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16.4 MOBILITY MODEL AND TRAFFIC PARAMETERS Although several mobility models exist for LEO satellites [7,8], it is customary to assume a one-dimensional mobility model where the MHs move in straight lines and at a constant speed, essentially the same as the orbital speed of the satellite [7]. Since the speed of users (even in fast moving vehicles) is negligible compared to the satellite s speed and the Earth s rotation, MH speed can be ignored. For example, users in fast vehicles move with a maximum speed of 80 m/s, while a LEO satellite s ground track speed is more than 5700 m/s and the speed of the rotation of the Earth at the equatorial level is nearly 460 m/s. For simplicity, all the spotbeams (also referred to as cells) are identical in shape and size. Although each spotbeam is, in reality, circular, the use of squares to approximate spotbeams is justi able. Some authors use regular hexagons instead of squares. We assume an orbital speed of 26,000 km/h. The width of a cell is taken to be 425 km. Thus, the time ts it takes an end-user to cross a cell is, roughly, 65 s. Referring to Figure 16.2, the MH remains in the cell where the



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2 One issue in the TA was the approval of our work programme It was very dif cult for SMG to comply with the proce2 TDoc SMG 31/94, TDoc SMG 179/94 and TDoc SMG 508/94, chairman s reports to SMG describe typical issues discussed at Technical Assembly meetings..

In a patent (Grimes, 1989) it is suggested that the lowest-order mode may be produced by a dipole, the next mode may be produced by two parallel dipoles fed 180 out of phase, etc, and similarly for the loops (see Fig 187) Of course, what happens is that the mutual coupling of three closely spaced dipoles is very strong, with the result that all the dipoles revert to a single.





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of sets of elementary events, as we promised in Section 2410 Computing a marginal distribution can be seen as computing the degree of possibility of specific sets of elementary events, namely those that can be defined using a subset of all attributes (cf Definition 327 and its extension to general possibility measures) In a multidimensional domain taking the maximum to compute the degree of possibility of sets of elementary events is useful, because it serves the task to identify attribute by attribute the values of the tuple or tuples of the joint domain that have the highest degree of possibility.

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where cimax (j) is the value of attribute C for which pij (or equivalently pi|j ) i. i. is maximal given that attribute A has the value aj . This measure is based on the same idea as the relief measure, namely that for a reliable identification of the value of a (class) attribute C it is best if each value of a (descriptive) attribute A uniquely indicates a value of C. Consequently, the conditional probability pi|j of the most probable value ci of C given that the attribute A has the value aj should be as large as possible. However, in order to avoid giving false merits to an attribute A for a value ci with a high prior probability, these probabilities are considered relative to the prior probability pi. . 2 Measure In Section 7.1.2 we interpreted Shannon information gain as a measure for the difference of the actual joint distribution and a hypothetical independent distribution of two attributes C and A. The 2 measure, which is well known

Note also that this property of maximum projections, which may appear as an advantage at first sight, can also turn out to be a disadvantage, namely in the case where we are not interested in a tuple over all unobserved attributes that has the highest degree of possibility The reason is that as indicated above we cannot get rid of the implicitly fixed values of the attributes that were projected out If we want to neglect an attribute entirely, we have to modify the universe of discourse and then compute the possibility distribution and its decomposition on this modified universe The probabilistic setting is, in this respect, more flexible.

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Whereas in possibilistic networks, we can only compute the mode (the tuple with the highest degree of possibility), probabilistic networks allow us to choose: we may compute the conditional probabilities of the values of individual attributes, or we may compute the mode of the probability distribution That this can be achieved with an approach that is completely analogous to the procedure that yields conditional probabilities, can be seen by considering the simple geometrical objects example, especially the computations carried out on pages 79ff Instead of P(B = b | A = aobs ) or P(C = c | A = aobs ), we now compute b dom(B) : max max.

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