Wayne D. Grover University of Alberta, Dept. of Electrical & Computer Engineering

Sigma Xi Guest Lecture February 27, 2002Sigma Xi Guest Lecture February 27, 2002

Survivable Networks: Survivable Networks: Protecting the Internet and phones from Protecting the Internet and phones from

“backhoe-fades” and other hazards“backhoe-fades” and other hazards

Wayne D. Grover

University of Alberta, Dept. of Electrical & Computer Engineering

TRLabs, Network Systems Group

Sigma Xi Guest Lecture “Survivable Networks” W.D. Grover, Feb. 27, 2002 2

Outline (selected topics)

• Background– Fiber Optics, DWDM, – Multiplexing & Concept of a Transport Network – Goals and Impacts of Protection / Restoration times

• Rings– types– multi-ring network design

• Span-restorable mesh– concept, self-organizing approach– capacity design

• Path-restorable networks

• p-cycles

• Some Current Research


US Circuit Switched Voice and Internet Traffic

CAGR 1996-2005

Internet 95.8%

Voice over IP 30%

Data Traffic

30%Circuit Switched 12.1%

Tera

byte

s /

day

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

Source: Renaissance Analysis via Marconi PLC 2001


Fiber Optics and WDM:

Wavelength (nm)

1600 1700140013001200 1500

Atte

nuat

ion

(dB

/km

)

0.1

0.2

0.3

0.4

0.5

0.6

1310nm 1550nm


Dense WDM: ITU Channel Spacing

1600 1700140013001200 1500

Atte

nuat

ion

(dB

/km

)

Wavelength (nm)

0.1

0.2

0.3

0.4

0.5

0.6

15

25

15

30

15

35

15

40

15

45

15

50

15

55

15

60

15

65

ITU Channel Spacing

ITU Channel Spacing

And each wavelength can carry ~ OC-192 (10 Gb/s)


How important is one little fiber?

If 64Kb/s = 1 lane

Then Based on Current Technology, a singleFiber would = 25 Million Lanes,

or a Highway that was 60,000 Miles Wide

Then Based on Current Technology, a singleFiber would = 25 Million Lanes,

or a Highway that was 60,000 Miles Wide

Adapted from Marconi OctoBrief 2001



British Telecom



The Level(3) N. American Network


TORINO

GENOVA

ALESSANDRIA

PISA

MILANOBRESCIA

SAVONA

BOLOGNA

VERONA

VICENZA

VENEZIA

FIRENZEANCONA

PESCARA

PIACENZA

MILANO2

PERUGIA

L’AQUILA

ROMA

ROMA2

NAPOLI SALERNO

CATANZARO

POTENZA

BARI

TARANTO

CAGLIARI

SASSARI

FOGGIA

PALERMOMESSINA

REGGIO C.

32-node Italian backbone transport

network

some real network topologies


Belgiannational transport

network

(Belga 39 - 39 nodes, 59 spans)



“COST 239” European Communityproject model

( 19 nodes, 40 spans)



“MCI” North Americancontinental backbone

(disguisedtopology only)

0

1

2

345

6

7

8

9

10

11

12

13

14

15

16

17

18

19

2021

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

5152



So everything is fine until....

“ Universal Cable Locator “ !!


News Reports

• Massive fiber cuts interrupt Net traffic– "Let me tell you, it really hurts right now," said AboveNet's

chief technology officer. "We were given a 1 hour estimate for this problem to be corrected."

• SEA-ME-WE3 cable cut again

– The cable was damaged by sand-mining operations in Indonesian territorial waters about 50 kilometers south of Singapore. International traffic from Australia was seriously affected.

• Massive Fiber Cut Pauses East-West Traffic– A fiber-optic cable cut in Ohio interrupted all forms of traffic

across the United States for nearly 12 hours Wednesday has been repaired. ... four OC-192 lines that were accidentally severed by a gas company employee digging with a backhoe.


Service Impact of failure duration

0.01 0.1 1 10 100 1K

Ser

vice

Im

pac

t S

ever

ity

Time (sec)10K

50 - 150 ms 100s of ms 10sec to mins 15 min to 30 min

Severe Business Impact:

Regulatory reporting

Application timeout, Business Impact

TCP Session timeout, X25 disconnect

TCP Backoff, unfairness, User terminates session,

All voice calls lost Business Impact

TCP re-transmit, minor delays, Some voice calls dropped,

Video degradation

No impact, TCP recovers,

Reframe

No impact, TCP recovers, 5%

Voice disconnect

2 sec : all circuit-switched connections dropped Target range

Impact (Log scale)


Concept of a “transport network”

End-users

Service layer

Logical layer

Physical layersystem

geographical

di,j = 76

M U L T I P L E X

Telephony: 500 DS1s

ATM: 5 STS3c

Video: 8 DS3s

Private networks: 100 DS1

Frame-relay services: 36 DS1

SITE i traffic sources to: SITE j

SERVICES

TRANSPORT

Bulk equivalent= 76 STS-1s

(18)

(30)

(15)

(8)

(5)

Internet: 5 STS3c

Sigma Xi Guest Lecture “Survivable Networks” W.D. Grover, Feb. 27, 2002

Network Layers

Logical Trunk Group of n x DS1

OCn

Switch

DCS

New YorkSan Francisco

Service Layer

Transport Layer

n x DS3

Switch


Concept of a transport network: one physical network - billions of logical network possibilities…through cross-connects

A

BC

D

K

ZA

BC

D

K

ZA

BC

D

K

Z


Optical cross-connect

Optical transport system(1.55 m)

Optical transport system(1.55 m)

FibersIn

FibersOut

-Mux

Add ports Drop ports

...

...

...

...

...

...

...

...

...

...

Transparency= node-bypass

Optical-layerCross-connect

(Optical orElectronic

Fabric)


Chip size: 1 cm x 1 cmChip size: 1 cm x 1 cm

Source: L-Y. Lin (AT&T)Optical Layer Switching

An 8x8 Switch


Each layer has a native form of “demand units” that are aggregated into capacity units of the next lower layer

End-users

Service layer

Logical layer

Physical layersystem

geographical

Erlangs, packets, private lines, ATM VCs

#s of: DS-0, DS-1, VPs, STS-n(PL), STSn(IP)

#s of: OC-48, OC-192, wavelengths

#s of fibers, wavelength regens, add-drop

#s of cables, ducts, transponders, spectral allocations

“the transportnetwork”


Some basic approaches to network survivability …

• (APS systems)– 1+1– 1:1– 1:N

• -> rings – UPSR: unidirectional path

switched rings– BLSR: bi-directional line-

switched rings

• -> mesh– span - restorable– path - restorable

• (shared backup path protection)

• -> p-cycles

• (ring-mesh hybrids)– based on access / core

principles– based on forcer clipping

principle

Introduction to ring types, Introduction to ring types, sizing and loadingsizing and loading


Unidirectional Path-switched Ring ...

Unidirectional - because in normal operation all working demand flows in one direction only. i.e., A sends to B clockwise,

B also sends to A clockwise

Path-switched - because in restoration each receiver selects an alternate end-to-end path through ring, regardless of whereactual break occurred.

Two main types of “survivable ring”.... UPSR


Protection fibre

Working fibre 1

2

3

4

5

Tail-end Switch

UPSR Animation...


A

D

E B

C

A -> B

B -> A

UPSR (OPPR) ...line capacity requirement

•Consider a bi-directional demand quantity between nodes A, B: dA,B.- A to B may go on the short route- then B to A must go around the longer route

•Thus, every (bi-directional) demand paircircumnavigates the entire ring.

•Hence in any cross section of the ring,we would find one unidirectional instanceof every demand flow between nodes of the ring.

•Therefore, the line capacity of the UPSRmust be:

UPSR iji j

c d

“ The UPSR must have a line rate (capacity) greater (or equal to)the sum of all the (bi-directional)demand quantities between nodes of the ring. “


Bi-directional Line-switched Ring...Principle of operation (“4-fibre” BLSR illustrated)

(a) Normal Operation (before failure) (b) Protection Operation (after failure)

Cable cut

Loop Back

Bi-directional - because in normal operation working demand flows travel in opposite directions over the sameroute through the ring

Line-switched - because in restoration the compositeoptical line transmission signal is switched to the other direction around the ring (on the other fibre pair)specifically around the failed section.

Two main types of “survivable ring”.... BLSR


Protection fibres

Working fibres

Loop-back

Loop-back

1

2

34

5

(4 fibre) BLSR Animation...


BLSR …(OPSR) line capacity requirement

• both directions of a bi-directional demand can follow the short (or long) route between nodes

• “Bandwidth reuse”

• The line capacity of the BLSR must be:

• Planning issues / inefficiencies:

- better than UPSR for non-hubbed

- capacity dependence on demand pattern

- “stranded capacity”

- span exhaust

A

D

E B

C

A -> B

B -> A

max k kBLSR ij cw ij ccw

i jk

c d d

“ The BLSR must have a line rate (capacity) greater (or equal to)the largest sum of demands routedover any one span of the ring. “


• From preceding it is evident that BLSR demand-serving ability depends in general on the demand pattern.

• Some of the recognized tendencies in real demand patterns are:

HubDemand

Node-to-Adjacent Node Double HubSingle HubUniform

or “mesh”

ideal case for BLSRperfect bw re-use

BLSR much moreefficient than UPSR

no optimization required

this is thegeneral tendency in inter-city backbone

network

optimization of ring loading

this is a fairly exact model for access ring applications

BLSR efficiency = UPSR

same basic “access” demand pattern but dual hubs employed

for access survivability

Effect of some demand patterns on BLSR


0%

100%

200%

300%

400%

500%

600%

2 3 4 5 6 7 8 9 10

no. of nodes

rela

tive

cap

acity

Uniform

Single and double hub

0%

100%

200%

300%

400%

500%

600%

2 3 4 5 6 7 8 9 10

no. of nodes

rela

tive

cap

acity

Uniform

Single and double hub

with perfect bw re-useBLSR gets proportionallybetter as ring size increases

with perfect hubbing demand patterns, BLSR never has any advantage over UPSR

in this range optimized BLSR loading (and ring selection)can give significant benefitsover UPSR

To

tal d

em

an

d s

erv

ing

ca

pa

bili

ty

Effectiveness of BLSR relative to UPSR depends on demand pattern


1. Ring “Sizing”

- CONTEXT: A number of demand pairs are to be served by a BLSR

- QUESTION IS: What is the minimum line rate BLSR required?

demands that must be served

Required BLSRline capcity

• line rate = f (demands, routing in ring)

Q. What is it that has to be optimallydecided to minimize the required

line rate ? i.e. (What do we have control over here?)

A. for each demand: cw, or ccw ?

BLSR related optimization problems


2. Ring “Loading”

- CONTEXT: A number of demand pairs are to be served, but not necessarily all in same ring.

i.e., there is a “pool” of outstanding demands to consider for selection into a given ring.

- QUESTION IS: What is the maximum number of these demands that a BLSR with given capacity

can serve?

or... (alternate goal)

Which set of demands (and routings) achieves greatest utilization of ring capacity?

pool of demandsneeding to be served ? which demands

to pick ?

fixed ringcapacity

BLSR related optimization problems


Multi-Ring Network Design Problem

Design MethodDesign Method

Given• Network topology• Demand pattern• Ring types• Cost model

Min-cost Design• Ring Systems

Type OC-n size Topological layout Glass-through locations

• Routing Ring assignment Inter-ring transit locationsSubject to:

• All demands served• Capacity constraints• Max. ADMs per ring• Inter-ring transit locations• Partial add/drop constraints• Matched-nodes requirements, etc.


• Upper bound on number of ring candidates for each graph cycle:

Every combination of 2, 3, 4....up to N nodes defines a prospective collectionof active ADM nodes that could be grouped together to define one ring.

2

2 12

NN

i

NQ N

• Upper bound on the number of different multi-ring designs that exist:

Every combination of 1, 2, 3, 4....up to some pre-determined maximumnumber of rings can be considered as a multi-ring design solution..

1

1

N

i

Q

i

and ... also multiply by the number of “ring technologies”

being considered.

On the complexity of multi-ring design


0

10

20

30

40

50

60

70

3 4 5 6 7 8 9 10 11 12 13 14 15 16

No. of Nodes

No

. o

f P

oss

ible

Des

ign

s

10

10

10

10

10

10

10

10

illustration: a 10 node network: 1013 possible rings, 1021 possible multi-ring networks

(over 100 million years to evaluate all designs at 10 6 design evaluations / sec.) !

Question: How big is ?


Concept (each follows in more detail):

• graph coverage:

• Balance

• Capture

• Span elimination

• Dual-ring interconnect

• transit sites

•glass-throughs

....a set of rings that covers every edge of the graph. This is one class of ring network.

....in a BLSR, how well are the wi quantities “balanced” ? (sincethe largest of them dictates the protection capacity).

....to what extent does a given ring tend to serve demands that both originate and terminate in the same ring.

....a multi-ring design may not “cover” all graph edges, if the working demands can take non-shortest path routes.

....for the highest service availability, some demands may employ geographically redundant duplicate inter-ring transfers

....not all nodes may be sites where demands can switch rings.

....each ring needs ADMs where demands add / drop, but not elsewhere ( ~> Express rings etc.).

Concepts and principles in multi-ring design


• a set of rings that uses or overlies all edges of the physical facilities graph is called a “ring cover”.

• “Coverage-based” design is a special (simpler) case of multi-ring design.

a three ring “cover” a single ring design that may also serve all

demands

example

“span eliminations”

“Graph coverage” and concept of span elimination


1A

2A

3A

4A

(primary)

(secondary)

r1 r

2

C3

C4

C1

C2

C5

the primary gateway node has a 1+1 receive

selection setup here.

protected byBLSR line-loopback

reaction in r1

protected byBLSR line-loopback

reaction in r2

protected by1+1 APS inter-ring

setup

Concept of dual-ring interconnect (DRI)

“drop-and-continue” method for BLSRs (also called Matched Nodes arrangement)


• RCG is a transformation of the graph that represents the opportunities to transition from ring to ring.

• example: with ring-set given, r1 is connected to r2 through only one node.

• For DRI routing, only the RCG edges with 2 or more parallel arcs are available for routing

n1

n3

n6

n2

n5

n7

n4

r1

r2

r3 r4n7

n3 n4

n5

n1

n1

n3 n4

r1

n3 n5

n7

n4

r4

n6 n7

r3

n1 n2

n5

r2

(a) Network graph (b) Ring design

(c) Ring connectivity graph

Ring Connectivity Graph (RCG) for routing through ring networks


•SCIP = “span coverage IP” *

•Fixed charge and routing model

•Modular aggregating routing *

•Iterated greedy ring placement *

•Eulerian decomposition

•demand re-packing *

•Hierarchical Rings

•Tabu Search *

* = techniques used in combination in RingBuilder™

Some Mathematical Tools and Approaches to multi-ring network design


RingBuilder .... Main User Interface


RingBuilder .... “Advisor” Mode


State of the art and Research Directions in Multi-Ring Network Design

SolutionQuality

Model Accuracy

Eulerian Ring Covers(Gardner et al., ‘94).

Ring Coverage IP(Kennington, ‘97).

RingBuilder™ (Slevinsky,Grover, ‘93)

Net-Solver (Gardner et al., ‘95)

Simulated Annealing(Roberts, ‘94).

Hierarchical Rings (Shi,Fonseka, ‘96).

Strategic Options (Wasem,Wu ‘91)

Researc

h Goals

RingBuilder™ (Slevinsky,Grover, ‘95)

Capacitated Multi-technology Multi-period • Probabilistic• Topology

Tabu Search (Morley,Grover, ‘01)

Mesh-restorable NetworkMesh-restorable NetworkDesignDesign


The concept and vision of distributed mesh restoration

• on-line simulation of “Selfhealing network” Tellium Corp.

Key attributes:

•sharing of spare capacity over failure scenarios

•completely adaptive to current network state (network is the database)

•real time ( << 1 second)

•assurances of 100% restorability with theoretical minimum of spare capacity

•self-monitoring

•no central control (except for oversight)

•no global view databases of network state required•no conventional inter-nodal signalling protocols; “self-organizing”


SHN Protocol Overview

• Node states:– Pre-failure state– Sender state -----------> multi-index “forward flooding”– Chooser state ----------> initiates reverse linking / index– Tandem node state ---> forward flood competition– ---> reverse linking, cross-connection

• Key concept of a “statelet”– not inter-processor messaging– fixed fields, channel associated– space / location encodes problem information

The SHN protocol is an event-driven finite state machine (FSM)


SHN Tandem Nodes Rules

1) Keep list of ports where precursor statelets are presently found and sort statelets by:

– increasing repeat count– increasing number of the port where they appear

2) Replace precursors by better ones when better ones appear

3) Try as much as possible to re-broadcast statelets to all other spans

3a) When full re-broadcast is not possible, consider statelets in order of repeat count starting with the lowest values.

4) When complement statelet is received it is copied to the port of the precursor, all re-broadcast of forward flooding statelets for the corresponding index is stopped and a cross-connection is made

• After any of these events the rebroadcast pattern is revised to follow rule 3


Self-Organizing Networks: other applications

• The basic mechanism (search and formation of paths), also referred to as “Capacity scavenging” used for SHN can be adapted for other tasks:– Automated service paths provisioning (“broad-band dial-up”)– Network Audit (advance detection of restorability limitations and/or

locations where capacity will soon be exhausted)– Improved restorability to complete node failures

• For more details, see:[1] W. Grover, “Self-organizing broad-band transport networks,”

Proceedings of the IEEE, vol. 85, no. 10, October 1997.


Basics of Mesh-restorable networks : SHN Protocol

(28 nodes, 31 spans)

30% restoration70% restoration100% restoration

span cut


Basics of Mesh-restorable networks

(28 nodes, 31 spans)

span cut

40% restoration70% restoration100% restoration



Spans where spare capacity was shared over the two failurescenarios ? .....

This sharing efficiency

increases with the degree of

network connectivity

“nodal degree”


• Consider two idealizations:– (1) restoration is “end node limited”

• i.e., the min cut governing restoration path number is at one or the other of the custodial nodes

– (2) node has span degree d

– (3) all working span capacities are equal at the node

then:

. . .

OCX

W

WW

W

d spans in total

if any one span fails, the total sparecapacity on the surviving (d-1) spansmust be >= to w.

hence....

redundancy =(node)

1( 1)( 1)

wd

spare dworking d w d

d

A simple lower-bound on achievable redundancy



Nodal Degree vs. Average Capacity(Network: CSELTNet, Gravity Demand, Least Usage Elimination)

0

100

200

300

400

500

600

700

800

900

2.0 2.5 3.0 3.5 4.0

Average Nodal Degree

Cap

acit

y R

equ

ired

w orking

spare

capacity

Mesh networks require less capacity as graph connectivity increases (sample result)

~ 3x factorin potential

networkcapacity

requirement


Where:

• S, ci, si, wi are spans, costs and capacities

• Pi is a set of “eligible routes” for restoration of span i

• is an assignment of restoration flow for span i to the pth eligible route

• encodes the eligible restoration routes: = 1 if span j is in the p th eligible route for restoration of span i

,p

i j

pfi

mini

c sii

S

2( , ) .i j i j S

p i

pf wii

P

.i S

,p i

p pf sji ij

P

Subject to:

Restorability :

Spare capacity :

A basic model for spare capacity allocation


Understanding the span-restorable mesh spare capacity problem

Net

wor

k st

ruct

ure

Failure scenarios

Failure scenarios

Failure scenarios

Greatest requirement on

all spans

Total sparecapacity

(minimize)

Failure scenarios

Flows overeligible routes Flows simulta-

neously imposed on any span

All other spare capacities

si values

pfi

Represented in the

eligible route - defining

information input ,p

i j


500

550

600

650

700

750

800

850

900

2 3 4 5 6 7 8 9

Design Hop Limit, H

To

tal

Sp

are

Cap

acit

y

(864, 51)

(678, 191)

(625, 1351)

(625, 1687)

(642, 476)

(625, 896)

Threshold value( for the network shown )

( Total spare capacity, total number of eligible restoration routes )

Minimum spare

• Below the design threshold hop-limit, solution quality is affected.

• Above the threshold hop limit, computational difficulty grows unnecessarily

How hop-limit affects complexity and solution quality in basic SCA


Other approaches and refinements studied

• Sakauchi - “cut oriented” formulation

• “Transportation-like” problem formulation

• Max-latching heuristic

• jointly optimized routing of working paths and spare capacity

• Modular transmission system capacities

• Economy-of-scale in cost-optimization

• Secondary optimization to maximize dual-failure restorability

• Secondary optimization to control optical path properties

path restorationpath restoration


“path restoration:” what we mean• The set of working paths severed by a span cut are restored by establishing

a set of replacement paths end-to-end, simultaneously, between each O-D pair affected.

• The replacement paths are formed on-demand using only shared spare capacity (and possibly released working capacity (stub release).)

– There is no dedicated reservation of a 1-for-1 backup path for each working path.

• Path restoration is equivalent to abandoning the damaged pre-failure paths entirely and rapidly re-provisioning new paths end-to-end.

• Path restoration distributes the impact of failures and the recovery effort more widely over the network as a whole and therefore generally permits greater efficiency in spare capacity design.

• The capacity design and real-time restoration problems for path restoration are considerably more complex than span-restoration

– the fall-back to each O-D pair creates a capacitated multi-commodity max-flow problem.

– issue of mutual capacity constraints very important


Comparative illustration of span versus path restoration

Pre-failure

3 service paths


Failure occurs

Comparative illustration of span versus path restoration

All 3 service paths are lost

until …


Span restoration reaction

First look at a span restoration reaction …

Note: example only, exact routes depend on working and spare capacities

3 service paths are lost

failed working capacity

restored by span

restoration


A span restoration reaction …(2)

Loopback / backhaul

Loopback / backhaul

This restoration path could stop hereThis restoration path could stop here


Now view a path restoration reaction...

Same failure occurs


Path restoration reaction …with “stub release”

Path restoration action

Stub release


• Stub release is an option / issue which does not exist in span

restoration.

• From a capacity design standpoint it is preferable to have stub-

release.

• From an operational viewpoint stub release complicates things:

– a means of automatic signaling needed to rapidly release the surviving working

“stub” capacities,

• AIS (Alarm inhibit signal) usually serves nicely for this, however

– after physical repair, the reversion process is more complex.

Notes about stub release in path restoration


mCj

rxi

,r qg

0

,si j

, prfi

,,r p

i j

riP

* some variables become pre-computable parameters in the variations that follow

Input data

Intermediate (internal) variables

Design output variables

Cost of mth modulesize on span j.

D

,r qj

S

rd

rQ

Set of all point to pointdemand quantities, indexed

by r

amount of demand on relation r

Set of all spans betweenmesh cross-connection points

Set of eligible working routes for relation r

Encodes routes in= 1 if span j is in qth route

for relation r

rQ

Set of eligible restoration routes for relation r

upon failure i.

= 1 if span j is in pth routefor relation r upon failure i

Stub release quantity on span j

from failure i

Amount of demand loston relation r for

failure i

mnj

jw

js

No. of operatingworking and spare

links (channels)on span j

No. of modules oftype m to install

on span j for min cost

mZCapacity of mth

module size

Working andrestoration

routingsolutions

N.B. “relation” = “OD pair”

Parameters and variables in path-restorable capacity design(in the master formulation)*


m mj j

m j

Minimize C n

M S

Cost of modules of all sizes placed on all spans

S. t.

;i r S D, ,r q r qi

q

rg xi

rQ

Defines the amount of damaged working flow for each relation under each failure scenario

,

r

r q r

q

g d

Q

r D

, ,r q r qj j

r q

g w

rD Q

j S

All demands must be routed

Working capacity on spans must be adequate

(1)

(2)

(3)

Master formulation for path-restorable capacity design


, , ,

0

,0

r q r q r qj i

r q

gsi j

rD Q

With stub release

Without stub release

2( , )i j

i j

S

rP

,

p i

p rrf xii

;i r S D

0

rP

,,,

pr i

r p pf s si i i jij

D

Restorability of working flows for each relation

Spare capacity on spans must be adequate(see note on stub release)

M

m

mmjjj Znws

1

j S Modularity of installed capacity

(4)

(5)

(6)

(7)

Master formulation for path-restorable capacity design (2)


O D

Relation r

Route q

Failure span i

Other span j Working flow gr,q

, 1r qj

, 1r qi

Span j enjoys a stub release “credit” of spare capacity = g r,q for any

failure on span i such that: , ,( 1) ( 1)r q r qj i true

, , ,0

,r q r q r qj i

r q

s gi j

rD Q

Understanding how the formulation effects “stub-release”


• If integer but non-modular capacity is desired:

– change objective function to cost-weighted sum of spares (and / or working, if joint)

– drop set M (the family of modularities), variables and constraint (7)

• If non-joint design is desired:

– drop (1), (2), (3), and (6)

– pre-compute all and as input parameters based on the pre-defined routing

– pre-compute all stub-release quantities according to (6)

• If stub-release is not desired:

– drop (6), i.e., set all = 0

mnj

rxi jw0,i js

Variations and options within the master formulation

0,i js


• joint optimizedrouting makes alargedifference in span restoration

Typical result comparing span and path-restorable network designs

4000

4200

4400

4600

4800

5000

1 2 3 4 5 6

To

tal N

etw

ork

Cap

aci

ty (

Lin

ks)

Combined workingand spare capacityoptimization

Spare capacityoptimization only

Design Case

Span restorablePath restorablePath restorablewith stub release

“non joint”

“joint” designs

• joint-span is aboutas efficient as non-joint path

• joint designadds relativelylittle benefit to path restoration


100 000

200 000

300 000

400 000

500 000

600 000

700 000

800 000

900 000

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

Wo

rkin

g a

nd

Sp

are

Cap

acit

y (d

ista

nce

-wei

gh

ted

)

SCASpare

JCA Spare

M-M Spare

PathSpare

SBPPSpare

M-M Working

JCA Working

Shortest Path Working

Network Average Nodal Degree, d

Capacity Comparison of various schemes vs. Network Connectivity (Nodal Degree)

x3x3


p-cycles: Background and Motivation

“ Ring “

A. 50 msec restoration times

B. Complex network planning and growth

C. High installed capacity for demand-served

D. Simple, low-cost ADMs

E. Hard to accommodate multiple service classes

“Mesh”

F. Possibly up to 1.5 sec restoration

times

G. Simple, exact capacity planning solutions

H. well under 100% redundancy

I. Relatively expensive DCS / OXC

J. Easy / efficient to design for multiple service classes

“ Shopping list” : A, D, G, H (and J) please...keep the

rest


Background - ideas of mesh “preconfiguration”

X

Node X forfailure 1

Node X forfailure 3

Node X forfailure 2

Node X forfailure 4

Q. How could you ever have the spare capacity of a mesh network completely pre-connected in advance of any failure?


Restoration using p-cycles

A p-cycle

A span on the cycle fails - 1 Restoration Path, BLSR-like

A span off the p-cycle fails - 2 Restoration Paths, Mesh-like

A. Form the spare capacity into a particular set of pre-connected cycles !

," 1 " case

i jx

," 2 " case

i jx

If span i fails,p-cycle j provides

one unit of restoration capacity

If span i fails,p-cycle j provides

two units of restoration capacity

i j

i

j


Optimal Spare capacity design with p-cycles

Step 1: Find set of elementary cycles of the network graph

Step 2: For each cycle, determine x i,j : the no. of restoration paths that cycle i contributes for failure j. x i,j

Step 3: Integer Program to select optimal p-cycle set:

Objective: minimize: total cost of spare capacity.

Subject to:

1. Restorability: All working links on each span have

(simultaneously feasible) access to one or more p-cycles.

2. Spare Capacity: All p-cycles placed are feasible within the

span spare capacities assigned


Optimal Spare capacity design - Typical Results

TestNetwork

Excesssparecapacity

# of unit-capacityp-cyclesformed

# ofdistinctcyclesused

1 9.09 % 5 52 3.07 % 88 103 0.0 % 250 104 2.38 % 2237 275 0.0 % 161 39

i.e., “mesh-like” capacity


Understanding why (optimally planned) p-cycles are so efficient...

9 Spares cover 9 Workers

9 Spares

cover 19 Workers

Spare

Working Coverage

UPSR or

BLSR

p-Cycle…same spare

capacity

“the clam-shell diagram”


Another p-cycle example

This 6-span p-cycle

covers

4 x 2 + 6 = 14 working demands for each unit of

spare capacity on itself

Recent Theoretical results:

(1) p-cycles are most efficient possible pre-configured structure.

(2) up to S protection relationships per link in p-cycle, where S = # spans in cycle.


Where is it all going? Current Research:

• p-cycle networking concept: “Ring speed with mesh efficiency”

• Availability analysis of ring, mesh and p-cycle networks

• Ring-mesh hybrid networks

• Distributed pre-planning

• Fundamental topology design & evolution

• Ring to mesh evolution: “ring mining” strategy

• Capacity design theory for uncertain demand forecasts

• Optimal location of wavelength converters & regens

• Optimal design for multiple Quality of Protection classes

• Traffic and failure adaptive Self-organizing networks

• Controlled over-subscription of capacity (for IP / MPLS)

• meta-mesh design concept (for sparse graphs)

• “maintenance immunity”


Other info and resources

• web site: www.ee.ualberta.ca/~grover

• some popular / general articles: – “Self-organizing broad-band transport networks,” Proceedings of the

IEEE, vol. 85, no. 10, October 1997.– "New Options and Insights for Survivable Transport Networks,"

IEEE Communications Magazine, January 2002. – W.D. Grover, “Network Survivability: A Crucial Issue for the

Information Society,” IEEE Canadian Review Magazine, Summer 1997, pp. 16-21.

• EE 681 web site (password needed for lectures)

Sigma Xi Guest Lecture “Survivable Networks” W.D. Grover, Feb. 27, 2002

For related papers or further information or clarification on topics within this presentation

please contact:

Wayne D. Grover

TRLabs / Univ. of Alberta

780 - 441 - 3815

[email protected]

www.ee.ualberta.ca/~grover


People and Technologyfor the Future

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Wayne D. Grover University of Alberta, Dept. of Electrical & Computer Engineering

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