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Unformatted text preview: e explore the trade-oﬀ between
total utility and total power usage in a wireless network in which the link transmit powers can
be adjusted. The network consists of a set of nodes and a set of links over which data can be
transmitted. There are n routes, each corresponding to a sequence of links from a source to a
destination node. Route j has a data ﬂow rate fj ∈ R+ (in units of bits/sec, say). The total utility
(which we want to maximize) is
n U j ( fj ) , U (f ) =
j =1 where Uj : R → R are concave increasing functions.
143 The network topology is speciﬁed by the routing matrix R ∈ Rm×n , deﬁned as
Rij = 1 route j passes over link i
0 otherwise. The total traﬃc on a link is the sum of the ﬂows that pass over the link. The traﬃc (vector) is thus
t = Rf ∈ Rm . The traﬃc on each link cannot exceed the capacity of the link, i.e., t c, where
c ∈ Rm is the vector of link capacities.
+ The link capacities, in turn, are functions of the link transmit powers, given by p ∈ Rm , which
cannot exceed given limits, i.e., p pmax . These are related by
ci = αi log(...
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- Fall '13
- The Aeneid