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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：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：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...
