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作者：Delcoigne, F; De La Fortelle, A
作者单位：Electricite de France (EDF); Inria
摘要：We are interested in analyzing the effect of bandwidth sharing for telecommunication networks. More precisely, we want to calculate which routes are bottlenecks by means of large deviations techniques. The method is illustrated in this paper on a star network, where the bandwidth is shared between customers according to the so-called min policy. We prove a sample path large deviation principle for a rescaled process n(-1) Q(nt), where Q(t) represents the joint number of connections at time t. ...
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作者：Lefebvre, M
作者单位：Universite de Montreal; Polytechnique Montreal
摘要：Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled until it reaches either end of the interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost equal to zero (resp. a large constant) if the process exits the interval through its left (resp....
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作者：Chi, ZY
作者单位：University of Chicago
摘要：We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees and frequencies of types within trees, a higher-order asymptotic of the relative frequency estimator of the left eigenvector of the mean matrix, a higher-order joint asymptotic of the maximum likelihood estimators of the offspring probabiliti...
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作者：Gangopadhyay, S; Roy, R; Sarkar, A
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi
摘要：Consider the d-dimensional lattice Z(d) where each vertex is open or closed with probability p or 1 - p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth coordinates of v and w satisfy w(d) = v(d) - 1. In case of nonuniqueness of such a vertex w, we choose any one of the closest vertices with equal probability and independently of the other random mechanisms. It is shown that this random graph is a tree almost surely for d = 2 and 3 and it i...
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作者：Gromoll, HC
摘要：Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We show that under mild assumptions, including standa...
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作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let X-n = (x(ij)) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R-n = (rho(ij)) be the p x p sample correlation matrix of X-n; that is, the entry rho(ij) is the usual Pearson's correlation coefficient between the i th column of X-n and j th column of X-n. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H-0: the p variates of the population are ...
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作者：Puha, AL; Williams, RJ
作者单位：California State University System; California State University San Marcos; University of California System; University of California San Diego
摘要：This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches infinity. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffi...
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作者：Kelly, FP; Williams, RJ
作者单位：University of Cambridge; University of California System; University of California San Diego
摘要：We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal limits under law of large numbers scalings when the average load on at least one resource is equal to its capacity. We establish convergence to equilibria for fluid models and identify the invariant manifold. The form of the invariant manifold gives insight into...
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作者：León, CA; Perron, F
作者单位：Universidad de Concepcion; Universite de Montreal
摘要：We build optimal exponential bounds for the probabilities of large deviations of sums Sigma(k)(=1)(n) f (X(k)) where (X(k)) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean Sigmapi f the end-points of the support of f, the sample size n and the second largest eigenvalue lambda of the transition matrix.
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作者：Huisinga, W; Meyn, S; Schütte, C
作者单位：Free University of Berlin; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Diffusion models arising in analysis of large biochemical models and other complex systems are typically far too complex for exact solution or even meaningful simulation. The purpose of this paper is to develop foundations for model reduction and new modeling techniques for diffusion models. These foundations are all based upon the recent spectral theory of Markov processes. The main assumption imposed is V-uniform ergodicity of the process. This is equivalent to any common formulation of expo...
