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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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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