bv_cvxbook_extra_exercises

the n 1 reliability constraint requires that for

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Unformatted text preview: ned as Rij = 1 flow j passes through link i 0 otherwise. Thus, the vector of link traffic, t ∈ Rm , is given by t = Rf . The link capacity constraint can be expressed as Rf c. The (logarithmic) network utility is defined as U (f ) = n=1 log fj . j The (average queuing) delay on link i is given by di = 1 c i − ti 129 (multiplied by a constant, that doesn’t matter to us). We take di = ∞ for ti = ci . The delay or latency for flow j , denoted lj , is the sum of the link delays over all links that flow j passes through. We define the maximum flow latency as L = max{l1 , . . . , ln }. We are given R and c; we are to choose f . (a) How would you find the flow rates that maximize the utility U , ignoring flow latency? (In particular, we allow L = ∞.) We’ll refer to this maximum achievable utility as U max . (b) How would you find the flow rates that minimize the maximum flow latency L, ignoring utility? (In particular, we allow U = −∞.) We’ll refer to this minimum achievable latency as Lmin . (c) Expl...
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