Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.     

On multiparameter ergodic and martingale theorems in infinite measure spaces

Summary A unified proof is given of several ergodic and martingale theorems in infinite measure spaces.The research of this author is in part supported by the National Science Foundation, grant MCS-8301619     

Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ℝ ^d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces. This work was supported by the National Natural Science Foundation of China (Grant No. 10671088) and the Major State Basic Research Development Program of China (Grant No. 2006CB805903)     

Ergodicity of reversible reaction diffusion processes

Summary Reaction-diffusion processes were introduced by Nicolis and Prigogine, and Haken. Existence theorems have been established for most models, but not much is known about ergodic properties. In this paper we study a class of models which have a reversible measure. We show that the stationary distribution is unique and is the limit starting from any initial distribution.The work was begun while the first author was visiting Cornell and supported by the Chinese government. The initial results (for Schlögl's first model) was generalized while the three authors were visiting the Nankai Institute for Mathematics, Tianjin, People's Republic of ChinaPartially supported by the National Science Foundation and the Army Research Office through the Mathematical Sciences Institute at Cornell UniversityPartially supported by NSF grant DMS 86-01800     

一类随机环境中的随机游动

研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论.     

Semi-uniform Sub-additive Ergodic Theorems for Skew-product Quasi-flows

The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses     

Window flow control in FIFO networks with cross traffic

We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region. This revised version was published online in June 2006 with corrections to the Cover Date.     

非Lipschitz仿射映射的半拓扑半群的强遍历定理(英)

本文在Banach空间中给出了非Lipschitzian仿信射拓扑半群的强遍历定理。     

Application of average dynamic programming to inventory systems

We show the existence ofaverage cost (AC-) optimal policy for an inventory system withuncountable state space; in fact, the AC-optimal cost and an AC-optimal stationary policy areexplicitly computed. In order to do this, we use a variant of thevanishing discount factor approach, which have been intensively studied in recent years but the available results not cover the inventory problem we are interested in.The work of the first author (OVA) was partially supported by Fondo del Sistema de Investigación del Mar de Cortéz under grant SIMAC/94/CT-005. The work of the second author (RMdO) was partially supported by Consejo Nacional de Ciencia y Tecnologia (CONACyT) under grant 0635P-E9506.     

The tightness in the ergodic analysis of regenerative queueing processes

The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed network, where the basic discrete time process is embedded at the service completion epochs. An extention of Kiefer and Wolfowitz's “key” lemma to a nonhomogeneous multiserver queue with an arbitrary initial state is obtained. These results are applied to get the ergodic theorems for the basic regenerative network processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stochastic partial differential equations in Hölder spaces

Summary We prove the existence and regularity of solutions to stochastic partial differential equations of parabolic Itô type in Hölder spaces under the usual sublinear growth and local Lipschitz conditions. Some examples are given to which our main theorems apply.The work of the first author was supported in part by the NSF grant DMS-91-01360     

Multiparameter ratio ergodic theorems for semigroups

After one-parameter treatment of ratio ergodic theorems for semigroups, we formulate the Sucheston a.e. convergence principle of continuous parameter type. This principle plays an effective role in proving some multiparameter generalizations of Chacon?s type continuous ratio ergodic theorems for semigroups and of Jacobs? type continuous random ratio ergodic theorems for quasi-semigroups. In addition, a continuous analogue of the Brunel–Dunford–Schwartz ergodic theorem is given of sectorially restricted averages for a commutative family of semigroups. We also formulate a local a.e. convergence principle of Sucheston?s type. The local convergence principle is effective in proving multiparameter local ergodic theorems. In fact, a multiparameter generalization of Akcoglu–Chacon?s local ratio ergodic theorem for semigroups of positive linear contractions on _L1$L_1$ is proved. Moreover, some multiparameter martingale theorems are obtained as applications of convergence principles.     

Stationarity and almost sure divergence of time averages in interval-valued probability

Our work is motivated by the study of empirical processes (such as flicker noise) that occur in stable systems yet give rise to observations with seemingly divergent time averages. Stationary models for such processes do not exist in the domain of numerical probability, as the ergodic theorems dictate the convergence of time averages of stationary and bounded processes. This has led us to investigate such models in the wider framework of interval-valued probability. In this paper we construct interval-valued probabilities on the space of infinite binary sequences that combine properties of (i) strict stationarity, (ii) unicity of extension from the algebra of cylinder sets to a wider collection containing salient asymptotic events, and (iii) almost sure support of divergence of time averages. These properties are not shared by conventional stochastic models.     

Exact sequences of algebras generated by singular integral operators

An abstract theorem concerning exact sequences of Banach algebras of operators and symbol homomorphisms relative to groups of operators is derived. This general result is used to deduce many of the classical spectral inclusion theorems and short exact sequences for algebras of singular integral operators.This work partially supported by a grant from the National Science Foundation.     

Effects of service disciplines inG/GI/s queueing systems

Transient extremal properties of some service disciplines are established in theG/GI/s queueing system for the minimization and maximization of the expectations of the Schur convex functions, convex symmetric functions and the sums of convex functions of the waiting times, response times, lag times and latenesses. When resequencing is required in the system, the FCFS and LCFS disciplines are shown to minimize and maximize, respectively, the expectations of any increasing functions of the end-to-end delays. All of these results are presented in terms of stochastic orderings. The paper concludes with extensions of the results to the stationary regime and to tandem as well as general queueing networks.This work was supported in part by the National Science Foundation under grant ASC 88-8802764.The work of this author was also partially supported by CEC DG-XIII under the ESPRIT-BRA grant QMIPS.     

Noncommutative maximal ergodic theorems

This paper is devoted to the study of various maximal ergodic theorems in noncommutative -spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on and the analogue of Stein's maximal inequality for symmetric positive contractions. We also obtain the corresponding individual ergodic theorems. We apply these results to a family of natural examples which frequently appear in von Neumann algebra theory and in quantum probability.

     

Convergence of almost-orbits of nonexpansive semigroups in Banach spaces

The purpose of this paper is to show that the study of mean ergodic theorems for almost-orbits of semigroups of nonexpansive mappings on closed convex subsets of a Banach space can be reduced to the study of orbits for semigroups of nonexpansive mappings. This provides a unified approach to various mean ergodic theorems for almost-orbits in the literature and new applications.

     

Using the refinement equation for the construction of pre-wavelets III: Elliptic splines

The purpose of this paper is to provide multiresolution analysis, stationary subdivision and pre-wavelet decomposition onL ²(R ^d ) based on a general class of functions which includes polyharmonic B-splines.The work of this author has been partially supported by a DARPA grant.The work of this author has been partially supported by Fondo Nacional de Ciencia y Technologia under Grant 880/89.     

有限域上遍历矩阵的特性研究

对有限域上遍历矩阵的性质进行了分析,给出了有限域上遍历矩阵的计数定理,并对遍历矩阵序对(A,B)关于矩阵M的双侧幂乘集〈A〉M〈B〉的秩及基数进行了全面分析.给出了R_k(A,B)集的构成及其基数的有关定理,所得到的结论对利用遍历矩阵实现有关的公钥密码具有理论上的指导意义.     

Convergence of polynomial ergodic averages

We prove theL ² convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials. Dedicated to Hillel Furstenberg upon his retirement The second author was partially supported by NSF grant DMS-0244994.