V.F. Kolchin, B.A. Sevast'yanov, V.P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....reproductions is negligible, the study of the measures of distinctness becomes meaningful and important. The number of distinct outcomes in a sequence of multinomial trials (the classical occupancy problem) has wide applications; see, for example, Knuth [34] Johnson and Kotz [28] Kolchin et al. [35], Arat o and Bencz ur [5] and Vitter and Chen [50] The number of distinct sites visited by a random walk plays an important role in a number of applications in physics and chemistry; see Larralde and Weiss [36] and the references therein. Finally, since distinct irreducible factors over finite ....

V. F. Kolchin, R. A. Sevast'yanov, and V. P. Chistyakov. Random allocations . V. H. Winston and Sons, Washington, D. C., (1978).

....reproductions is negligible, the study of the measures of distinctness becomes meaningful and important. The number of distinct outcomes in a sequence of multinomial trials (the classical occupancy problem) has wide applications; see, for example, Knuth [34] Johnson and Kotz [28] Kolchin et al. [35], Arato and Benczur [5] and Vitter and Chen [50] The number of distinct sites visited by a random walk plays an important role in a number of applications in physics and chemistry; see Larralde and Weiss [36] and the references therein. Finally, since distinct irreducible factors over finite ....

V. F. Kolchin, R. A. Sevast'yanov, and V. P. Chistyakov. Random allocations . V. H. Winston and Sons, Washington, D. C., (1978).

....the node density to asymptotically increase to infinity. In the next section, we will improve the results of [1,11] for the case d=1 by means of a more accurate analysis of the conditions leading to disconnected communication graphs. The analysis will use some results of the occupancy theory [3], which are presented next. The occupancy problem can be described as follows: assume we have C cells, and n balls to be thrown independently in the cells. The allocation of balls into cells can be characterized by means of random variables describing some property of the cells. The occupancy ....

....of the random variable (n,C) is different. These domains are: the central domain (CD for short) when n=#(C) the right hand domain (RHD for short) when n= #(ClogC) the left hand domain (LHD for short) when n=#( C ) All the results presented in this section are taken from [3]. the right hand intermediate domain (RHID for short) when n=#(C) but C logC n; the left hand intermediate domain (LHID for short) when n=O(C) but n C . The following theorem describes the limit distribution of (n,C) in the different domains. Theorem 2. The limit distribution of ....

V.F. Kolchin, B.A. Sevast'yanov, and V. P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.

.... ; however, if a cell contains h nodes, the load can be evenly divided among them, and the last node in the cell will die at time hT.Hence,alower bound to the network lifetime can be obtained by evaluating the probability distribution of the minimum number of nodes in a cell, and occupancy theory [13] can be brought to bear on the problem. 4. ALOWERBOUNDTONETWORKLIFETIMEFORTHEIDEALIZEDAPPROACH In this section we will use the standard notation regarding the asymptotic behavior of functions, which we recall. Let f and g be functions of the same parameter x.Wehave: f(x) O(g(x) if there ....

.... and f(x) #(g(x) In this case, we also use the notation f(x) g(x) f(x) o(g(x) if f(x) g(x) 0asx ##; f(x) g(x)org(x) f(x)iff(x) o(g(x) The probability distribution of the minimum number of nodes in a cell can be evaluated using some results of the occupancy theory [13], which studies properties of the random independent allocations of n balls into N urns when n, N ##.Let#(n,N) be the random variable denoting the minimum number of nodes in a cell. The form of the limit distribution (i.e. of the probability distribution of #(n, N) when n, N ##) depends on ....

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V. Kolchin, B. Sevast'yanov, and V. Chistyakov. Random Allocations. V.H. Winston and Sons, Washington D.C., 1978.

.... is the normal distribution [26] the limit distribution of the total edge length of the Voronoi diagram and of the Delaunay triangulation is the normal distribution [23] the limit distribution of the number of empty cells is the normal distribution of parameters ( q n(1 (2=e) [15]. In the following sections, we will use these statistics to test our hypothesis H . 3 The mobility models Two mobility models will be used in the following to test the statistical hypothesis described in the previous Section. The rst model is the random waypoint model [13] which is commonly ....

V.F. Kolchin, B.A. Sevast'yanov, V.P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.

.... is the normal distribution [21] the limit distribution of the total edge length of the Voronoi diagram and of the Delaunay triangulation is the normal distribution [19] the limit distribution of the number of empty cells is the normal distribution of parameters ( e ; q n(1 (2=e) e ) [14]. In the following sections, we will use these statistics to test our hypothesis H. 3. THE MOBILITY MODELS Two mobility models will be used in the following to test the statistical hypothesis described in the previous section. The rst model is the random waypoint model [12] which is commonly ....

V.F. Kolchin, B.A. Sevast'yanov, V.P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.

....of this process is that the maximum allocation time is additionally bounded by O(log log n) 1 Introduction In the classical balls into bins game m balls are thrown independently and uniformly at random (i.u.a.r. into n bins. The distribution of the balls in the bins is well known ([KSC78]) For m = n there exists a bin getting Theta Gamma log n log log n Delta balls with high probability (w.h.p. 1 . Azar et al. ABKU94] consider a modified sequential game where each ball chooses i.u.a.r. d 2 bins and is placed in the bin with the smaller load. They show a Theta (log ....

V.F. Kolchin, B.A. Sevsatyanov, and V.P. Chistyakov. Random Allocation. V.H. Winston and Sons, 1978.

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V.F. Kolchin, B.A. Sevast'yanov, V.P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.

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V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov, Random Allocations. V. H. Winston and Sons, Washington D.C., 1978.

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V.F. Kolchin, B.A. Sevast'yanov, V.P. Chistyakov, Random Allocations, V.H. Winston and Sons, Washington D.C., 1978.

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V. F. Kolchin, R. A. Sevast'yanov, and V. P. Chistyakov. Random allocations. V. H. Winston and Sons, Washington, D. C., 1978.

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V. F. Kolchin, R. A. Sevast'yanov, and V. P. Chistyakov. Random allocations. V. H. Winston and Sons, Washington, D. C., 1978.

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