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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...
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作者：Redmond, C.; Yukch, J. E.
作者单位：Lehigh University; Lehigh University
摘要：A Beardwood-Halton-Hammersley type of limit theorem is established for a broad class of Euclidean functionals which arise in stochastic optimization problems on the d-dimensional unit cube. The result, which applies to all functionals having a certain quasiadditivity property, involves minimal structural assumptions and holds in the sense of complete convergence. It extends Steele's classic theorem and includes such functionals as the length of the shortest path through a random sample, the mi...
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作者：Hu, Yiming; Woyczynski, W. A.
作者单位：University System of Ohio; Case Western Reserve University
摘要：We prove that a certain (centered unimodal) rearrangement of coefficients in the moving average initial input process maximizes the variance (energy density) of the limit distribution of the spatiotemporal random field solution of a nonlinear partial differential equation called Burgers' equation. Our proof is in the spirit of domination principles developed in the book by Kwapien and Woycznski.
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作者：Choudhury, Gagan L.; Lucantoni, David M.; Whitt, Ward
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T; Nokia Corporation; Nokia Bell Labs; AT&T
摘要：We develop an algorithm for numerically inverting multidimensional transforms. Our algorithm applies to any number of continuous variables (Laplace transforms) and discrete variables (generating functions). We use the Fourier-series method; that is, the inversion formula is the Fourier series of a periodic function constructed by aliasing. This amounts to an application of the Poisson summation formula. By appropriately exponentially damping the given function, we control the aliasing error. W...
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作者：Hall, Peter; Roy, Rahul
作者单位：Australian National University; Indian Statistical Institute; Indian Statistical Institute Delhi
摘要：For Gaussian processes there is a simple and well-known relationship between the fractal dimension of sample paths and the fractal index of the covariance function. This property is of considerable practical interest, since it forms the basis of several estimators of fractal dimension. Motivated by statistical applications involving non-Gaussian processes, we discuss the relationship in a wider context. We show that the relationship fails in some circumstances, but nevertheless does hold in a ...
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作者：Meyn, Sean P.; Tweedie, R. L.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Colorado State University System; Colorado State University Fort Collins
摘要：Recent results for geometrically ergodic Markov chains show that there exist constants R < infinity, rho < 1 such that sup(vertical bar f vertical bar <= V) vertical bar integral P-n(x, dy)f(y) - integral pi(dy)f(y)vertical bar <= RV(x)rho(n), where pi is the invariant probability measure and V is any solution of the drift inequalities integral P(x, dy)V(y) <= lambda V(x) + b1(c)(x), which are known to guarantee geometric convergence for lambda < 1, b < infinity and a suitable small set C. In ...
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作者：Rhee, WanSoo T.
作者单位：University System of Ohio; Ohio State University
摘要：A fleet of vehicles located at a common depot must serve customers located throughout the plane. Without loss of generality, the depot will be located at the origin. Each vehicle must start at the depot, travel in turn to each customer its serves and go back to the depot. Each vehicle can serve at most k customers. The objective is to minimize the total distance traveled by the fleet. In our model, the customers X1, . . . , X-n are independent and uniformly distributed over the unit disc. If R...
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作者：Coffman, E. G., Jr.; Mallows, C. L.; Poonen, Bjorn
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T
摘要：Let (r(1), s(1)), ... ,(r(n), s(n),) be a sequence of requests to place arcs on the unit circle, where 0 <= r(i), s(i), <= 1 are endpoints relative to some origin on the circle. The first request is always satisfied by reserving, or parking, the shorter of the two arcs between r(1) and s(1) (either arc can be parked in case of ties). Thereafter, one of the two arcs between r(i) and s(i), is parked if and only if it does not overlap any arc already parked by the first i - 1 requests. Assuming t...
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作者：Roos, Malgorzata
摘要：In the present paper, compound Poisson approximation by Stein's method is considered. A general theorem analogous to the local approach for Poisson approximation is proved. It is then applied to a reliability problem involving the number of isolated vertices in the rectangular lattice on the torus.
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作者：Alexander, Kenneth S.
作者单位：University of Southern California
摘要：Given two i.i.d. sequences of n letters from a finite alphabet, one can consider the length L-n of the longest sequence which is a subsequence of both the given sequences. It is known that ELn grows like gamma n for some gamma is an element of [0, 1]. Here it is shown that gamma n >= ELn >= gamma n - C(n log n)(1/2) for an explicit numerical constant C which does not depend on the distribution of the letters. In simulations with n = 100,000, ELn/n can be determined from k such trials with 95% ...
