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作者：Stolyar, AL
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T
摘要：We consider a generalized switch model, which includes as special cases the model of multiuser data scheduling over a wireless medium, the input-queued cross-bar switch model and a discrete time version of a parallel server queueing system. Input flows n = 1,...,N are served in discrete time by a switch. The switch state follows a finite state, discrete time Markov chain. In each state m, the switch chooses a scheduling decision k from a finite kset K(m), which has the associated service rate ...
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作者：Wilson, DB
作者单位：Microsoft
摘要：We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Randall and Sinclair to generate random tilings of regions by lozenges. For an l x l region we bound the mixing time by O(l(4) log l), which improves on the previous bound of O(l(7)), and we show the new boun...
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作者：Guillemin, F; Robert, P; Zwart, B
作者单位：Orange SA; Eindhoven University of Technology
摘要：The behavior of a connection transmitting packets into a network according to a general additive-increase multiplicative-decrease (AIMD) algorithm is investigated. It is assumed that loss of packets occurs in clumps. When a packet is lost, a certain number of subsequent packets are also lost (correlated losses). The stationary behavior of this algorithm is analyzed when the rate of occurrence of clumps becomes arbitrarily small. From a probabilistic point of view, it is shown that exponential ...
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作者：Dai, JG; Hasenbein, JJ; Vate, JHV
作者单位：University System of Georgia; Georgia Institute of Technology; University of Texas System; University of Texas Austin
摘要：This article proves that the stability region of a two-station, five-class reentrant queueing network, operating under a nonpreemptive static buffer priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean interarrival and service times are not enough to determine the stability of a queueing network under a particular policy. We prove that when all distributions are exponential, the network is unsta...
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作者：Avram, F; Kyprianou, AE; Pistorius, MR
作者单位：Universite de Pau et des Pays de l'Adour; Utrecht University; University of London; King's College London
摘要：We consider spectrally negative Levy process and determine the joint Laplace transform of the exit time and exit position from an interval containing the origin of the process reflected in its supremum. In the literature of fluid models, this stopping time can be identified as the time to buffer-overflow. The Laplace transform is determined in terms of the scale functions that appear in the two-sided exit problem of the given Levy process. The obtained results together with existing results on...
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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...
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作者：Le Gland, F; Oudjane, N
作者单位：Inria; Electricite de France (EDF)
摘要：We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.
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作者：Weissman, T; Merhav, N
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：Let X = {(X-t, Y-t)}(tis an element ofZ) be a stationary time series where X-t is binary valued and Y-t, the noisy observation of X-t, is real valued. Letting P denote the probability measure governing the joint process {(X-t, Y-t)}, we characterize U(l, P), the optimal asymptotic average performance of a predictor allowed to base its prediction for X-t on Y-1,.., Yt-1, where performance is evaluated using the loss function l. It is shown, that the stationarity and ergodicity of P, combined wi...
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作者：Korolyuk, VS; Limnios, N
作者单位：National Academy of Sciences Ukraine; Institute of Mathematics of NASU; Universite de Technologie de Compiegne
摘要：Stochastic evolutionary systems of additive functional type, described by processes with locally independent increments, are considered with Markov switching in an asymptotic split state space having a stoppage state. The average and diffusion approximation limit theorems are established in both single and double merging. The proofs of these results are obtained using a singular perturbation approach of linear reducible-invertible operators and the tightness of processes. Particular cases of t...
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作者：Zhang, JF
作者单位：University of Southern California
摘要：In this paper we propose a numerical scheme for a class of backward stochastic differential equations (BSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong L-2 sense and derive its rate of convergence. As an intermediate step we prove an L-2-type regularity of the solution to such BSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an L-2 sense, is new. Some other features of our scheme includ...
