Large deviations and the generalized processor sharing scheduling for a two-queue system

We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

One-dimensional non-nearest-neighbor random walks in the presence of traps

A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site.     

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

LetB ₁ be a ball of radiusr ₁ inS ⁿ (ℍⁿ), and letB ₀ be a smaller ball of radiusr ₀ such thatB ₀ ⊂B ₁ . ForS ⁿ we considerr ₁ π. Let u be a solution of the problem- δm = 1 in Ω :=B ₁ /B ₀ vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on Ω is maximal if and only if the balls are concentric.     

刘维尔与伽罗瓦数学手稿的发表

1846年,刘维尔在自己主办的杂志“纯粹与应用数学杂志”首次出版了伽罗瓦的数学研究,这对于伽罗瓦理论的传播与发展是具有决定意义的事件.伽罗瓦去世14年后,刘维尔发表伽罗瓦数学研究的原因是什么?采用数学历史文献分析法,得出四个重要原因:①伽罗瓦的朋友和弟弟的请求;②力图弥补科学院曾经造成的不公正;③刘维尔积极扶持年轻人的高贵品质使然;④刘维尔与利布里学术论战的促进.     

Measurement of the First Hyperpolarizability of Substituted Ketene N，S－acetals by Hyper－Rayleigh Scattering in Solution

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On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

On the structure of stationary sets

We isolate several classes of stationary sets of [k]ωand investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.     

A duality relation for busy cycles inGI/G/1 queues

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.     

Relative versions of some star-selection principles

We introduce some relative versions of star selection principles first considered in [5], [11]. Some of the work extends results from [4], [5] and gives some examples.      

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22