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Communication Networks E. Mulyana, S. Zhang, U. Killat
1
ITC19 2005 – Beijing – 30.08.2005
Internet Traffic Engineering for Partially Uncertain Demands
Eueung Mulyana, Shu Zhang, Ulrich Killat FSP 4-06 Communication Networks
Hamburg University of Technology (TUHH)
Communication Networks E. Mulyana, S. Zhang, U. Killat
2
Motivation Routing control
Demand uncertainty
Partially uncertain demands:
fixed part predictable or guaranteed traffic
uncertain part variable traffic
Outline Formulation
Calculating link loads
Simulated Annealing (SA)
Computational results
Concluding remarks
Communication Networks E. Mulyana, S. Zhang, U. Killat
3
Weight system
Maximum Utilization
Objective Function
Formulation
} { min max
max
,
,
, ji
ji
ji
c
l
Aji ),(
How to compute link load li,j for our case ?
fixed part trivial
uncertain part „hose“ model
Optimization Result u
f out
uf inu
. . . v
„Hose“ model
Network
Akwwww Ak },,,,,{ ||21
Communication Networks E. Mulyana, S. Zhang, U. Killat
4
Calculating Link Loads Case I : Fixed Demands
20 - 1
2
3
4
)(,vu
f
1 2
20 20
3 4
- 20 20
- 20
-
20
20
20
20
20 20
1
1
1
1
1 2
3 4
uv
uv
jiji ll ,,
40
1 2
3 4
40
40
40
40
Link Loads
Dijkstra, ECMP
Communication Networks E. Mulyana, S. Zhang, U. Killat
5
Calculating Link Loads Case II : Uncertain Demands (1)
uf out
u Network
}{\
out
,
uNv
uvuff
„Outbound“ model
. . . v
1
2
3
4
60
40
60
40
)( out
uf
60 1 2
3 4
60 30
30
90
1 2
3 4
60
80
90
60
70
vu
jiuNv
uu
ji fl,
,}{\
out, max
1
1
1
1
1 2
3 4
u
u
jiji ll ,,
Link Loads [Upperbound values]
vu
ji
,
,Traffic fraction
of flow (u,v) on link (i,j)
Communication Networks E. Mulyana, S. Zhang, U. Killat
6
Calculating Link Loads Case II : Uncertain Demands (2)
uf out
uf in
u
}{\
out
,
uNv
uvuff
}{\
in
,
uNv
uuvff
. . . v
„Hose“ model 90
1 2
3 4
60
80
90
60
70
60
1 2
3 4
90
80
60
90
70
60
1 2
3 4
80
60
70
)max,maxmin(,
,}{\
in
,
,}{\
out,
u
uv
jiuNv
u
u
vu
jiuNv
u
ji ffl
hose
inbound outbound
60
40
60
40
)( in
uf
1
2
3
4
60
40
60
40
)( out
uf
1
1
1
1
1 2
3 4
Link Loads [Upperbound values]
Communication Networks E. Mulyana, S. Zhang, U. Killat
7
Calculating Link Loads Case III : Partially Uncertain Demands
20 - 1
2
3
4
)(,vu
f
1 2
20 20
3 4
- 20 20
- 20
-
20
20
20
20
20 20
60
40
60
40
)( in
uf
1
2
3
4
60
40
60
40
)( out
uf
,maxmin()(,
,}{\
outunc,
u
vu
jiuNv
u
ji fl
uv
vu
ji
vu
ji fl,
,
,
fix, )(
unc,fix,, )()( jijiji lll
40
1 2
3 4
40
40
40
60
1 2
3 4
80
60
70
100
1 2
3 4
120
100
110
uncertain (hose)
fixed
partially uncertain
)max,
,}{\
in
u
uv
jiuNv
uf
Communication Networks E. Mulyana, S. Zhang, U. Killat
8
Representation
Move Operators
Simulated Annealing Approach for Optimization Task (1)
w1
2 1 2 2
21 w
12 w 23 w
24 w
w2 w3 w4
w1
2 1 2 2
w2 w3 w4 w1
2 1 5 2
w2 w3 w4
1 2
3 4
current solution x
.
.
.
)(1 xH
)(2 xH
)(3 xH
neighbours x‘(H3)
Variable Neighbourhood
solution vector
Communication Networks E. Mulyana, S. Zhang, U. Killat
9
Simulated Annealing Approach for Optimization Task (2)
Joint with plain local search (PLS):
concentrate the search around best solution (small ) first before exploiting other regions
speed-up convergence at small number of iterations
SA PLS
otherwise
satisfied are PLS performingfor conditions if
0
1
PLS
0PLS
1PLS
0PLS 1PLS
Communication Networks E. Mulyana, S. Zhang, U. Killat
10
Case Study (1)
3
13
9
14
11
8
10
6
5
74
2
1
12
2.5 Gbps
Network instance
14 nodes; 44 directed-links
Uncertain demands
300 Mbps {10,13}; 200 Mbps {2,6,7,9,11,14};
100 Mbps for the rest u
f out
Fixed demands
random in the inteval [10,150] Mbps
uf in
vuf
,
Communication Networks E. Mulyana, S. Zhang, U. Killat
11
Case Study (2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0
200
400
600
800
1000
1200
1400
Outbound/Inbound Demands
Mb
ps
Node
fixed part uncertain part
Communication Networks E. Mulyana, S. Zhang, U. Killat
12
Results (1): Resource Occupancy
0 5 10 15 20 25 30 35 40 45 0
10
20
30
40
50
60
Capacity occupied (USP case)
Link Number
Occu
pan
cy (
%)
uncertain part fixed part
InvCap (72.65%)
Optimized – MSP (55.97%)
Maximum capacity occupancy
USP: Unique Shortest Path MSP: Multiple Shortest Path
Optimized – USP (56.87%)
Communication Networks E. Mulyana, S. Zhang, U. Killat
13
Results (2): Partially vs. Fully Uncertain Demands
v
vuuufff
,
1out2,out
v
uvuufff
,
1in2,in
)(,
1
vuf
)( in2,
uf)( out2,
uf
)( in
uf)( out
uf
Partially uncertain (56.87%)
Capacity occupancy for the USP case
(max)
Fully uncertain (166.6%)
Occu
pan
cy (
%)
Communication Networks E. Mulyana, S. Zhang, U. Killat
14
Summary and Conclusion
Model for partially uncertain demands:
capturing traffic variation
inaccurate traffic matrix
Optimization framework based on Simulated Annealing
fully deterministic
fully uncertain
partially uncertain
resource efficiency
Communication Networks E. Mulyana, S. Zhang, U. Killat
16
References (Partial List)
(1) Duffield N.G. et. al.„A Flexible Model for Resource Management in Virtual Private Networks“, Proceedings of ACM SIGCOMM, 1998.
(2) Ben-Ameur W., Kerivin H.„Routing of Uncertain Demands“, INFORMS, 2001.
(3) Fortz B., Thorup M. „Optimizing OSPF/IS-IS Weights in a Changing World“, IEEE JSAC, 20(4):756-767, 2002.
(4) Mulyana E., Killat U. „Optimizing IP Networks for Uncertain Demands Using Outbound Traffic Constraints“, Proceedings of 2nd INOC, 2005.
Communication Networks E. Mulyana, S. Zhang, U. Killat
17
Routing Examples and Per-Flow Load Fractions
1
1
1
1
1 2
3 4
Link Weights
1
1
2
1
1 2
3 4
1 2
3 4
2
3 4
1
1
1
1
1
0.5
0.5 0.5
0.5
1 2
3 4
1
1
0.5
0.5
1 2
3 4
1
1
0.5
0.5
1 2
3 4
2
3 4
1
1
1
1
1
1 1
1 2
3 4
1
1
1
1 2
3 4
1
1
1
Communication Networks E. Mulyana, S. Zhang, U. Killat
18
Intra-Domain IP Routing : IGP
(b)(a)
6
11
1
1
1
1
2
21
2
3
5
5
121
3 4
5 6
2
3 4
5 6
1
2
4
6
5
3
1
2 3
4 5
1
Driven by link metrics (weights/costs)
Unique shortest path routing vs. Equal-Cost Multi-Path (ECMP)
ECMP e.g. [1-2-4-6] 50% [1-3-4-6] 25% [1-3-5-6] 25%
Unique shortest path routing: 1 unique path for all node pairs