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link usage as small as possible Interestingly, the experimental comparison in [31] shows that, at least for some probability distribution, it is fundamental to avoid the use of highly loaded links and the use of paths with sub-optimal length Indeed, the worse strategy turns out to be the min hops one, and the min hop min load strategy performs better than the revised one From On-line to Off-line: Precomputed Routes In [6], the deterministic behavior of the network has been also exploited to enhance the performance (in terms of call blocking probability) of the routing strategies In particular, the authors compare a min-cost strategy (similar to those mentioned above) to a static routing, in which the routes are computed off-line in advance The network is modeled as a FSA (see Section 22313) and, for each state (ie, network topology), a set of routes is precomputed.



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Perhaps an advantage of Spearman s rs is that it is a bridge, so to speak, between Pearson s r and the tau correlation because it incorporates properties of both. Like Pearson s r, Spearman s rs uses distances between numbers, and like Kendall tau, the computation of Spearman s rs is based on the order of the variables. The Spearman correlation can be shown to be equivalent to a Pearson correlation applied to ranks. Assuming no ties,





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Clearly, this reduces the communication overhead due to the periodic broadcast operations required to update the link state (ie, the load) information Somewhat surprisingly, this approach also has a better call blocking probability This is mainly due to the fact that, after a network change, the solution provided by the min-cost algorithm is rather unstable, so several calls are rerouted This idea of moving the complexity of routing from an on-line problem to an off-line one is also the basis of [38, 37] There, for each possible demand pair (ie, for each possible communication), k different shortest paths are computed Those paths are then used during the on-line phase, in which the routing algorithm chooses a route between such k candidates Based on this idea, an upper bound on the ISL s capacity is given by the number of such paths containing a link.

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Informally speaking, it is assumed that there is a request for each possible pair of satellites and the goal is to compute the minimum l such that, if every ISL capacity is l, then every request can choose between k different paths of minimal length This problem is formulated by means of a linear programming system In [37] the authors also consider the problem of relating subsequent states of the network, so that rerouting is performed only when necessary More precisely, a routing state will be computed and optimized while keeping some remaining routes of the previous states 22424 Predicting Link Handovers Another approach consists in taking advantage of link handovers to manage the mobility of the network The Probabilistic Routing Protocol Upon a call arrival, a first route through the satellites has to be assigned to the call.

Monotonic convergence of the empirical distribution. Let pn denote the empirical probability mass function correspond ing to X1 , X2 , . . . , Xn i.i.d. p(x), x X. Speci cally, 1 pn (x) = n

Such a route can be chosen based on any criterion, such as minimum number of hops, least congestion, minimum cost, etc The deterministic movement of the satellites allow the prediction of the time frame in which a link handover is to occur Hence, the probabilistic routing protocol (PRP) proposed in [33] tries to establish an arriving communication through a route that has minimum probability to be cut by a link handover For this, it supposes the existence of a probability distribution function (PDF) of the call time duration over a route The protocol applies Dijkstra s algorithm to find the routes The cost of each ISL is set to one, implying that the route will be minimum hop The PDF is used to remove from consideration of Dijkstra s algorithm those ISLs that are likely to hand over during the communication.

It is easy to see that the PRP works for very short calls, since a direct consequence of.

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