BROADNETS 2004 San José, California, USA October 25-29, 2004 p-Cycle Network Design with Hop Limits and Circumference Limits Adil Kodian, Anthony Sack,

BROADNETS 2004San José, California, USA

October 25-29, 2004

pp-Cycle Network Design with Hop -Cycle Network Design with Hop Limits and Circumference LimitsLimits and Circumference Limits

Adil Kodian, Anthony Sack, Wayne D. Grover

Department of Electrical and Computer Engineering

p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover

BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering

Presentation Overview

• What are p-cycles?

• Hop-limited p-cycle design

• Results

• Summary






• Results

• Summary



What Are p -Cycles?• A survivability mechanism for transport networks

Physical network topology – nodes (cities) with spans

(fibers) between them

Working capacity layer – individual demands are routed

between node pairs

Spare capacity layer – p-cycles are built to protect

working capacity on all spans



How Do p -Cycles Protect Against Span Failure?

Sample p-Cycle

loopback

loopback

On-Cycle Failure

Break-in

Break-in

Straddling Span failure






• Results

• Summary



Why use short protection paths ?

• Simplify network design.

• Simplify network operation.

• Increase service availability.



Path Length Constraints in Network Design

• Commonly used techniques to limit path length:

In mesh network design: limit the length of the longest route in the eligible route set Length <= H (Hop Limit)

In p-cycle network design: limit the circumference of the longest cycle in the eligible cycle set Length <= C (Circ. Limit)

Note: C = H +1

Straddling Span - Prot path length =

4

On-cycle Span - Prot path length = 7

Protection path length limit = 4



Motivating Example

Initial Scenario

• All protection path lengths should be 4 hops (or less)

• Working capacities to be protected are as shown

1

1

1 1 1

2

1

12

1

Solution 1 (Hamiltonian p-cycle)

• No hop or circumference limits

• Only 8 units of spare capacity

• But some protection paths are longer than 4 (too long)

1



Solution 3 (Shorter Paths)

• Corresponding hop limit of 4

• Only 18 units of spare capacity

• All protection paths are still adequate (within 4 hop limit)

1 1

1

Motivating Example

Solution 2 (Smaller Cycles)

• Circumference limit of 5

• 20 units of spare capacity

• No protection paths are too long (all within 4 hop limit)

(a)

1

1

1 1 1

2

1

12

11

2

1



Hop-limited p -Cycle Design

• New parameters defined:

,Lpix

,Rpix



• Minimize: Total modular capacity cost (spare + working)

• Subject to (along with other standard design constraints):

Highlights of ILP Design Model

,L ,L ,R ,Rp p p pi i i i i

p

x n x n w

P

Place enough cycles, considering each side separately, to protect all working units.

,Lp pin n,Rp p

in n

Number of copies of p-cycle p must be the maximum number required by any one failure, on either the L or R side of the p-cycle.






• Results

• Summary



Test Networks

(a) (b)

13n23s (501 cycles)

15n26s1 (871 cycles)

12n19s (127 cycles)

NSFNET (139 cycles)



Results

5000

10000

15000

20000

25000

30000

3 4 5 6 7 8 9 10 11 12 U

Hop Limit

Dis

tan

ce-w

eig

hte

d C

apac

ity

Co

st

15n26s1 p-Cycles (Hop-limited model)

15n26s1 Mesh

13n23s p-Cycles (Hop-limited model)

13n23s Mesh


12n19s Mesh

NSFNET p-Cycles (Hop-limited model)

NSFNET Mesh

5000

10000

15000

20000

25000

30000

3 4 5 6 7 8 9 10 11 12 U

Hop Limit

Dis

tan

ce-w

eig

hte

d C

apac

ity

Co

st


15n26s1 Mesh


13n23s Mesh


12n19s Mesh


NSFNET Mesh

• Threshold hop limit effect



Results

5000

10000

15000

20000

25000

30000

3 4 5 6 7 8 9 10 11 12 U

Hop Limit

Dis

tan

ce-w

eig

hte

d C

apac

ity

Co

st


15n26s1 Mesh


13n23s Mesh


12n19s Mesh


NSFNET Mesh

5000

10000

15000

20000

25000

30000

3 4 5 6 7 8 9 10 11 12 U

Hop Limit

Dis

tan

ce-w

eig

hte

d C

apac

ity

Co

st


15n26s1 Mesh


13n23s Mesh


12n19s Mesh


NSFNET Mesh

• Exact comparison of mesh and p-cycle network design



0

500

1000

1500

2000

2500

3000

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Hop Limits

Nu

mb

er o

f C

han

nel

s

Span-Restorable Mesh

C-Limited

H-Limited

Results

• Non-joint hop and circumference limited designs

• p-Cycle threshold occurs about 3 or 4 hops higher than for the corresponding mesh

•C and H limited designs perform equally well



Results

• Actual path lengths in hop and circumference limited designs

0

50

100

150

200

250

300

350

400

450

500

2 3 4 5 6

Hop Length

Nu

mb

er o

f P

rote

ctio

n P

ath

s

Circumference Limited Path Length Limited

•Relatively lower number of long paths



Results

• Bi-criteria objective function – reduces average path length

0

200

400

600

800

1000

1200

1400

1600

2 3 4 5 6

Hop Length

Num

ber of P

rote

ctio

n P

ath

s

Circumference Limited Path Length Limited Path Length Limited w / Bi-Criteria Objective

•Engineered for lower number of long paths






• Results

• Summary



Summary

• Circumference limiting is an accurate and simple surrogate for true hop-limited p-cycle designs.

• p-Cycles exhibit a threshold hop limit effect (like span restorable mesh) – but the threshold hop limit is higher than the corresponding mesh design.

• Above the threshold, p-cycle and mesh networks are equally efficient.

• Below the threshold, p-cycle capacity cost rises faster than in the corresponding mesh design.

Documents

BROADNETS 2004 San José, California, USA October 25-29, 2004 p-Cycle Network Design with Hop Limits and Circumference Limits Adil Kodian, Anthony Sack,