Greening Backbone
Networks
Emaad Ahmed Manzoor
CSE691: Green IT & Smart Grid
March 2016
Will Fisher, Martin Suchara, Jennifer Rexford
First Workshop on Green Networking, SIGCOMM ’10
Not power-proportional
https://farm4.staticflickr.com/3572/3567497578_aa942f35dd_b.jpg
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Power-proportional Router: Architectural Design
and Experimental Evaluation, Bin Liu et. al. IWQoS 2014.
Not power-proportional
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Cannot be put to “sleep”*
Not power-proportional
https://farm4.staticflickr.com/3572/3567497578_aa942f35dd_b.jpg
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Cannot be put to “sleep”*
Not power-proportional
*(2010)
https://farm4.staticflickr.com/3572/3567497578_aa942f35dd_b.jpg
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Average link-utilisation
in backbone networks is
30-40%.
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Can we power-down
links (line cards) and
adjust data flow based on
traffic demand?
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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Input
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G(V, E)
s t
w
u
v
c(u,t)
c(w,v)
c(v,t)
c(s,w)
c(s,u)
Topology
Input
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G(V, E)
s t
w
u
v
c(u,t)
c(w,v)
c(v,t)
c(s,w)
c(s,u)
Topology
D
(s1, t1, h2)
(s2, t2, h2)
. . .
Demands
Input
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G(V, E)
s t
w
u
v
c(u,t)
c(w,v)
c(v,t)
c(s,w)
c(s,u)
Topology
D
(s1, t1, h2)
(s2, t2, h2)
. . .
Demands
Cables per link
B
Input
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Output
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s t
w
u
v
c(u,t)
c(w,v)
c(v,t)
c(s,w)
c(s,u)
Flow of demand d on each link
fd(s,u)
fd(s,w)
fd(w,v)
fd(v,t)
fd(u,t)
fd(u, v)
Output
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s t
w
u
v
c(u,t)
c(w,v)
c(v,t)
c(s,w)
c(s,u)
Flow of demand d on each link
fd(s,u)
fd(s,w)
fd(w,v)
fd(v,t)
fd(u,t)
Total flow on link (u,v)
f(u, v) =
X
d
fd(u, v)
fd(u, v)
Output
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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min number of powered cables
s.t. link loads ≤ capacities
flow conservation
carries all traffic demands
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min
s.t. link loads ≤ capacities
flow conservation
carries all traffic demands
X
(u,v)2E
f(u, v)
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min
s.t.
flow conservation
carries all traffic demands
X
(u,v)2E
f(u, v)
X
D
fd(u, v) c(u, v), 8(u, v) 2 E
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min
s.t.
carries all traffic demands
X
(u,v)2E
f(u, v)
X
D
fd(u, v) c(u, v), 8(u, v) 2 E
X
v2V
fd(u, v) =
X
w2V
fd(w, u), 8d, 8u 6= sd, td
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min
s.t.
X
(u,v)2E
f(u, v)
X
D
fd(u, v) c(u, v), 8(u, v) 2 E
X
v2V
fd(sd, v) =
X
w2V
fd(w, td) = hd, 8d
X
v2V
fd(u, v) =
X
w2V
fd(w, u), 8d, 8u 6= sd, td
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min number of powered cables
s.t. link loads ≤ capacities
flow conservation
carries all traffic demands
Models what if
links are
energy
proportional?
• Fractional linear
program
• Bounds on power
savings
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Upper bound on
energy savings
f(u,v) = 6.3 Gbps
(solution of FLP)
c(u,v) = 10 Gbps
(given topology)
B = 10
(given cables per link)
— Round down: 6 Gbps
— Turn off: 4 cables
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Lower bound on
energy savings
f(u,v) = 6.3 Gbps
(solution of FLP)
c(u,v) = 10 Gbps
(given topology)
B = 10
(given cables per link)
— Round up: 7 Gbps
— Turn off: 3 cables
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Unfortunately, the lower
bound solution is feasible
but can be extremely
suboptimal.
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(S, Ti, ✏)
(Bi, Bi+1, ✏)
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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The bundle size B needs
to be explicitly taken into
account.
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min
X
(u,v)2E
nuv
Minimise the sum of the
number of active cables
on each link
f(u, v)
nuv
B
c(u, v), 8(u, v) 2 E
Number of active cables need to
be sufficient for the demand
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min
X
(u,v)2E
nuv
Minimise the sum of the
number of active cables
on each link
f(u, v)
nuv
B
c(u, v), 8(u, v) 2 E
Number of active cables need to
be sufficient for the demand
NP-Complete — D2CIF
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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Fast Greedy Heuristic
1. Solve FLP
- Obtain f(u,v), round up.
2. Find (u,v) with the most unused capacity
- Remove one cable from the link.
- Solve the FLP with the new capacities.
Feasible? Remove a
cable from the link (u,v).
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Fast Greedy Heuristic
1. Solve FLP
- Obtain f(u,v), round up.
2. Find (u,v) with the most unused capacity
- Remove one cable from the link.
- Solve the FLP with the new capacities.
Feasible? Remove a
cable from the link (u,v).
Not feasible? Mark
link (u,v) as final.
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Fast Greedy Heuristic
1. Solve FLP
- Obtain f(u,v), round up.
2. Find (u,v) with the most unused capacity
- Remove one cable from the link.
- Solve the FLP with the new capacities.
Feasible? Remove a
cable from the link (u,v).
Not feasible? Mark
link (u,v) as final.
Repeat from 2, ignoring all final links
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Exhaustive Greedy Heuristic
Remove the cable that
- Retains solution feasibility.
- Minimises the marginal
penalty of each removal.
Marginal penalty
- Increases as excess traffic is
rerouted along longer paths.
- Measures as the FLP objective
difference after cable removal.
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Bi-level Greedy Heuristic
Exhaustive greedy heuristic
with pairs of cables.
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future
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FGH EGH BGH
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Abilene Topology
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54% savings with B = 1
73% savings with B = 3
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Problem formalisation
Naive solution
Integer linear program
Efficient heuristics
Evaluation
Future