By Riis M., Lodahl J.
We reflect on means enlargement of a telecommunications community within the face of doubtful destiny call for and power destiny mess ups of community parts. the matter is formulated as a bicriteria stochastic software with recourse during which the entire expense of the capability enlargement and the likelihood of destiny capability requisites to be violated are at the same time minimized. Assuming the lifestyles of a finite variety of attainable destiny states of the area, an set of rules for the matter is elaborated. The set of rules determines all non-dominated suggestions to the matter by way of a discounted possible sector process, fixing a chain of constrained subproblems through a slicing aircraft strategy. Computational effects are stated for 3 various challenge circumstances, considered one of that is a real-life challenge confronted by means of SONOFON, a Danish communications community operator.
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Extra info for A bicriteria stochastic programming model for capacity expansion in telecommunications
Let vy be the first segment of xv. Then y must be a terminal point. If y is not identical to v, then we can shorten December 27, 2007 34 18:43 WSPC/Book Trim Size for 9in x 6in Steiner Tree Problems in Computer Communication Networks Tmht by deleting an edge incident to y. If y is identical to v, then we go back to Case 1. Case 3. ux is a straight edge and xv is a nonstraight edge without a segment in the same direction as ux. 17. Such a movement increases the number of full components. It follows from facts (F1-2) that the new location of x belongs to C(t∗ ; x).
Suppose that P (l ∗ ) = P (t∗ ; y). Then for any m ∈ M (t∗ ; x∗ ), l(m(t∗ ; y)) = l(m(t∗ ; x∗ )). Since both x∗ and y are minimum points, we have gt∗ (x∗ ) = gt∗ (y), that is, the length of a minimum inner spanning tree for P (t∗ ; x∗ ) equals that for P (t∗ ; y). Hence M (t∗ ; x∗ ) ⊆ M (t∗ ; y). However, x∗ is a critical point. Thus M (t∗ ; x∗ ) = M (t∗ ; y). 4, y is an interior point of Xt∗ . This means that there exists a neighborhood of l ∗ such that for l in it, the Steiner tree of topology t∗ exists for the point set P (l).
This means that there exists a neighborhood of l ∗ such that for l in it, the Steiner tree of topology t∗ exists for the point set P (l). Hence there exists an l ∈ (lM , l∗ ) such that P (l) = P (t∗ ; z) for some vector z (not necessarily in Xt∗ but du˙hu˙book December 27, 2007 18:43 WSPC/Book Trim Size for 9in x 6in du˙hu˙book 29 Minimax Approach and Steiner Ratio h z ∈ Xt∗ for some h > 0). Since l(m(t∗ ; x)) is continuous with respect to x, there is a neighborhood of y such that for every point y in the neighborhood, M (t∗ ; y ) ⊆ M (t∗ ; y).
A bicriteria stochastic programming model for capacity expansion in telecommunications by Riis M., Lodahl J.