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In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N-(V, E)-queue. Exact asymptotic rates of the loss probability are obtained for the cases in which the traffic intensity is smaller than, equal to and greater than one, respectively. When the vacation time is zero, the model considered degenerates to the standard M/G/1/N queue. For this standard queueing model, our analysis provides new or extended asymptotic results for the loss probability. In terms of the duality relationship between the M/G/1/N and GI/M/1/N queues, we also provide asymptotic properties for the standard GI/M/1/N model.  相似文献
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This paper proposes an ODE-based nonmonotone method for unconstrained optimization problems, which combines the idea of IMPBOT with the nonmonotone technique. The main characteristic of this method is that at each iteration, a system of linear equations is solved only once to obtain a trial step, via a modified L-BFGS two loop recursion that requires only vector inner products, thus reducing the matrix computation and storage. Then a modified nonmonotone line search is performed to generate next iterative point instead of resolving the linear system. Under some reasonable assumptions, the method is proven to be globally and superlinearly convergent. Numerical results show the efficiency of this proposed method in practical computation.  相似文献
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In this paper we propose a numerical method for approximating connecting orbits on a manifold and its bifurcation parameters. First we extend the standard nondegeneracy condition to the connecting orbits on a manifold. Then we construct a well-posed system such that the nondegenerate connecting orbit pair on a manifold is its regular solution. We use a difference method to discretize the ODE part in this well-posed system and we find that the numerical solutions still remain on the same manifold. We also set up a modified projection boundary condition to truncate connecting orbits on a manifold onto a finite interval. Then we prove the existence of truncated approximate connecting orbit pairs and derive error estimates. Finally, we carry out some numerical experiments to illustrate the theoretical estimates.  相似文献
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We investigate deviation matrix for discrete-time GI/M/1-type Markov chains in terms of the matrix-analytic method, and revisit the link between deviation matrix and the asymptotic variance. Parallel results are obtained for continuous-time GI/M/1-type Markov chains based on the technique of uniformization. We conclude with A. B. Clarke's tandem queue as an illustrative example, and compute the asymptotic variance for the queue length for this model.  相似文献
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For three types of triples, unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large set are introduced. The spectrum of LEDTS(v) for even v has been given in our paper (Liu and Kang (2009) [9]). In this paper, we shall discuss the existence problem of LEDTS(v) for odd v and give the almost complete conclusion: there exists an LEDTS(v) for any positive integer v≠4 except possible v=95,143,167,203,215.  相似文献
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In this paper, subgeometric ergodicity is investigated for continuous-time Markov chains. Several equivalent conditions, based on the first hitting time or the drift function, are derived as the main theorem. In its corollaries, practical drift criteria are given for ?-ergodicity and computable bounds on subgeometric convergence rates are obtained for stochastically monotone Markov chains. These results are illustrated by examples.  相似文献
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Let P be a positive recurrent infinite transition matrix with invariant distribution π and be a truncated and arbitrarily augmented stochastic matrix with invariant distribution (n)π. We investigate the convergence ‖(n)ππ‖→0, as n, and derive a widely applicable sufficient criterion. Moreover, computable bounds on the error ‖(n)ππ‖ are obtained for polynomially and geometrically ergodic chains. The bounds become rather explicit when the chains are stochastically monotone.  相似文献
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A directed triple system of order v, denoted by DTS(v), is a pair (X, $ \mathcal{B} $ ) where X is a v-set and $ \mathcal{B} $ is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of $ \mathcal{B} $ . A DTS(v) (X, $ \mathcal{A} $ ) is called pure and denoted by PDTS(v) if (a, b, c) ∈ $ \mathcal{A} $ implies (c, b, a) ? $ \mathcal{A} $ . An overlarge set of PDTS(v), denoted by OLPDTS(v), is a collection {(Y {y i }, $ \mathcal{A}_i^j $ ): y i Y, jZ 3}, where Y is a (v + 1)-set, each (Y {y i }, $ \mathcal{A}_i^j $ ) is a PDTS(v) and these $ \mathcal{A}_i s $ form a partition of all transitive triples on Y. In this paper, we shall discuss the existence problem of OLPDTS(v) and give the following conclusion: there exists an OLPDTS(v) if and only if v ≡ 0,1 (mod 3) and v > 3.  相似文献
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For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.  相似文献
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