 85%. The in-cloud temperature profile is then retrieved from GPS RO data modeled by a weighted sum of refractivities with and without the assumption of saturation. Compared to the standard wet retrieval, the cloudy temperature retrieval is consistently warmer within clouds by ∼2 K and slightly colder near the cloud top (∼1 K) and cloud base (1.5 K), leading to a more rapid increase of the lapse rate with height in the upper half of the cloud, from a nearly constant moist lapse rate below and at the cloud middle (∼6°C km−1) to a value of 7.7°C km−1, which must be closer to the dry lapse rate than the standard wet retrieval.

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptive methods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general.

Minimization of gradient errors of piecewise linear interpolation on simplicial meshes

The paper is devoted to the analysis of optimal simplicial meshes which minimize the gradient error of the piecewise linear interpolation over all conformal simplicial meshes with a fixed number of cells N T . We present theoretical results on asymptotic dependencies of L p -norms of the gradient error on N T for spaces of arbitrary dimension d. Our analysis is based on a geometric representation of the gradient error of linear interpolation on a simplex and a relaxed saturation assumption. We derive a metric field M p such that a M p -quasi-uniform mesh is quasi-optimal, for arbitrary d and p ∊ ]0, +∞]. Quasi-optimal meshes provide the same asymptotics of the L p -norm of the gradient error as the optimal meshes.

Resonance saturation of the chiral couplings at next-to-leading order in1/NC

The precision obtainable in phenomenological applications of chiral perturbation theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-${N}_{C}$ resonance Lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the $1/{N}_{C}$ expansion within the framework of resonance chiral theory. We find that, by imposing QCD short-distance constraints, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of resonance chiral theory. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance Lagrangian. Going beyond leading order in the $1/{N}_{C}$ counting allows us to keep full control of the renormalization scale dependence of the LEC estimates.

Steady-state biofilter performance under non-isothermal conditions

In recent years, due to the economical and environmental benefits, biofiltration has been chosen by industries as the preferred technology for volatile organic compound (VOC) removal even in regions such as the Middle East where a warmer climate prevails throughout the year. In this work, a theoretical non-isothermal steady-state model is developed and the model has been used to evaluate temperature effects of biofilter performance. The model predicts that toluene removal increases as the inlet and surrounding air temperatures increase. A 5 °C increase in the inlet air temperature results in a 20% increase in the percent removal of toluene. A complete sensitivity analysis of the model is carried out. Heat of biological reaction (−Δ H R) has only a negligible effect on biofilter performance for the range of values (10–100 kJ/g) considered and overall heat transfer coefficient ( U ov), for values <25 J s −1 m −2 K −1, have shown a profound effect on toluene removal. Although the results of this study are based on the assumption of complete saturation of incoming air, and negligible moisture loss from the media, the results and this non-isothermal model will be useful in estimating key design parameters for full scale systems.

A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation

In this note we consider residual-based a posteriori error estimation for finite element approximations of the transport equation. For the discretization we use piecewise affine continuous or discontinuous finite elements and symmetric stabilization of interior penalty type. The lowest order discontinuous Galerkin method using piecewise constant approximation is included as a special case. The key elements in the analysis are a saturation assumption and an approximation result for interpolation between discrete spaces.

Energy norm based a posteriori error estimation for boundary element methods in two dimensions

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. We analyze the mathematical relation between the h- h / 2 -error estimator from [S. Ferraz-Leite, D. Praetorius, Simple a posteriori error estimators for the h-version of the boundary element method, Computing 83 (2008) 135–162], the two-level error estimator from [S. Funken, Schnelle Lösungsverfahren für FEM-BEM Kopplungsgleichungen, Ph.D. thesis, University of Hannover, 1996 (in German); P. Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R 3 , Computing 60 (1998) 243–266], and the averaging error estimator from [C. Carstensen, D. Praetorius, Averaging techniques for the effective numerical solution of Symm's integral equation of the first kind, SIAM J. Sci. Comput. 27 (2006) 1226–1260]. We essentially show that all of these are equivalent, and we extend the analysis of [S. Funken, Schnelle Lösungsverfahren für FEM-BEM Kopplungsgleichungen, Ph.D. thesis, University of Hannover, 1996 (in German); P. Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R 3 , Computing 60 (1998) 243–266] to cover adaptive mesh-refinement. Therefore, all error estimators give lower bounds for the Galerkin error, whereas upper bounds depend crucially on the saturation assumption. As model examples, we consider first-kind integral equations in 2D with weakly singular integral kernel.

On estimators for eigenvalue/eigenvector approximations

We consider a large class of residuum based a posteriori eigen-value/eigenvector estimates and present an abstract framework for proving their asymptotic exactness. Equivalence of the estimator and the error is also established. To demonstrate the strength of our abstract approach we present a detailed study of hierarchical error estimators for Laplace eigenvalue problems in planar polygonal regions. To this end we develop new error analysis for the Galerkin approximation which avoids the use of the strengthened Cauchy-Schwarz inequality and the saturation assumption, and gives reasonable and explicitly computable upper bounds on the discretization error. A brief discussion is also given concerning the design of estimators which are in the same spirit, but are based on different a posteriori techniques-notably, those of gradient recovery type.

Global sensitivity of weathering rates to atmospheric CO2 under the assumption of saturated river discharge

AbstractThe sensitivity of the global river-borne flux of Ca2+ to atmospheric pCO2 was obtained from model simulations under the assumption of saturation of CaCO3. The response was subdivided into contributions from changes in runoff, temperature and partial CO2 pressure and these were then used to parameterize the different direct and indirect effects of a changing climate on carbonate weathering and equilibria. The parameterizations are comparable/compatible to those of Walker et al. (1981) for silicate weathering, but are taken directly from models demonstrating the potential of this approach in weathering studies.

FE determination of the plasticity induced during diffusive transformation in the case of nucleation at random locations and instants

The evolution of TRansformation Induced Plasticity (TRIP) in a steel where the parent phase has been strain-hardened, for a martensitic as well as a bainitic transformation, can only be predicted with models taking into account the interaction between classical plasticity and TRIP. One of the most famous, due to Leblond [J.B. Leblond, Int. J. Plasticity 5 (1989) 573–591], does not provide satisfying predictions in the experimental cases of pre-hardening explored by Taleb and Petit-Grostabussiat [L. Taleb, S. Petit-Grostabussiat, J. Phys. IV 12 (2002) Pr11–187–194; L. Taleb, S. Petit, Int. J. Plasticity 22 (2006) 110–130]. This has motivated the development of alternative approaches based on Finite Element (FE) analysis, which calculates equilibrium at the local scale of the interaction between phases without adopting any particular assumption on stress and strain fields. Our studies concern in particular diffusional transformation where the last improvement has consisted in introducing a new law to govern the kinetics of nucleation: whereas previous works were based on the assumption of site saturation (instantaneous nucleation), it is considered here that nucleation happens randomly in space as well as in time, with a controlled probability distribution and evolution in time.