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作者：Bramson, Maury
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Consider a queueing network with customers arriving according to a rate-1 Poisson process. Each customer proceeds along the same prescribed route, waiting at the different queues until exiting from the system. The service times are assumed to be independent and exponentially distributed. Individual queues may be visited more than once by a customer, with the mean service time perhaps depending on the stage along the route. The network is assumed to be first-in, first-out. An obvious necessary ...
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作者：Ingrassia, Salvatore
作者单位：University of Catania
摘要：In this paper we obtain bounds on the spectral gap of the transition probability matrix of Markov chains associated with the Metropolis algorithm and with the Gibbs sampler. In both cases we prove that, for small values of T, the spectral gap is equal to 1 A2, where A2 is the second largest eigenvalue of P. In the case of the Metropolis algorithm we give also two examples in which the spectral gap is equal to 1 Amm, where Amu., is the smallest eigenvalue of P. Furthermore we prove that random ...
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作者：Alon, Noga; Bollobas, Bela; Brightwell, Grajham; Janson, Svante
作者单位：Tel Aviv University; University of Cambridge; University of London; London School Economics & Political Science; Uppsala University
摘要：We study asymptotics of the number of linear extensions of the random G(n, p) partial order, where p is fixed and n -> infinity. In particular, it is shown that the distribution is asymptotically log-normal.
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作者：Bertsimas, Dimitris; Paschalidis, Ioannis Ch.; Tsitsiklis, John N.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We consider open and closed multiclass queueing networks, with Poisson arrivals (for open networks), exponentially distributed class dependent service times and class dependent deterministic or probabilistic routing. The performance objective is to minimize, over all sequencing and routing policies, a weighted sum of the expected response times of different classes. Using a powerful technique involving quadratic or higher order potential functions, we propose methods for deriving polyhedral an...
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作者：Grey, D. R.
作者单位：University of Sheffield
摘要：Let Q and M be random variables with given joint distribution. Under some conditions Qn this joint distribution, there will be exactly one distribution for another random variable R, independent of (Q, M), with the property that Q + MR has the same distribution as R. When M is nonnegative and satisfies some moment conditions, we give an improved proof that if the upper tail of the distribution of Q is regularly varying, then the upper tail of the distribution of R behaves similarly; this proof...
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作者：Fouque, Jean-Pierre; Merzbach, Ely
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Bar Ilan University
摘要：The asymptotic behavior of the solutions of linear equations with random coefficients, random external forces and with affine boundary conditions is studied, motivated by a transmission-reflection problem for a one-dimensional wave equation in a random slab. The fluctuations of the coefficients are on a small scale in such a way that our problem is a diffusion-approximation problem except that we impose boundary conditions which force the solution to be anticipating. In the limit we obtain lin...
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作者：Davis, M. H. A.; Zervos, M.
作者单位：Imperial College London
摘要：In this paper a simple problem of combined singular stochastic control and optimal stopping is formulated and solved. We find that the optimal strategies can take qualitatively different forms, depending on parameter values. We also study a variant on the problem in which the value function is inherently nonconvex. The proofs employ the generalised Ito formula applicable for differences of convex functions.
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作者：Schwerer, Elizabeth; Van Mieghem, Jan A.
作者单位：Stanford University
摘要：We study a closed, three-station queueing network with general service time distributions and balanced workloads (that is, each station has the same relative traffic intensity). If the customer population is large, then the queue length process of such a network can be approximated by driftless reflected Brownian motion (RBM) in a simplex. Building on earlier work by Harrison, Landau and Shepp, we develop explicit formulas for various quantities associated with the stationary distribution of R...
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作者：Redmond, C.; Yukch, J. E.
作者单位：Lehigh University; Lehigh University
摘要：A Beardwood-Halton-Hammersley type of limit theorem is established for a broad class of Euclidean functionals which arise in stochastic optimization problems on the d-dimensional unit cube. The result, which applies to all functionals having a certain quasiadditivity property, involves minimal structural assumptions and holds in the sense of complete convergence. It extends Steele's classic theorem and includes such functionals as the length of the shortest path through a random sample, the mi...
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作者：Hu, Yiming; Woyczynski, W. A.
作者单位：University System of Ohio; Case Western Reserve University
摘要：We prove that a certain (centered unimodal) rearrangement of coefficients in the moving average initial input process maximizes the variance (energy density) of the limit distribution of the spatiotemporal random field solution of a nonlinear partial differential equation called Burgers' equation. Our proof is in the spirit of domination principles developed in the book by Kwapien and Woycznski.
