pp-Cycle Network Design: from -Cycle Network Design: from Fewest in Number to Smallest in SizeFewest in Number to Smallest in Size

Diane P. OnguetouDiane P. Onguetou and Wayne D. GroverWayne D. Grover

TRLabs and ECE, University of Alberta TRLabs and ECE, University of Alberta

donguetou@trlabs.ca, grover@trlabs.ca

October 8th, 2007

What is a What is a pp-Cycle?-Cycle?

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

on-c

ycle

spa

ns

straddling spans

pp-Cycle Operating -Cycle Operating PrinciplePrinciple

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

Loopback in the event of on-cycle span failure

Break-in handling a straddling span failure

Hamiltonian: One Type of Hamiltonian: One Type of pp--Cycle Cycle

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

Visits all nodes once,

Not necessarily crosses all spans,

Single structure can be enough for full single failure restorability.

Hamiltonian Hamiltonian pp-Cycle -Cycle Network DesignNetwork Design

Having only a single structure may be Having only a single structure may be attractive from the network management view:attractive from the network management view:

HOWEVERHOWEVER Some network graphs are not Hamiltonians.

Even if the graph is Hamiltonian, this is only one option for p-cycle network design.

The most capacity-efficient The most capacity-efficient pp-cycle network -cycle network design is not obtained by using a Hamiltoniandesign is not obtained by using a Hamiltonian.

Hamiltonians may be very long structures.

Recall the “3 Little Recall the “3 Little Bears”Bears”

"This porridge is too hot!" "This porridge is too hot!"

"This porridge is too cold," "This porridge is too cold,"

"Ahhh, this porridge is just right,""Ahhh, this porridge is just right,"

Our aim: show how with p-cycle networks you can have just what you want….Fewest cycles, or least capacity, or anything in between,,,,Whatever is “just right” for Goldilocks Networks or your network.

This clarifies a misunderstanding of late in part of the field.

However, fewest and smallest structures at minimum capacity are some interesting new design goals suggested by the focus on number of structures and their size-circumference as well.

number

of

structure

s

spare capacity

size of structures

OutlinesOutlines

1. Motivations

2.2. Conventional Conventional pp-Cycle Network -Cycle Network DesignDesign

3. Design with an Emphasis on Fewest Number of Structures

4. Controlling the Size of p-Cycles

5. Concluding Discussion

The COST239 NetworkThe COST239 Network

11 nodes and 26 spans, average nodal degree of 4.72.

3531 distinct eligible p-cycles of which 394 are Hamiltonians.

55 demand-pairs uniformly distributed on [1…20].

Shortest distance based routing.

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

Working Capacities to Be Working Capacities to Be ProtectedProtected

MIL

VIEZURPAR

LUXBRU

LONAMS

COP

BER

PRA

1 4 7

0

2613

11

13

13 2

17

18

11

9

08

8

18

22

826

11

5

5

24

3MIL

VIEZURPAR

LUXBRU

LONAMS

COP

BER

PRA

3

255

ObjectiveObjective:: Minimize spare capacity cost while ensuring full restorability against single span failures.

Basic Minimum Capacity Basic Minimum Capacity DesignDesign

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

MIL

VIEZUR

PAR

LUXBRU

LONAMS

COP

BER

PRA

55% of redundancy.

9 distinct structures of which 4 are Hamiltonians.

16 unit-channel copies.

2 copies

2 copies

3 copies

1 copy 2 copies

1 copy

1 copy 1 copy 3 copies

Comparison with Comparison with Hamiltonian SolutionsHamiltonian Solutions

Eligible Cycles

All cycles (3531)

Hamiltonian cycles

(394)

One single Cycle

The shortest Hamiltonian

Redundancy

55% 58% 66% 90%

Distinct Structures

9 6 1 1

OutlineOutline

1. Motivations

2. Conventional p-Cycle Network Design

3.3. Design with an Emphasis on Design with an Emphasis on Fewest Number of StructuresFewest Number of Structures

4. Controlling the Size of p-Cycles

5. Concluding Discussion

Fewest Structures…Fewest Structures…A Different A Different Goal in DesignGoal in Design

Another property of the conventional p-cycle ILP is the fact that it might have multiple solutions for the same capacity cost.

Therefore, using a bi-criterion objective in the ILP design model could help to bias the model towards always using the fewest number of cycle structures without capacity penalty.

Doing so in the COST239 network, we found that there is a solution involving 8 structures (instead of 9) for zero capacity penalty.

Set a Fixed Number of Set a Fixed Number of StructuresStructures

It is also possible to force the ILP to design under a given maximum number of structures.

Of course this involves capacity penalty, but apparently this is not so significant.

So it might be more useful to design with fewest structures and no significant increase in spare capacity.

e.g. +1%5 structures,

+5%3 structures,

(versus 8 or 9).

48%

50%

52%

54%

56%

58%

60%

62%

64%

66%

68%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Maximum Number of Structures Allowed

Redu

ndan

cy

RR22 Restorability vs. Fewest Restorability vs. Fewest StructuresStructures

However, be certain that playing with the number of structures matches all your goals.

For instance, selecting fewer structures somewhat harms the robustness under dual failure conditions.

72%

74%

76%

78%

80%

82%

84%

86%

88%

90%

1 2 3 4 5 6 7 8 9 10 11 12 14 15

Number of Structures

R2 R

esto

rabi

lity

OutlinesOutlines

1. Motivations

2. Conventional p-Cycle Network Design

3. Design with an Emphasis on Fewest Number of Structures

4.4. Controlling the Size of Controlling the Size of pp-Cycles-Cycles

5. Concluding Discussion

Impacts on Capacity Impacts on Capacity RequirementsRequirements

0%

20%

40%

60%

80%

100%

120%

2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000

Maximum Size of p-Cycles (km)

Red

unda

ncy

Well known that limiting the circumference-size of eligible cycles

Not feasible for veryvery small limits,

Requires some additional capacities (especially for small limits),

Decreasing function in general,

and Steady state for large limits.

Already discussed by D. Schupke, C. G. Gruber and A. Autenrieth in ICC’02.

Fewest Structures vs. Fewest Structures vs. Smallest SizesSmallest Sizes

0

2

4

6

8

10

12

14

16

2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000

Maximum Size of p-Cycles (km)

Few

est S

truc

ture

s w

ithou

t Pen

alty

More structures tend to be required when p-cycles are constrained to the smallest sizes.

However, the plot fluctuates between successive values of fewest structures.

For very large maximums, the ILP model keeps the optimal solution and thus, the same number of fewest p-cycle structures.

RR22 Restorability vs. Restorability vs. Smallest CyclesSmallest Cycles

65%

70%

75%

80%

85%

90%

2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000

Maximum Circumference of p-Cycles (km)

R2

Res

tora

bilit

y

As the design is forced to use smaller cycles, the R2 benefits significantly

In fact, as a side-effect of their being more protection structures over which dual failures are in effect dispersed as parts of single failures which are less likely to affect the same cycle.

OutlinesOutlines

1. Motivations

2. Conventional p-Cycle Network Design

3. Design with an Emphasis on Fewest Number of Structures

4. Controlling the Size of p-Cycles

5.5. Concluding DiscussionConcluding Discussion

ConclusionConclusion

Hamiltonian Solutions vs. Conventional p-Cycle Network Design. -Clarifies the misunderstanding in some papers.

Since using a single shortest Hamiltonian cycle is attractive from a management view, study of designs with an Emphasis on Number of Structures.

Small-circumference cycles might be desired to eliminate the need of signal regeneration en-route: controlling the size of p-cycles in the design

Tradeoff between capacity requirements, number of structures and circumference-size of p-cycles.

Thank You!!!Thank You!!!