An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy traffic conditions. In this paper, we propose a new approximation technique, which combines the light and heavy traffic characteristics. This interpolation approximation is based on the theory of multipoint Padé approximation which is applied at two points: light and heavy traffic. We show how this can be applied for estimating the waiting time moments of the ^GI/G/1 queue. The light traffic derivatives of any order can be evaluated using the MacLaurin series analysis procedure. The heavy traffic limits of the ^GI/G/1 queue are well known in the literature. Our technique generalizes the previously developed interpolation approximations and can be used to approximate any order of the waiting time moments. Through numerical examples, we show that the moments of the steady state waiting time can be estimated with extremely high accuracy under all ranges of traffic intensities using low orders of the approximant. We also present a framework for the development of simple analytical approximation formulas. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Convergence of a Difference Equation and Its Applications

In this paper, we establish a sufficient condition for every solution of the forced difference equation $$x_{n+1} - x_n + p_nx_{n-k} = r_n, \ \ n=0, 1, \ldots$$     

Conditions of Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for a System of Generalized Ordinary Differential Equations

Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem where is a matrix-function with bounded variation components, is a vector-function belonging to the Carathéodory class corresponding to are continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.     

Zinc(II)-porphyrin Receptors in Multi-point Molecular Recognition: Recent Progress

The tremendous efforts made in order to control the coordination chemistry of hemoprotein models have considerably enhanced the synthesis of functionalized porphyrins, whose carefully designed architectures allowed for selective bindings of exogenic substrates. The common use of zinc(II) in place of pentacoordinated iron(II) has induced the use of zinc(II) porphyrins as building blocks for selective receptors. These receptors offer a convenient combination of multi-point recognition of substrates, and monitoring of the complexation due to the chromophoric nature of the tetrapyrrolic unit. This review is dedicated to recent progress made in the field of molecular recognition involving multi-point selective binding processes, in whichthe establishment of a strong coordination bond is finely tuned by one or more weak interactions adequately introduced in the architecture of a functionalized zinc(II)-porphyrin.     

Estimating deflection of a simple beam model using fiber optic bragg-grating sensors

In this paper, we develop a method to estimate the bridge deflection using fiber optic Bragg-grating (FBG) strain sensors. For most structural evaluation of bridge integrity, it is very important to measure the geometric profile, which is a major factor representing the global behavior of civil structures, especially bridges. In the past, because of the lack of appropriate methods to measure the deflection curve of bridges on site, the measurement of deflection has been restricted to just a few discrete points along the bridge, and the measuring points have been limited to the locations installed with displacement transducers. However, by applying classical beam theory, a formula is rearranged to estimate the continuously deflected profile by using strains measured directly from several points. In addition, FBG strain sensors, which are electromagnetic, noise-free and multipoint measurable, are employed to obtain flexural strains more accurately and stably. The regression analysis is performed to obtain a strain function from the measured strain data. Finally, the deflection curve can be estimated by applying the strain function to the formula. An experimental test has also been carried out to verify the developed method.     

A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization

A new algorithm for solving smooth large-scale minimization problems with bound constraints is introduced. The way of dealing with active constraints is similar to the one used in some recently introduced quadratic solvers. A limited-memory multipoint symmetric secant method for approximating the Hessian is presented. Positive-definiteness of the Hessian approximation is not enforced. A combination of trust-region and conjugate-gradient approaches is used to explore useful information. Global convergence is proved for a general model algorithm. Results of numerical experiments are presented.     

Complex differential games of pursuit-evasion type with state constraints,part 1: Necessary conditions for optimal open-loop strategies

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.This paper is dedicated to the memory of Professor John V. Breakwell.The authors would like to express their sincere and grateful appreciation to Professors R. Bulirsch and K. H. Well for their encouraging interest in this work.     

Weighted Best Local Approximation

In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the Lpspaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.