2003

最新文章

• Fluid and heavy traffic diffusion limits for a generalized processor sharing model AI翻译
  作者：Ramanan, K; Reiman, MI
  作者单位：AT&T; Alcatel-Lucent; Lucent Technologies
  摘要：Under fairly general assumptions on the arrival and service time processes, we prove fluid and heavy traffic limit theorems for the unfinished work, queue length, sojourn time and waiting time processes associated with a single station multiclass generalized processor sharing model. The fluid limit of the unfinished work process is characterized by the Skorokhod map associated with a Skorokhod problem formulation of the generalized processor sharing model, while the heavy traffic diffusion lim...
• A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations AI翻译
  作者：Talay, D; Vaillant, O
  作者单位：Inria
  摘要：We are interested in statistical solutions of McKean-Vlasov-Fokker-Planck equations. An example of motivation is the Navier-Stokes equation for the vorticity of a two-dimensional incompressible fluid flow. We propose an original and efficient numerical method to compute moments of such solutions. It is a stochastic particle method with random weights. These weights are defined through nonparametric estimators of a regression function and convey the uncertainty on the initial condition of the c...
• The stepping stone model: New formulas expose old myths (vol 12, pg 1348, 2002) AI翻译
  作者：Cox, T; Durrett, R
  作者单位：Syracuse University; Cornell University
• Some probability distributions in modeling DNA replication AI翻译
  作者：Lachal, A
  作者单位：Institut National des Sciences Appliquees de Lyon - INSA Lyon
  摘要：By using some quasi-renewal-like equations and functional differential equations, we explicitly compute the Laplace transforms of some random variables introduced by Cowan and Chiu in modeling the mechanism of replication of a DNA molecule [J. Appl. Probab. (1994) 31 301-308]. These Laplace transforms are expressed by means of infinite products arising in the theory of partitions.
• Control of end-to-end delay tails in a multiclass network: LWDF discipline optimality AI翻译
  作者：Stolyar, AL
  作者单位：Alcatel-Lucent; Lucent Technologies; AT&T
  摘要：We consider a multiclass queueing network with N customer classes, each having an arbitrary fixed route through the network. (Thus, the network is not necessarily feedforward.) We show that the largest weighted delay first (LWDF) discipline is an optimal scheduling discipline in the network in the following sense. Let w(i) be the (random) instantaneous largest end-to-end delay of a class i customer in the network in stationary regime. For any set of positive constants alpha(1), . . . , alpha(N...
• Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models AI翻译
  作者：Caputo, P; Martinelli, F
  作者单位：Roma Tre University
  摘要：Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diffusions on the lattice, we consider an anisotropic simple exclusion process with N particles in a rectangle of Z(2). Every particle at row h tries to jump to an arbitrary empty site at row h +/- 1 with rate q(+1), where q is an element of (0, 1) is a measure of the drift driving the particles toward the bottom of the rectangle. We prove that the spectral gap of the generator is unifo...
• Weak laws of large numbers in geometric probability AI翻译
  作者：Penrose, MD; Yukich, JE
  作者单位：Durham University; Lehigh University
  摘要：Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly nonuniform) density of the point process. The general result is applied to the minimal spanning tree, the k-nearest neighbors graph, the Voronoi graph and the sphere of influence graph. Functionals of interest include total edge length with arbitrary weighting, number of vertices of specified degree...
• A broader view of Brownian networks AI翻译
  作者：Harrison, JM
  作者单位：Stanford University
  摘要：This paper describes a general type of stochastic system model that involves three basic elements: activities, resources, and stocks of material. A system manager chooses activity levels dynamically based on state observations, consuming some materials as inputs and producing other materials as outputs, subject to resource capacity constraints. A generalized notion of heavy traffic is described, in which exogenous input and output rates are approximately balanced with nominal activity rates de...
• A degenerate central limit theorem for single resource loss systems AI翻译
  作者：Fricker, C; Robert, P; Tibi, D
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
  摘要：Loss networks in heavy traffic under Kelly's scaling are analyzed. In the case of a single node and R classes of calls, a degenerate diffusion approximation theorem around the corresponding fluid limit in an (R - 1)-dimensional hyperplane is proved.
• Convergence to equilibrium for granular media equations and their Euler schemes AI翻译
  作者：Malrieu, F
  摘要：We introduce a new interacting particle system to investigate the behavior of the nonlinear, nonlocal diffusive equation already studied by Benachour et al. [3, 4]. We first prove an uniform (with respect to time) propagation of chaos. Then, we show that the solution of the nonlinear PDE converges exponentially fast to equilibrium recovering a result established by an other way by Carrillo, McCann and Vilanni [7]. At last we provide explicit and Gaussian confidence intervals for the convergenc...