bv_cvxbook_extra_exercises

In addition we are given upper limits on some of the

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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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