internet traffic engineering for partially uncertain demands

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)


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


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


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


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)


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]


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


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


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


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

,


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


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%)


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 (

%)


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


15

Thank You !


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.


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


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

internet traffic engineering for partially uncertain demands

Education