E E Module 19 Availability Analysis of Paths through Ring-based Networks W. D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003

E E Module 19 © Wayne D. Grover 2002, 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 Td 1 () when dual-fed Td 2 () –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

E E Module 19 © Wayne D. Grover 2002, “Restorability” = 100 % Availability = 100 % So what causes unavailability in a restorable network ?: Restoration time ? Multiple failures ?  Insignificant  Yes Dual-failure: Probability  U s 2 Higher order failures: Probability  U s n << U s 2 Basics: Availability of Restorable Networks

E E Module 19 © Wayne D. Grover 2002, t 1 U1U1 U2U2 UnUn T … U3U3 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. our basic approach: Background on Availability

E E Module 19 © Wayne D. Grover 2002, O D Network Service path System 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” ?

E E Module 19 © Wayne D. Grover 2002, Reminder: why we can “add unavailabilities” rather than “multiply availabilities”

E E Module 19 © Wayne D. Grover 2002, 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

E E Module 19 © Wayne D. Grover 2002, Node-Node Failure: Span-Span Failure: Consider: 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?

E E Module 19 © Wayne D. Grover 2002, 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 ?

E E Module 19 © Wayne D. Grover 2002, Then so what is it in each set that can fail ?... 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...

E E Module 19 © Wayne D. Grover 2002, 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 : Two-failure unavailability of intra-ring service path...

E E Module 19 © Wayne D. Grover 2002, (3) the number of node x node failure combinations to consider is: and the probability of each of these combinations is : where: U S = unavailability of a span (assumes all spans same length) U N = unavailability of a node (from the optical line through signal standpoint) i.e., does not consider any add-drop signal path effects Two-failure unavailability of intra-ring service path...

E E Module 19 © Wayne D. Grover 2002, S = number of spans in the ring W = number of spans on the path L{S-W} = total circumferential distance of the ring excluding the path L{W} = total distance of the working path in the ring UsL = unavailability per-unit length of a span Initial statement of result (spans all identical): Refined model (spans each have own distance and Us is per-unit-length): class exercise: show that the identical result also applies for the UPSR ! hence result....Td 1 (W,S)

E E Module 19 © Wayne D. Grover 2002, unavailability of an ADM node from a line-through standpoint (previously just U N ) unavailability of an ADM node due 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...

E E Module 19 © Wayne D. Grover 2002, Vancouver Edmonton Toronto Ottawa “entry” “intra” “inter” “egress” Ring Set Network graph service path Next step...Unavailability of Paths through Multiple Rings: (First a view of the “big picture”) “intra”

E E Module 19 © Wayne D. Grover 2002, Now consider paths through several rings: Inter-Ring Interconnection schemes RING 1RING 2 Common Point-of- Presence (building) “Cross-Office” Wiring Add-drop Multiplexer (ADM) Primary Gateways Secondary Gateways RING 1RING 2 A B W X Y Z Inter-ring Single Redundancy Approach Inter-ring Dual Redundancy Approaches Single Feeding Matched Nodes RING 1RING 2 Dual Feeding

E E Module 19 © Wayne D. Grover 2002, RING 1RING 2 “inter-ring” “intra-ring” adding up contributors.... #1#2#K... Td1() 2(U NA + U NL ) (U NA + U NL ) “Single - Fed Path”: K rings in total, single-fed entry, egress, and inter-ring transitions

E E Module 19 © Wayne D. Grover 2002, RING 1RING 2 “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

E E Module 19 © Wayne D. Grover 2002, Dual-Failure Analysis for mn Transfer Arrangement analysis approach: there are 8 elemental items involved in the transfer consider all C 2 8 = 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 Td 1 () already covers result:

E E Module 19 © Wayne D. Grover 2002, 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 U access_line Question: Why must we take this “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

E E Module 19 © Wayne D. Grover 2002, #1#K unavailability contributors: - 2 access / egress - K intra-ring Td1() contributions - (K-1) inter-ring transfers RING 1 the access/egress failures classes that are considered: class: why does the access contribution not include a term ? RING 1 hence, end-to-end “pure mn” path unavailability expression....

E E Module 19 © Wayne D. Grover 2002, Matched Nodes Dual Feeding Matched Nodes Dual Feeding 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”

E E Module 19 © Wayne D. Grover 2002, (a) Normal Operation (before failure)(b) Protection Operation (after failure) Cable cut Loop Back SONET Bi-directional Line Switched Ring

E E Module 19 © Wayne D. Grover 2002, Node-Node Failure Span-Node FailureSpan-Span Failure No Failure Intra-Ring Failure Scenarios on Dual Fed Path (Outage Causing)

E E Module 19 © Wayne D. Grover 2002, DF MN DF #1#2#3#4#5#6 #1#4#5 #2#3#6 Intra-Ring: Inter-Ring: DF MN Other Failure Scenarios: Total Unavailability = Intra-Ring + Inter-Ring + Other Failure Scenarios MN/DF Combination Path End-to-End Path Availability Analysis

E E Module 19 © Wayne D. Grover 2002, Interface compatibility of mn and df showing that technically you can “mix and match” mn and df treatments, if desired... RING 1RING 2 mn... interfacing to.... df “A” “B”

E E Module 19 © Wayne D. Grover 2002, Interface compatibility of mn and df and, the other way around... df... interfacing to.... mn RING 1RING 2 “A” “B”

E E Module 19 © Wayne D. Grover 2002, example: - 8 node /span ring - entry gateways 3 apart, egress 1 - W for mn = Wa for df= 2 spans..... S-2Etot = 8- 2x4 =0 df preferred Matched Nodes: Dual Feeding: df less costly whenever *: where: W a = length of ( shorter) “A” path signal feed S = length (or number) of all spans in ring E tot = total (length or hops) separation of gateway nodes W Wa Wb “A” “B” E 2 =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 E 1 =3 General decision criterion between mn / df What are the general conditions when df is a more attractive alternative ?

E E Module 19 © Wayne D. Grover 2002, #1#K 1+1 redundant access 1+1 redundant egress K rings with dual-fed intra-ring signals (K-1) df-df inter-ring interfaces [access/ egress terms] + [(K-1) inter-ring transfers] + [K dual-fed intra-ring outage contributors] requires new intra-ring unavailability function...Td2() requires new inter-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:

E E Module 19 © Wayne D. Grover 2002, analysis method is similar to Td 1 () but For {X} and Rev{x} are replaced by For{A} and For{B} outage now requires: For{“B”} For{“A”} result is: Wa = number of nodes on the first path Wb = number of nodes on the second path {Wa} = distance of the shortest dual-fed path inside ring path {Wb} = distance of the second path Td 2 () for df Intra-Ring Unavailability

E E Module 19 © Wayne D. Grover 2002, 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”.... RING 1 RING K U NA U NL

E E Module 19 © Wayne D. Grover 2002, 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”.... RING 1 U NA U NL RING K

E E Module 19 © Wayne D. Grover 2002, result is end-to-end “pure df “ path availability model “A” “B”.... RING 1 U NA U NL RING K.... “A” “B”.... U NA U NL 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

E E Module 19 © Wayne D. Grover 2002, DF MN DF #1#2#3#4#5#6 example 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 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...

E E Module 19 © Wayne D. Grover 2002, 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 N df = N mn =2 description of segments K df (i) = {2,1} K mn (j) = {1,2}

E E Module 19 © Wayne D. Grover 2002, new class of 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. new class of failures spanning multi-df segment structure Result: availability of arbitrary mixed path model 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