Resilient Networks 3.2 Resilient Network Design Restoration & - - PowerPoint PPT Presentation

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Resilient Networks

3.2 Resilient Network Design – Restoration & Protection

Prepared along: Michal Pioro and Deepankar Medhi - Routing, Flow, and Capacity Design in Communication and Computer Networks, The Morgan Kaufmann Series in Networking, 800 pages, 2004

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Link-Demand-Path-Identifier-based Notation

Notation Summary

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Restoration and Protection Design

• New dimension in Network Design Problems (NDP): Failures
• Adds resilience dimension to network design
• Restoration Design Problems (RDP)

– Designing networks that are robust to failures – Networks are able to carry (possibly decreased) demands also when part of network resources fail temporarily – Re-establishing flows on paths that survived failure situation

• Different failure situations specified by

– availability status of links and nodes – possibly decreased demand volumes requested for particular situation – total or partial failure of links / nodes

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Restoration and Protection Design - Outline

• Introduction to Re-establishment Mechanisms

–

Initial model for re-establishment mechanisms (protection and restoration)

–

Characterization of failure states

• Resilience via path diversity
• Link capacity re-establishment mechanisms

– Link restoration with shared capacity – Hot-standby link protection with dedicated capacity

• Path flow re-establishment mechanisms

– Path flow restoration with shared capacity – Hot-standby path protection with dedicated capacity

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Re-Establishment Mechanisms (1)

• Network resilience via re-establishment of resources in case of failures

– Protection: actions to restore before failure happens, typically used to protect against single link failures – Restoration: actions taken after failure

• Goal of re-establishment:

– Protecting demand volumes or at least certain portion of them

• Protection / restoration capacity

– Needed for both, traffic networks and transport networks – Traffic networks (e.g., Internet): restoration capacity – Transport networks (physical facility providers): protection capacity

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Re-Establishment Mechanisms (2)

Link vs. path re-establishment

• Link Re-establishment (LR)

– Link is re-established in case of failure – All flows that use link are reconstructed together

• Path Re-establishment (PR)

– End-to-end flows that use failed links are re-established individually – PR used at neighboring lower layer of LR to reconstruct missing demand capacity units in between end-points of failed link 1 5 6 3 4 2 Link Re-establishment 1 5 6 3 4 2 Path Re-establishment

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Re-Establishment Mechanisms (3) – Paths

• Path Protection (PP)

– Reservation of resources at the time the flow on the path is set up – Restoration is guaranteed as protection (backup) paths are pre-calculated in advance and protection capacity is reserved – Re-establishing of flows on protection paths after failure

• Path Restoration (PR)

– Restoration after path has broken by calculating backup paths using available restoration (spare and released) capacity and re-establishing flows – Network management system has to be invoked after failure

• Capacity design: No difference between protection and restoration

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Re-Establishment Mechanisms (4) - Capacity

Dedicated vs. shared capacity

• Dedicated capacity

– Spare capacity required to re-establish a link/path that is reserved exclusively for re-establishing this link/path – Spare capacity cannot be used for re-establishing other links/paths – Used in protection schemes, e.g., Automated Protection Switching (APS) – Expensive resource-wise but simple to operate

• Shared capacity

– Common pool of spare resources used for re-establishing broken links/paths – Typically used for restoration schemes, same capacity used for protecting different resources – Restoration schemes can also utilize normal capacity released along broken paths – Requires less spare capacity but much more complicated to control

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Re-Establishment Mechanisms (5)

• Hot-standby path protection

– 1+1 protection: Data transmitted redundantly via two paths simultaneously – 1:1 protection: Data transmitted via one path, after failure switch to backup paths – 1:N protection: One backup path protects N regular paths

• Link re-establishment can be entire or partial

– If links are modular then only one part of its modules may be re-established (partial re-establishment)

• Re-establishment may be

– Splittable (bifurcated): link or path re-established on several backup paths – Unsplittable (non-bifurcated): link or path is re-established on exactly one backup path

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Re-Establishment Mechanisms (6)

Network Design perspective

• Whether re-establishment scheme is of protection
• r restoration type is not important
• But it is important

– whether they use dedicated or shared capacity – and if they can use the released capacity or not

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Restoration and Protection Design – Naming Naming conventions for restoration and protection problems

1. DR (Restoration Design), D (Dimensioning for the normal state), P (Protection design), D+P (normal Design + Protection design) 2. CF (Continuous Flows), MF (Modular Flows) 3. BR (Bifurcated Routing), NBR (Non-Bifurcated, i.e., single-path Souting) 4. CC (Continuous link Capacity), MC (Modular link Capacity) 5. LIN (LINear cost), MOD (MOdular Cost), CX (ConveX cost), CV (ConcaVe cost), BC (Budget Constraint); we will use mostly the LIN option 6. LR (Link Restoration), LP (Link Protection), HS (Hot Standby), SBP (Single Backup Path), LR + BR (BifuRcated Link Restoration), ...

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Recapitulation from Last Chapter DP: Minimizing capacity costs

4 3 1 2 2 3 1 Demand Network

𝑄

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𝑄22 𝑄21 𝑄32 𝑄31 𝑄

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F*=85

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Restoration and Protection – Initial Model (1)

• Failure model:

– Links become totally unavailable, but do not fail simultaneously – Each failure state consists of one link failure per time (rest is operative)

• Example: DP – Minimizing capacity costs

– Network results in 5 failures states s = 1,2,...,5 corresponding to each link – In state s link e = s is failed, remaining links intact – Normal state (all links available): s = 0

• Goal:

– Find cheapest link capacity configuration together with routing and flow allocation so that in all states demand volumes are fully realized 4 3 1 2 2 3 1 Demand Network

𝑄

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𝑄22 𝑄21 𝑄32 𝑄31 𝑄

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Restoration and Protection – Initial Model (2)

• State s requires new identifier, e.g., for demand d=1:
• Six equations instead of one for demand d=1, in general form:
• Capacity constraints

– Since 𝑡 = 1 corresponds to failure of link 𝑓 = 1, no capacity should be assigned to that link in that state (right side is 0) – Notation 𝛽𝑓𝑡 set to 1 if link e is up and 0 if it is down in state 𝑡

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Restoration and Protection – Initial Model (3)

• Solution for 4-Node Network Example
• Optimal capacity y*

e of link e

– Computed as maximum load of link over all states s=0,1,...,5

• Optimal cost of F*=245

(in contrast to F*=85 without failure consideration)

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Restoration and Protection – Initial Model (4)

• Optimal flow allocation for all flow allocations: all flows are non-bifurcated
• However, this is not always the case
• Simple example network with two nodes

– Only one demand d=1 – Three links (E=3), three failure situations (S=3) – Demand volume in all situations: h1s=3, s = 0,1,2,3 – Unit cost of all three links is 1 – In failure situation only one link fails

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Restoration and Protection – Initial Model (5)

1 1 1 (1,5) (1,5) (1,5) 1 1 (1,5) (1,5) (1,5) 1 1 (1,5) (1,5) (1,5) 1 1 (1,5) (1,5) (1,5) 1 1 1 (0) (3) (3) 1 1 (0) (3) (3) 1 1 (0) (3) (3) 1 1 (0) (3) (3) demand h10=3 demand h11=3 demand h12=3 demand h13=3 demand h10=3 demand h11=3 demand h12=3 demand h13=3

s=0 s=1 s=2 s=3 s=0 s=1 s=2 s=3

Non- Bifurcated Solution Bifurcated Solution

F*=4,5 F*=6

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Re-establishment Mechanisms – Initial Model (6)

• Design problems related to network robustness to failures do not follow

shortest-path rule that works for normal operating state

• Number of equations, inequalities, and variables grow with introduction of

states to capture different failure situations

• Restoration problems difficult and time-consuming to solve
• But restoration problems are important class of DP and can help to find

network configurations that are resilient and survivable

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Characterization of Failure States (1)

• Capacity /demand protection or capacity /demand restoration mechanism

activated when failure situation occurs

• Failure state (situation) s characterized by vector of link availability

coefficients αs = (α1s, α2s,..., αEs) with 0 ≤ αes ≤ 1

– Each coefficient 𝛽𝑓𝑡 determines proportion of normal capacity 𝑧𝑓 of link e, 𝛽𝑓𝑡𝑧𝑓, available on link e in situation 𝑡 – 𝑡 = 1,2, … , 𝑇 is the predefined list of failure situations – Frequently, we will assume that availability coefficients are binary 𝛽𝑓𝑡 ∈ {0,1}

• Multiple link failures at one time possible

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Characterization of Failure States (2)

• Failure state s described by vector of

demand coefficients 𝜓𝑡 = (𝜓1𝑡, 𝜓2𝑡, … , 𝜓𝐸𝑡)

• Each coefficient χds determines proportion of reference demand volume hd
• f demand d, ℎ𝑒𝑡 = 𝜓𝑒𝑡ℎ𝑒 that must be realized in situation s

– Demand coefficients used to account for possible decrease in demand volume d realized in failure situation s (𝜓𝑒𝑡 < 1) – 100% demand protection/restoration: 𝜓𝑡 = 1 – Normal state s=0 → αe0=1, χd0=1(reference demand volume)

• Modeling node failures via link availability coefficients

– Set αes=0 for all links incident to failed node v – Set χds=0for all demands d incident to failed node v (v is one of the end-nodes of d)

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Protection by Diversity (1) Diversity in demand flow assignment

• Simplest re-establishment (protection) mechanism
• Ensures that portion of demand volumes will simply survive failure
• Design problem D/PD: uncapacitated counterpart of flow allocation problem

that assumes Path Diversity (PD) in allocating demand volumes

• PD is a requirement to split demand volumes into several (link or node)

disjoint paths

• D/CF/BR+PD/CC/LIN (Dimensioning / Continuous Flow / Bifurcated Routing,

Path Diversity / Continuous Link Capacity / Linear Costs) Problem

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Protection by Diversity (2)

Diversity in demand flow assignment

• Optimal rule: allocate flow equal to hd/ndto next shortest path and so on
• Note: when candidate

paths are link (node) disjoint, a single link (node) failure results in at most 100/nd % of lost demand volume, the rest survives Ensuring that flow on path p for demand d does not exceed hd/nd

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Protection by Diversity (3)

Example: Cube-Network

• E=12 (undirected) links, D=12 (undirected) demands
• Link unit costs equal to 1 (𝜂𝑓 = 1), all demand volumes equal to 3 (hd=3)
• Solution of simple design problem (without considering failures)

– Flow allocation 𝒚′ – Demands allocated to direct paths – F(𝒚′ )=36

• Failure situation S=E, situation s > 0 corresponds

to total failure of e=s (αss=0 and αes=1 for e ≠s)

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Protection by Diversity (4)

Example: Cube-Network

• Goal: Path Diversity with nd ≡ 3
• Split each demand volume hd≡3 into three flows

𝑦𝑒1

′′ = 𝑦𝑒2 ′′ = 𝑦𝑒3 ′′ = 1 allocated to shortest set of

three node disjoint paths :

– one short one-link path – two three-links paths – Optimal solution 𝒚′′ of D/CF,BR+PD/CC/LIN with cost F(𝒚′′) = 12 1 + 2 ∗ 3 = 84

• At same time solution 𝒚′′ realizes at least 2/3 of

each demand volume in any failure situation

• We have achieved a 66% protected network at

the expense of a significant cost increase of 48!

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Protection by Diversity (5)

General formulation of protection problem

𝛽𝑓𝑡 is binary 𝜄𝑒𝑞𝑡 = ෑ

𝑓:𝜀𝑓𝑒𝑞=1

𝛽𝑓𝑡 𝜓𝑒𝑡 ℎ𝑒𝑡 = 𝜓𝑒𝑡ℎ𝑒

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Protection by Diversity (6) Remarks on Restoration Design with Generalized Diversity

• Link availability coefficients 𝛽𝑓𝑡 have to be binary
• Availability coefficient 𝜄𝑒𝑞𝑡 of path 𝑄𝑒𝑞 in state 𝑡

– is equal to the product of availability coefficients of all links belonging to path, – thus 𝜄𝑒𝑞𝑡 = 1 iff all links 𝑓 ∈ 𝑄𝑒𝑞 are available

• Assumption of binary availability coefficients necessary because in case of

partial link failure (represented by fractional coefficient, 0 < 𝛽𝑓𝑡 < 1) it is not known which particular flows going through the link are broken

𝜄𝑒𝑞𝑡 = ෑ

𝑓:𝜀𝑓𝑒𝑞=1

𝛽𝑓𝑡

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Protection by Diversity (7)

Modeling partial link failures

• Only reasonable way: multi-links between pairs of nodes
• If original link split into several links and capacity evenly divided among

them, partial multi-link failure equivalent to total failure of subset of this links

multi-link 𝑓 𝑡 = 0, 𝛽𝑓 = 1 𝑡 = 1, 𝛽𝑓1 = 3/4 𝑡 = 2, 𝛽𝑓2 = 1/2 𝑡 = 3, 𝛽𝑓3 = 1/4

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Protection by Diversity (8)

Modeling partial link failures

• Replacing constraint
• By

– With additional requirement: 𝑧𝑓 are non-negative integers – M denotes link capacity module (number of links the multi-link is split into)

• However, resulting Mixed Integer Programming (MIP)

problem becomes NP-complete

• Shortest path rule can no longer be applied

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Link Capacity Protection and Restoration

• Link Re-establishment (link protection or restoration)

– Assumption of single, total failures of individual links – Restoration of entire or partial capacity of failed link on one or several paths between two end-nodes of failed link – Spare capacity is shared

• Approaches

– Link Restoration – Link Restoration on Single Path – Hot-standby link protection 1 5 6 3 4 2 Link Re-establishment

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Link Capacity Restoration (1)

• Path diversity demand volume protection is costly and passive
• Active protection mechanisms required that provide more efficient demand

re-establishment in case of failures

• Candidate restoration paths 𝑟 = 1,2, … , 𝑅𝑓 for link e
• Design with Link Restoration - LP: DR/CF/BR/CC/LIN/LR+BR Problem

– DR – Restoration Design – CF - Continuous Flow – BR Bifurcated Routing – CC – Continuous Link Capacity – LIN – Linear Costs – LR+BR –Bifurcated Link Restoration

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Link Capacity Restoration (2)

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Link Capacity Restoration (3)

• Indices
• Constants

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Link Capacity Restoration (4)

• Variables
• Objective function

1 5 6 3 4 2 Link Re-establishment 𝑧′𝑓 𝑧𝑓 𝑨𝑓𝑟 𝑧′𝑓 𝑧′𝑓

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Link Capacity Restoration (5)

Constraints

• Normal demand volumes transported by using only normal link capacities
• Normal capacity of each link e can be restored using spare capacity of

remaining links l (𝑚 ≠ 𝑓)

• Hence, demand volumes are realized in all single (but total) link failure

situations

– In normal operating state, spare capacity 𝑧𝑓

′ is not used

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Link Capacity Restoration (5)

Example for DR/CF/BR/CC/LIN/LR+BR

• d=12 undirected demands (ℎ𝑒 ≡ 3) that coincide with links
• 1. Allocate normal flows to shortest single-link paths,

which results in 𝑧𝑓 = 3 for all links

• 2. Put extra protection capacity on each link equal to 𝑧𝑓

′ = 1 1 2

• Each link can be restored using two three-link paths

– Example: Link 1-2 can be restored via 1-6-7-2 and 1-8-3-2

• Extra protection cost is 18 and final cost 𝑮 = 36 + 18 = 54

– Substantial gain compared to PD solution, where extra cost was 48 – Moreover, when we admit restoration of only 66% of link capacity, extra cost would be only 12 (compared to 48 as needed for Path Diversity solution)

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Link Capacity Restoration (6) Example for DR/CF/BR/CC/LIN/LR+BR

• Now, assume additional demand 𝒆 = 𝟐𝟒 between

nodes 1 and 4 with demand volume 𝒊𝟐𝟒 realized on path 1-2-7-4

• Suppose link 2-7 fails and capacity is restored on

path 2-3-4-7

• We can see that affected flow 1-2-7-4 is effectively

restored on path 1-2-3-4-7-4, which traverses link 7-4 twice

• Link re-establishment can be intrinsically inefficient

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Partial Link Capacity Restoration

• Partial restoration of links requires

– To use notion of multi-links and its associated links, even though the entire link fails, i.e., all its links fail totally and simultaneously – Need to know exactly how flows using multi-links are realized and which ones traverse protected and which ones unprotected (multi-) links

• Example:

– May assume that only two upper links are reconstructed in case of failure – One half of capacity is restored in case of total failure, other half unprotected

• In practice, link re-establishment requires that

failed link capacity is restored on single path

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Link Capacity Restoration on Single Path (1)

• Design with Link Restoration on Single Path

LP: DR/CF/BR/CC/LIN/LR+SBP Problem

– DR – Restoration Design – CF - Continuous Flow – BR - Bifurcated Routing – CC – Continuous Link Capacity – LIN – Linear Costs – LR+SBP –Link Restoration on Single Backup Path

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Link Capacity Restoration on Single Path(2)

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Link Capacity Restoration on Single Path(3) Changelog

• Constants++ : 𝐿𝑓 upper bound on the normal capacity 𝑧𝑓 of link e
• Variables++ : 𝑣𝑓𝑟 binary flow variable associated with 𝑨𝑓𝑟
• Constraints

– New constraints force 𝑨𝑓𝑟 = 𝑣𝑓𝑟𝑧𝑓 (right side is multiplication of variables that is forbidden in MIP formulations)

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Link Capacity Restoration on Single Path(4)

Example for DR/CF/BR/CC/LIN/LR+SBP

• Non-bifurcated solution for cube network

different than the solution for bifurcated LR

• We could assign 𝑧𝑓

′ = 3 to each link and thus

would double normal capacity

• However, there is a cheaper and in fact optimal solution by

– forming a Hamiltonian cycle, e.g., 1-2-3-4-7-6-5-8-1, – and allocate spare capacity 𝑧𝑓

′ = 3 to every link on cycle

• Resulting Costs

– 8 links → protection costs of 24 and final cost 𝑮 = 36 + 24 = 60 – This is more than for bifurcated LR (36+18) but still much less than for PD (36+48) – If we admit only 66% restoration, extra cost is 16 (12 for bifurcated LR)

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Link Protection via Hot Standby (1)

• MIP:DR/CF/BR/CC/LIN/LP+HS

Link protection via Hot-Standby protection (HS)

– Protecting links via dedicated protection paths – Protection capacity for one link is not shared with the one for other links – Failed link is restored (entirely in case of 100% protection) on one single path – In case of link protection, HS assumes single failures

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Link Protection via Hot Standby (2)

෍

𝑓≠𝑚

෍

𝑟

𝛾𝑚𝑓𝑟𝑨𝑓𝑟 ≤ 𝑧𝑚

′

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Link Protection via Hot Standby (3)

• HS link protection differs from link restoration on single path in one line
• Link Restoration on Single Path
• Hot-Standby

– Difference comes from that HS assumes no shared protection capacity – Sufficient spare capacity on link l required to restore all other links as if they fail simultaneously

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Demand Flow Re-establishment (1)

• Path protection and restoration mechanisms deal directly with demand

flows

• Contrary to link re-establishment, Path Restoration (PR) mechanisms

– restore individual flows rather than link capacities – are not restricted to single link failures

• PR schemes can reuse capacity released by failed flows on

those links of broken paths which survived the failure

1 5 6 3 4 2 Path Re-establishment

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Demand Flow Re-establishment (2) Variants of Demand Flow Re-establishment

• Unrestricted configuration (DR-U)
• Restricted reconfiguration (DR-R)
• Path restoration with situation-dependent back-up paths (PR-SD)
• Path restoration with single back-up paths (PR-FBP and PR-FSBP)
• Hot-Standby path protection (PP-HS)

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Demand Flow Re-establishment - DR-U (1)

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Demand Flow Re-establishment – DR-U(2)

• Unconstrained reconfiguration of flows in case of a failure for decreased

demands ℎ𝑒𝑡 = 𝜓𝑒𝑡ℎ𝑒

• In state s all normal flows can be first disconnected and new flow pattern

can be established in surviving link capacities 𝛽𝑓𝑡𝑧𝑓, 𝑓 = 1,2, … , 𝐹

• Note that in this case the normal operating state 𝑡 = 0 of network plays no

role, situations are labeled with 𝑡 = 1,2, … , 𝑇

• Optimal solution of DR-U and most other restoration design problems

considered in the following are in general bifurcated

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Demand Flow Re-establishment – DR-U(3)

• Assuming single link failures and 100% restoration a DR-U solution is never

more expensive than the solution of link restoration schemes (e.g., DR/CF/BR/CC/LIN/LR+BR)

• Example: Backhaul due to restoration

– One demand d=1 between nodes 1 and 2 ℎ1 = 1 – One failure state with link between 3 and 4 totally failed – Link-re-establishment: restoration of link capacity via path 3-1-5-6-2-4 (protection cost 5) – Path restoration: restoration of broken flow

• n path 1-5-6-2 (protection cost of 3)

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Demand Flow Re-establishment - DR-R (1)

• LP:DR/CF/BR/CC/LIN/PR+RR {DR-R}

Path Restoration with Restricted Reconfiguration

• In transport networks full reconfiguration as with DR-U is not practical
• We need more restricted flow reconfiguration mechanisms
• First Natural Restriction Rule: Unbroken flows are not moved

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Demand Flow Re-establishment - DR-R (2)

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Demand Flow Re-establishment - DR-R (3)

• Indices
• Constants

– Binary availability coefficients required, otherwise with fractional availability coefficients it is unknown which particular flows on the link are broken and lost

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Demand Flow Re-establishment - DR-R (4)

• Variables
• Objective function
• Constraints

– Third constraint ensures that normal flows unaffected by a failure are not moved – But, still possible using unaffected paths for restoring flows from failed paths

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Demand Flow Re-establishment - DR-U vs. DR-R

• Solutions for DR-R (restricted reconfiguration) never cheaper than solutions

for DR-U (unrestricted reconfiguration), which allows to move all flows, even the ones unaffected by a failure

• Solution space of DR-R is in general a proper subset of solution space
• f DR-U
• Optimal DR-R solutions are not necessarily optimal solutions to DR-U

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Demand Flow Re-establishment - DR-SD (1)

• LP:DR/CF/BR/CC/LIN/PR+SDBP {DR-SD}

Path Restoration with Situation-Dependent Backup Paths

– As in DR-R, surviving normal flows are not touched – Next restriction that can be imposed on path restoration mechanisms: Each affected normal flow is moved entirely to pre-determined and situation-dependent backup-path – 100% restoration is assumed

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Demand Flow Re-establishment - DR-SD (2)

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Demand Flow Re-establishment - DR-SD (3) Indices

• Index p now labels whole sequence of paths 𝑸𝑒𝑞 = (𝑄𝑒𝑞𝑡, 𝑡 = 0,1, … , 𝑇)

pre-assigned to demand d;

• Each sequence of paths with fixed d, p is composed of

– normal path 𝑄𝑒𝑞0, – backup path 𝑄𝑒𝑞1 used to protect normal path in state s=1, – backup path 𝑄𝑒𝑞2 to protect in s=2, – ... – backup path 𝑄𝑒𝑞𝑇 that protects 𝑄𝑒𝑞0 in state s=S

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Demand Flow Re-establishment - DR-SD (4) Constants Variables

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Demand Flow Re-establishment - DR-SD (5) Objective function Constraints

• Left-hand side of second constraint is equal to load of link e in state s
• Expression in brackets is equal to part of link load of e induced by normal

flow 𝑦𝑒𝑞0 in state s, either

– directly (because flow survives in state s, including normal network operating state s=0 for which 1 − 𝜄𝑒𝑞0 = 0), – or indirectly because link e belongs to backup path for 𝑄𝑒𝑞0

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Demand Flow Re-establishment - DR-SD (6)

• A path, e.g., path 𝑄𝑗, can appear more than once in candidate path

sequences 𝑞 = 1,2, … , 𝑄𝑒

• 𝑄𝑗 can be assigned a non-zero flow in more than one path sequence

– Hence, total flow assigned to path 𝑄𝑗 can be restored on several paths

• Linear Programming formulation of DR-SD are equivalent to DR-R

in case 𝜓𝑓𝑡 = 1 (100% restoration)

• But in contrast to DR-R, DR-SD formulation allows for simple and concise

expression of requirement that normal flows of demand can be bifurcated, but restoration flows cannot

1 5 6 2 3

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𝑄𝑗 𝑄𝑗+1 𝑄𝑗−1

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Demand Flow Re-establishment – PR-FSBP (1)

• LP:DR/CR/BR/CC/LIN/PR+FDP

Path Restoration with Fixed Backup Paths

– Assumes situation-disjoint normal and backup paths – Formulation similar to DR-DS

• MIP: DR/CF/BR/CC/LIN/PR+FSBP

Path Restoration with Fixed Single Backup Paths

– Normal flow is moved entirely to one backup path – Backup path is the same for all failure situations affecting the normal flow – Normal path 𝑄𝑒𝑞 and its (single) backup path 𝑅𝑒𝑞 need to be situation-disjoint → in all situations when path 𝑄𝑒𝑞 is not available, 𝑅𝑒𝑞 must be available

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Demand Flow Re-establishment – PR-FSBP (2) Indices

• For each fixed d, index p labels all candidate normal paths for demand d
• For each normal path 𝑄𝑒𝑞, index q labels all candidate backup paths 𝑅𝑒𝑞𝑟, situation-

disjoint with path 𝑄𝑒𝑞

– Hence, for each d, a pair of indices (𝑞, 𝑟)(1 ≤ 𝑞 ≤ 𝑄𝑒, 1 ≤ 𝑟 ≤ 𝑅𝑒𝑞) identifies a pair of situation-disjoint paths (𝑄𝑒𝑞, 𝑅𝑒𝑞𝑟) – For fixed d and different p, normal paths 𝑄𝑒𝑞 are different

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Demand Flow Re-establishment – PR-FSBP (3) Constants

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Demand Flow Re-establishment – PR-FSBP (4) Variables

– 𝑣𝑒𝑞𝑟 ensures that entire path flow is moved to another path in case of a failures – Binary variable 𝑣𝑒𝑞𝑟 renders DR-F to be a Mixed Integer Programming Problem

Objective function

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Demand Flow Re-establishment – PR-FSBP (5)

Constraints

• Constraint σ𝑟 𝑣𝑒𝑞𝑟 ≤ 1 together with constraint 𝑦𝑒𝑞𝑟0 ≤ ℎ𝑒𝑣𝑒𝑞𝑟 ensures

– that there is at most one non-zero flow assigned to the set of all routing pairs with the same normal path – and that flow of backup path 𝑅𝑒𝑞𝑟 of normal path 𝑄𝑒𝑞 is equal to 𝑣𝑒𝑞𝑟𝑦𝑒𝑞𝑟0

• Last constraints determines link capacity analogous to DR-SD

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Demand Flow Re-establishment – HS (1)

• MIP:DR/CF/BR/CC/LIN/PP+HS – Path Protection with Hot Standby
• Similar to link protection, path protection can be also achieved via HS
• Paths (flows) are protected by means of dedicated protection paths
• Protection capacity is not shared with protection capacity used for other

paths that fail in other failure situations

• Each failed flow is restored on one single path
• PP+HS assumes that normal protected path and its standby path are

situation-disjoint

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Demand Flow Re-establishment – HS (2) Indices

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Demand Flow Re-establishment – HS (3) Constants

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Demand Flow Re-establishment – HS (4) Variables Objective function

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Demand Flow Re-establishment – HS (5) Constraints

• Constraint σ𝑟 𝑣𝑒𝑞𝑟 ≤ 1 and constraint 𝑦𝑒𝑞𝑟0 ≤ ℎ𝑒𝑣𝑒𝑞𝑟 ensure

– that there is at most one non-zero flow assigned to the set of all routing pairs with the same normal path – and that flow of backup path 𝑅𝑒𝑞𝑟 of normal path 𝑄𝑒𝑞 is equal to 𝑣𝑒𝑞𝑟𝑦𝑒𝑞𝑟0

• Last constraint ensures that backup capacity is reserved in advance

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Restoration Design Extensions

The presented restoration design problems can be extended in many ways

– Non-linear cost/dimensioning functions – Modular link capacities and/or integer flows – Budget constraint – Routing restrictions – Separated normal capacity and protection capacity – Separated normal design and protection design – ...

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Applicability of Resilient Network Design (1)

• Most presented protection/restoration mechanisms applicable to real

networks

• In almost all cases, modular link capacity required for solution
• Unrestricted path flow reconfiguration (DR-U) as most economical solution

in terms of spare (protection) capacity

– Due to least constrained way of utilizing resources that are available in failures states – Requires least amount of protection capacity compared to all other re-establishment mechanisms

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Applicability of Resilient Network Design (2)

End- system Layer 5 Layer 4 Layer 3

Application Layer Transport Layer Network Layer

Layer 2 Layer 1

Data Link Layer Physical Layer

IP

OpenFlow / MPLS / …

End- system Layer 5 Layer 4 Layer 3

Application Layer Transport Layer Network Layer

Layer 2 Layer 1

Data Link Layer Physical Layer

Optical Networks

UDP / TCP SMTP/ POP3 / IMAP/ HTTP / …

Ethernet / GMPLS

SONET/SDH

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Applicability of RND – Backbone IP

• Unrestricted flow reconfiguration (DR-U) as protection mechanism in IP

networks (network layer)

– via adaptively controlled packet routing tables

• Modified DR-U for IP backbone networks running OSPF

– with modification that flow induced by shortest path routing due to state- dependent link metric system 𝑥𝑡 for state s, is reflected as 𝑦𝑒𝑞𝑡(𝒙) (instead of simply 𝑦𝑒𝑞𝑡) – Binary failure coefficients 𝛽𝑓𝑡 should be assumed, otherwise weight-based routing would not work properly – Packet traffic entering network in failure state can throttled by admission control mechanisms in edge routers to control demand coefficients 𝜓𝑒𝑡

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Applicability of RND – MPLS

• Multi-Protocol Label Switching (MPLS) to control traffic for different service

classes, e.g., by MPLS tunnels, on link layer

• Tunnel capacity not necessarily in integral units

→ models with continuous flow variables allowed

• Protection of single end-to-end tunnels:

– Setting up backup tunnel for working tunnel – PR+FBP, PR+FSBP, PP+HS:

• Protection of demands tunneled over multiple parallel end-to-end tunnels

– Tunnels between pairs of nodes, treat them as links supporting IP demand flows – When set of tunnels affected by network failure, they can be restored individually in surviving links capacity – Protection as for single end-to-end tunnels Normal traffic Backup path

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Applicability of RND – Optical Systems

• SONET/SDH and WDM networks (optical networks, link and physical layer)
• Common protection mechanism: 1+1 or 1:1 hot-standby functionality, called

Automatic Protection Switching (APS)

– PP+HS (Hot standby path protection)

• Binary link availability coefficients αes
• Single link failures as most common case
• Manual restoration via network management center

– LR+SBP, PR+SDBP, PR+FBP, PR+FSBP

• SONET/SDH rings

– Link restoration mechanisms Normal traffic Backup path

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Resilient Network Design Summary

• Restoration design to protect and restore network resources (mostly link

capacity) at different layers against resource failures

• Modeling of failure states
• Path diversity
• Link re-establishment:

– Active link capacity restoration – Hot-standby

• Demand flow re-establishment

(path protection and restoration)

– Unrestricted flow reconfiguration – Restricted flow reconfiguration (unaffected flows are not moved) – Hot standby path protection