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71.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
72.
Jinyan Fan 《Computational Optimization and Applications》2006,34(2):215-227
In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The
new method preserves the global convergence of the traditional trust region methods in which the trust region radius will
be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition
which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic.
Finally, some numerical results are given.
This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong
University, and E-Institute of Computational Sciences of Shanghai Universities.
An erratum to this article is available at . 相似文献
73.
在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示.在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程.当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简. 相似文献
74.
Alberto Caprara Andrea Lodi Silvano Martello Michele Monaci 《Discrete Optimization》2006,3(4):317-326
We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature. 相似文献
75.
Carsten Franz 《Proceedings of the American Mathematical Society》2006,134(8):2437-2446
A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.
76.
四阶半线性椭圆型积分微分方程的奇摄动 总被引:5,自引:1,他引:4
本文研究了一个四阶椭圆型积分微分方程的奇摄动问题。证明了相应的比较定理并得到了解的一致有效的渐近展开式。 相似文献
77.
给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量,用投影梯度法修正有效约束所对应的变量,文中证明了方法的整体收敛性,并对方法进行了数值试验,且与子空间有限内存拟牛顿法进行了数值比较。 相似文献
78.
Liang Ruixi Peng Jun Shen Jianhua 《Annals of Differential Equations》2006,22(4):502-510
The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures. 相似文献
79.
Michal Johanis Jan Rychtá r 《Proceedings of the American Mathematical Society》2007,135(5):1511-1514
It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.
80.
Rostislav Vodák 《Mathematical Methods in the Applied Sciences》2007,30(1):43-75
We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross‐sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non‐smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献