E E 681 - Module 19 Availability Analysis of Paths through Ring-based Networks W. D. Grover TRLabs &...

E E 681 - Module 19

Availability Analysis of Paths Availability Analysis of Paths through Ring-based Networksthrough Ring-based Networks

W. D. Grover

TRLabs & University of Alberta

© Wayne D. Grover 2002, 2003

E E 681 - Module 19 © Wayne D. Grover 2002, 2003 2

• Approach– Recap a few basics of availability analysis– Re-familiarize with (BLSR) rings – Define an “elemental unavailabilities” model– Work out expression for intra-ring dual-failure unavailability

• when single-fed Td1 ()

• when dual-fed Td2 ()

– Look at schemes for inter-ring interconnections (i.e., where the service path has to transition from ring to ring)

– work out expressions for end-to-end path availability• multi-ring path purely using matched node (mn) inter-ring transitions• multi-ring path purely using dual-fed (df) inter-ring transitions• multi-ring path using mixture of mn and df inter-ring transitions

Approach and aims


“Restorability” = 100 % Availability = 100 %

So what causes unavailability in a restorable network ?:

• Restoration time ?• Multiple failures ?

Insignificant Yes

Dual-failure: Probability Us2

Higher order failures: Probability Usn << Us

2

Basics: Availability of Restorable Networks


lim

1

i

T

T U MTBFAvailability

T MTTR MTBF

Unavailability Availabilityt

1

U1 U2Un

T

…

U3

The availability of a service over a period T is the fraction of this period during which the service is up,

or... (equivalently) ....

availability is the probability that if the system state (here, a service path) is sampled at any random time in the future it will be found in the “up” state.

all service-affecting classes of failure,

no. combinations(each combination)

in class x

Unavailability px

our basic

approach:

Background on Availability


OD

Network

Service pathSystem 1

System 2

System 3

System 4

System 5

The “availability of a network” (as a whole) - or even of a single ring - (as a whole) is not actually a “well-founded” concept: whole networks are never entirely “up” nor entirely “down”.

•The only fundamental question that has a precise meaning is the availability of a stipulated path through a network.

•Network-wide average / worst-case etc. metrics can then be computed from an ensemble of individual path availabilities

Concept of a “hypothetical reference digital path” (HRDP):• A single “near-worst-case” path model on which a representative or characteristic end-

to-end availability calculation is done in lieu of attempting to characterize a network by the average availability of all possible paths through the network.

“Network Availability” or “Availability of a path through a network” ?


Appendix

The availability of a path is the probability of finding the path in the working state. For the path to be inworking state we need all the links to be working as well, therefore:

) workingn link() working2 link( working)1 link( working)path( PPPP

Equivalently:

1 2 n

1 2 n

1 2 n

1 2 1 3 (n-1) n

1 2 3 (n-2) (n-1)

1 1 1

1 ( )

( )

(

path link link link

path link link link

path link link link

link link link link link link

link link link link link l

A A A A

A U U U

A U U U

U U U U U U

U U U U U U

n

1 2 n

1 2 n

i1

)

1 ( )

1

ink

path link link link

path path link link link

n

path linki

A U U U

U A U U U

U U

NegligiblebecauseUlinki << 1

Reminder: why we can “add unavailabilities” rather than “multiply availabilities”


Node-Node Failure: outage

Span-Span Failure: outage

Any One Failure : no outage

Span-Node Failure: outage

Intra-Ring Failure Scenarios on Single Fed Path


Node-Node Failure:

Span-Span Failure:

Consider:

Node-Node Failure:Node-Node Failure:

Span-Span Failure:Span-Node Failure:

None of these dual-failures are outage-causing

So do all dual-failures cause outage of the service path?


Outage of a given service path occurs when one failure hits the normal working route of the path ....

and ....

the second failure falls on the route that would have provided the protection path

Let us define:

X = the intra-ring service path of interest

For{X} = the set of all elements in the forward path of X

Rev{X} = the set of all elements in the reverse path of X

For{X}

Rev{X}

What, then, is the key property of the dual-failure combinations that are outage-causing ?


• Then

• so what is it in each set that can fail ? ...

intra-ring

(1 failure For{X}) (1 failure Rev{X})U p p

For{X} = {W spans, W+1 nodes}

Rev{X} = {S-W spans, S-W-1 nodes}

where:

S = number of spans in the ring

W = number of spans that the service path has on its path through this ring

Two-failure unavailability of intra-ring service path ...


Therefore :

• (1) the number of dual span-failure combinations to consider is:

• and the probability of each combination is:

• (2) the number of span x node failure combinations to consider is:

• and probability of each of these combinations is :

Spans SpansFor{X} Rev{X} = W (S-W)

2SU

Spans nodes nodes spansFor{X} Rev{X} For{X} Rev{X}

= W (S-W-1)+(W+1) (S-W)

S NU U



• (3) the number of node x node failure combinations to consider is:

• and the probability of each of these combinations is :

nodes nodes

For{X} Rev{X} = W+1 (S-W-1)

2NU

where:

US = unavailability of a span (assumes all spans same length)

UN = unavailability of a node (from the optical line through signal standpoint) i.e., does not consider any add-drop signal path effects



S = number of spans in the ringW = number of spans on the pathL{S-W} = total circumferential distance of the ring excluding the pathL{W} = total distance of the working path in the ringUsL = unavailability per-unit length of a span

Initial statement of result (spans all identical):

2intra- SL SL Nring

21N

U (S-W-1)+(W+1) U U{W} {S-W} {

W+1 ( , ) (

W} {S-W

S-W-1) U

}

d

L L LU

W

L

T S

Refined model (spans each have own distance and Us is per-unit-length):

2intra- S S Nring

2N

W (S-W) U W (S-W-1)+(W+1) (S-W) U U

W+1 (S-W-1) U

U

class exercise:

show that the identicalresult also applies for

the UPSR !

hence result ....Td1 (W,S)


ADM ADM

ADM

Una

Una

Unl Us

= L • USL

inter-ringtransfer site

Unl

Una ring access

site

unavailability of an ADM nodefrom a line-through standpoint(previously just UN)

unavailability of an ADM nodedue to failure of the access(add-drop interface) function

.....includes 1/2 of any “cross-office wiring” unavailability

length-dependent unavailability of spans(due to all causes)

The “elemental unavailabilities” model that goes with this result...


VancouverEdmonton Toronto

Ottawa

“entry”

“intra”“inter”

“inter”

“egress”

Ring Set

Network graphservice path

Next step...Unavailability of Paths through Multiple Rings:(First a view of the “big picture”)

“intra”


Now consider paths through several rings: Inter-Ring Interconnection schemes

RING 1 RING 2Common Point-of-Presence (building)

“Cross-Office” Wiring

Add-drop Multiplexer (ADM)

Primary Gateways

Secondary Gateways

RING 1 RING 2

A B

W

X

Y

Z

Inter-ring SingleRedundancy Approach

Inter-ring Dual Redundancy Approaches

Single Feeding

Matched Nodes

RING 1 RING 2

Dual Feeding


RING 1 RING 2

“inter-ring”

1 1 1( , )dT W S 1 2 2( , )dT W S“intra-ring” “intra-ring”

11..

( ) 2 ( ) ( , )sf NA NL d i ii K

U K K U U T W S

2 NLU

2 NAU

adding up contributors....

#1 #2 #K...

Td1() Td1() Td1()

2(UNA

+ UNL)(UNA + UNL)(UNA + UNL)

“Single - Fed Path”:

K rings in total, single-fed entry, egress, and inter-ring transitions


RING 1 RING 2

1 1 1( , )dT W S 1 2 2( , )dT W S“intra-ring” “intra-ring”

• non-trivial sub-problem to solve here:

Q. what combinations of dual-failures cause inter-ring service-outage in the matched- node arrangement ?

“inter-ring”

“Pure matched - node path” :K rings in total, mn type entry, egress, and inter-ring transitions


Dual-Failure Analysis for mn Transfer Arrangement

1A

2A

3A

4A

(primary)

(secondary)

ring1 ring2

C3

C4

C1

C2“west” “east”

C5

analysis approach:

• there are 8 elemental items involved in the transfer

• consider all C28

= 28 combinations

• use functional understanding of system operation to ask if there is outage or not for each combination

• simplify task by recognizing classes of equivalent combinations

• don’t “double-count” things Td1() already covers

2 2one mntransfer

2 4NL NA NA NLU U U U U result:


1A

2A

3A

4A

(primary)

(secondary)

ring1 ring2

C3

C4

C1


C5

1A

2A

3A

4A

(primary)

(secondary)

ring1 ring2

C3

C4

C1


C5

ring 1 ...

origin

node

destination

node“ACCESS” “EGRESS” .... K-2 intermediate rings ...

concept: the same ADM functionality that supports matched-node inter-ring interfaces is used to convert dual-redundant customer signal access / egress into the required intra-ring signal in rings 1 and K.

alternate extent of the path unavailability model - define an additional Uaccess_line

Question: Why must we takethis “aside discussion” to consider

access / egress arrangements?

extent of present end-to-end path model

Access and egress arrangements assumed for “pure mn”

ring K


#1 #K

unavailability contributors:

- 2 access / egress

- K intra-ring Td1() contributions

- (K-1) inter-ring transfers

21

1..

2 2mn ( ) 2( 1)(2( ,2 4 )) ( )2 N d i i

iL NA

KNNA AL LNA N NU K K U U U U T SU U WU

RING 1

the access/egress failures classes that are considered:

class: why does the access contribution not include a term ? 2

NLU

RING 1

hence, end-to-end “pure mn” path unavailability expression....


MatchedNodes

DualFeeding

MatchedNodes

DualFeeding

Explicit “Dual feeding” of the signal path is another alternative for redundant inter-ring transfer ... It can sometimes have a lower resource cost than mn

5 spans used

6 spans used

(a) gateway nodes one hop apart (b) gateway nodes farther apart

6 spans used

4 spans used

“A”

“B”

“A”

“B”

Matched Nodes vs “Dual Feeding”


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

Cable cut

Loop Back

SONET Bi-directional Line Switched Ring


Node-Node Failure

Span-Node FailureSpan-Span Failure

No Failure

Intra-Ring Failure Scenarios on Dual Fed Path(Outage Causing)


DF DF MN MNMN DF

#1 #2 #3 #4 #5 #6

#1 #4 #5 #2 #3 #6Intra-Ring:

Inter-Ring:

DF DF MNMN

Other Failure Scenarios:

Total Unavailability = Intra-Ring + Inter-Ring + Other Failure Scenarios

MN/DFCombination Path

End-to-End Path Availability Analysis


Interface compatibility of mn and df

• showing that technically you can “mix and match” mn and df treatments, if desired...

RING 1 RING 2

mn ... interfacing to .... df

“A”

“B”


Interface compatibility of mn and df

• and, the other way around...

df ... interfacing to .... mn

RING 1 RING 2

“A”

“B”


example:

- 8 node /span ring

- entry gateways 3 apart, egress 1

- W for mn = Wa for df= 2 spans

.....

S-2Etot = 8- 2x4 =0 < Wa --> df preferred

MatchedNodes:

DualFeeding:

2a totW S E df less costly whenever *:

where:

Wa = length of ( shorter) “A” path signal feed

S = length (or number) of all spans in ring

Etot = total (length or hops) separation of gateway nodes

W

Wa

Wb

“A”

“B”

E2=1

* ref (on web site): W.D. Grover, “Resource management for fault tolerant paths in SONET ring networks,” J. of Networks and Systems Management (Plenum Publishing), vol.7, no.4, December 1999, pp. 373-394.

E1=3

General decision criterion between mn / df

• What are the general conditions when df is a more attractive alternative ?


#1 #K

1+1 redundant access

1+1 redundant egress

K rings with dual-fed intra-ring

signals

(K-1) df-df inter-ringinterfaces

[access/ egress terms] + [(K-1) inter-ring transfers] + [K dual-fed intra-ring outage contributors]

requires newintra-ring unavailability function...Td2()

requires newinter-ring analysis

consider “pure df” end-to-end path

• model of end-to-end path structure ...

• hence end-to-end path availability will be formed as before from:


• analysis method is similar to Td1() but For {X} and Rev{x} are replaced by For{A} and For{B}

• outage now requires:

For{“B”}

For{“A”}

intra-ring

(1 failure For{A})

(1 failure For{B})

U p

p

22

2

( , , ) [{ } { }] [( 1) { } ( 1) { }]

[( 1) ( 1)]

:

d a tot

b a tot

T S W E Wa Wb Usl Wa Wb Wb Wa Unl Usl

Wa Wb Unl

where

W S W E

result is:

Wa = number of nodes on the first pathWb = number of nodes on the second path{Wa} = distance of the shortest dual-fed path inside ring path{Wb} = distance of the second path

Td2() for df Intra-Ring Unavailability


Now consider df inter-ring outage combinations

....

• first observation: - single-failures at different df interfaces can combine to cause outage - by comparison the mn-interface is “failure isolating”

• failure combinations to consider: - one failure anywhere at a transfer interface on “A” feed crossed with any similar failure anywhere at an interface on “B” feed, i.e....

“A”

“B”

2inter-df ( ) [( 1) 2 ( )]NA NLU K K U U

....

RING 1 RING K

UNAUNL


add df access / egress considerations

....

• observation: access - egress failures are of same types as inter-ring df and also cross-combine with any other inter-ring or access interface failure on the opposite signal feed, end to end.

• Therefore just revise prior expression, i.e....

“A”

“B”

2access/inter-df

2

( ) [( 1) 2 ( ) 2 ( )]

[2 ( )]

NA NL NA NL

NA NL

U K K U U U U

K U U

....

RING 1

UNA UNL

RING K


result is end-to-end “pure df “ path availability model ...

....“A”

“B” ....

RING 1

UNA UNL

RING K

2 , ,.

f.

2d

1

( ) [2 ( )] ( , , )d A i i tot ii K

NA NL T W S EU K K U U

....“A”

“B”....

UNAUNL

Class Questions:

1. for same W=Wa, S, how does Td1() compare numerically to Td2() ?

2. for same K, how does inter-ring pure df unavailability compare to that of a pure mn path ? Why ?

A. 1 - Td2() lower than Td1()

A. 2 - df higher than mn - single “inter-” failures not isolated


DF DF MN MNMN DF

#1 #2 #3 #4 #5 #6example MN/DF

Combination Path

• Background:

1. mn and df treatments are technically compatible

2. df can sometimes cost less than mn

• Existence of 1. and 2. implies ...

3. a cost-minimal optimal mn-df path construction exists for

every application.

• Strategies for optimal mn-df path search / construction were topic of recent MSc.

thesis (Dec. ‘99) by E. Siu, (now with YottaYotta, Edmonton)

• Creates need for availability model for mixed mn-df path constructions...

Final step: End-to-End Path Availability of mixed mn-df path constructions...


Approach for mixed mn, df path model

• recognize the mn interfaces are “single-failure isolating”

• this allows mixed path structure to be ‘chopped up’ into:– “pure df “ path segments– “pure mn” path segments– deal with new segment-level failure combinations

• Example:

– decomposition of this path structure:• numbers of segments Ndf = Nmn=2

• description of segments Kdf(i) = {2,1} Kmn(j) = {1,2}

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mn segment 1 df segment 1 mn segment 2

A BC

df segment 2

D


new classof failures

arising only at mn-df segment

interfaces

• sum the segment unavailabilities using prior pure path type expressions:

• ... and add some new mn-df segment interaction terms:

• extra terms...df(i)= 1 if df segment i is embedded in mn.

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mn segment 1 df segment 1 mn segment 2

A BC

df segment 2

D

new classof failuresspanning

multi-df segmentstructure

Result: availability of arbitrary mixed path model

,1.. 1..

( ) ( ( )) ( ( )) ....df mn

mn df df mn df df mn mni N j N

U N N U K i U K j

2

1..

2

1..

2 ( ) ( 2 )

4(1 ( )) ( ( ) 1) ( )

df

df

df NA NA NLi N

df df NA NLi N

i U U U

i K i U U

dual mn-df “feed” cross-failures at outer edges of fully embedded df segments, e.g. A-D

• single mn-df segment “feed” failure crossed with any regular df failure on other feed signal, plus additional df-df, e.g. A-X, X-Y

X

Y

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E E 681 - Module 19 Availability Analysis of Paths through Ring-based Networks W. D. Grover TRLabs &...

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