Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations theory are consistent (in a certain sense) with the result using dominant pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the cell loss ratio, an important performance measure for service systems such as ATM networks. The analysis relies on a new generalization of the Taylor coefficients of a complex function which we call characteristic coefficients. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate multiclass M/D/n system.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

Consequences of the ‘Pedersen papers’ on crown type chemistry at Würzburg and Bonn Universities: From heteroaromatic crowns and podands to large molecular and crystalline cavities including multisite receptors,cascade molecules,chromoionophores, siderophores,surfactant-type,and extreme ligands

We thank the editors of this issue for the opportunity to present the historic development of crown chemistry at the Universities of Wurzburg and Bonn in memory of C. J. Pedersen, the originator of the crown ethers. His legacy of science has tremendously stimulated research at both universities.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

巢湖主要入湖河道磷的污染现状

为了解巢湖主要入湖河道中总磷的污染状况,进行了为期三年每月一次的污染调查,十五里河、南淝河、双桥河,污染较重,超出了(GH281-1999)《地表水环境质量标准》的V娄标准。污染主要来自工业废水、生活污水、和农业面源。认为只有开展农业面源污染治理,城市环境综合整治,城市环境综合整治,加强和削减农业化肥的使用量,使得入湖河道水质变好,巢湖的富营养化才能得到控制。     

Spectral density distribution moments of a Hamiltonian of N coupled Morse oscillators: The large‐N limit

The expressions for moments of spectral density distribution of a Hamiltonian representing a system of N coupled Morse oscillators are reduced to the large‐N limit. The effect of the values of coupling constants on the spectral density distribution is analyzed. For the values of coupling constants within the pertinent range for real molecules, the relations between moments appear to be close to those for a Gaussian distribution. Outside this range, the deviations from the normal distribution are substantial. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Coordination around thorium(IV) in aqueous perchlorate,chloride and nitrate solutions

The coordination around the thorium(IV) ion in aqueous perchlorate, chloride and nitrate solutions has been determined from large angle X-ray scattering measurements. In perchlorate solutions, where inner-sphere complexes are not formed, the first coordination sphere contains 8.0±0.5 water molecules with Th-H₂O bond lengths of 2.48₅ Å. In chloride solutions inner-sphere complexes are formed, which lead to an increase in the coordination number. In nitrate solutions the nitrate ions are bonded as bidentate ligands to the thorium ion. The bond lengths are similar to those found in crystalline hydrates of thorium nitrate. The coordination numbers found for thorium(IV) in solution are compared with previously reported values for lower charged ions of similar size.On leave from Department of Inorganic Chemistry Royal Institute of Technology S-10044 Stockholm Sweden