Publication Review: Cross-layer survivability in WDM-based networks

“Cross-Layer Survivability inWDM-Based Networks”

Genya Ishigaki

The University of Texas at Dallas

November 10, 2016

Agenda

1. Layered Networks

2. Survivability in Single layer networks3. Cross layer Survivability

▶ disjoint paths in layered networks▶ s-t cut▶ edge-connectivity of layered networks

4. Approximation algorithms

2

What is Cross-layer?

IP-over-WDM Networks

▶ Demand for high transmission rate for increasing traffic

▶ Electronic packet switched network (IP) upon fiber network (WDM)

1000 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 19, NO. 4, AUGUST 2011

Cross-Layer Survivability in WDM-Based NetworksKayi Lee, Member, IEEE, Eytan Modiano, Senior Member, IEEE, and Hyang-Won Lee, Member, IEEE

Abstract—In layered networks, a single failure at a lower layermay cause multiple failures in the upper layers. As a result, tra-ditional schemes that protect against single failures may not beeffective in multilayer networks. In this paper, we introduce theproblem of maximizing the connectivity of layered networks. Weshow that connectivity metrics in layered networks have signifi-cantly different meaning than their single-layer counterparts. Re-sults that are fundamental to survivable single-layer network de-sign, such as the Max-Flow Min-Cut Theorem, are no longer ap-plicable to the layered setting. We propose new metrics to measureconnectivity in layered networks and analyze their properties. Weuse one of the metrics, Min Cross Layer Cut, as the objective forthe survivable lightpath routing problem and develop several algo-rithms to produce lightpath routings with high survivability. Thisallows the resulting cross-layer architecture to be resilient to fail-ures between layers.

Index Terms—Connectivity, cross-layer survivability, disjointpaths, lightpath routing, max-flow, min-cut, multicommodity flow,survivable path set.

I. INTRODUCTION

M ODERN communication networks are constructedusing a layered approach, as shown in Fig. 1. Such a

network typically consists of an electronic packet switchednetwork (such as IP). Often, this packet-switched network isbuilt on top of one or more electronic circuit switched transportnetworks (e.g., ATM, SONET; sometimes neither or both), andthese in turn are built upon a fiber network. This multitude oflayers is used in order to simplify network design and opera-tions. However, this layering also leads to certain inefficienciesand interoperability issues. In this paper, we focus on the impactof layering on network survivability.

We examine this problem in the context of wavelengthdivision multiplexing (WDM)-based networks, although theconcepts discussed are equally applicable to other layeredarchitectures (e.g., IP over ATM, ATM over SONET, etc.). In aWDM-based network, the logical topology is defined by a set ofnodes and lightpaths connecting the nodes, while the physicaltopology is defined by a (possibly different) set of nodes andthe fibers connecting them. For example, an IP-over-WDM

Manuscript received September 27, 2009; revised July 09, 2010 andOctober 11, 2010; accepted November 02, 2010; approved by IEEE/ACMTRANSACTIONS ON NETWORKING Editor S. Subramaniam. Date of publicationNovember 29, 2010; date of current version August 17, 2011. This workwas supported by NSF Grants CNS-0626781 and CNS-0830961 and byDTRA Grants HDTRA1-07-1-0004 and HDTRA-09-1-0050. This work waspresented in part at the 28th IEEE Conference on Computer Communications(INFOCOM), Rio de Janeiro, Brazil, April 19–25, 2009.

The authors are with the Massachusetts Institute of Technology, Cambridge,MA 02139 USA (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TNET.2010.2091426

Fig. 1. IP-over-WDM network where the IP routers are connected using opticallightpaths. The logical links (arrowed lines on top) are formed using lightpaths(arrowed lines at the bottom) that are routed on the physical fiber (thick graylines at the bottom). In general, the logical and physical topologies are not thesame.

network consists of IP routers that are connected using (WDM)lightpaths as shown in Fig. 1. Each lightpath is realized bysetting up a physical connection using one of the wavelengthchannels in the optical fibers. For networks where wavelengthconversion capability [1] is unavailable, the lightpaths are alsosubject to the wavelength continuity constraint, which requiresthe lightpath to use the same wavelength channel along thephysical route [2].

Networks often rely on the logical layer for providing protec-tion and restoration services. However, even when the logicaltopology is designed to tolerate single logical link failures, oncethe logical topology is embedded on the physical topology, thelogical topology may no longer be survivable to single phys-ical (fiber) link failures. This is because each physical fiber linkmay carry multiple lightpaths. Hence, the failure of a singlefiber link can lead to the failure of multiple links in the logicaltopology, which may subsequently leave the logical topologydisconnected.

As a simple illustrative example, consider the physical andlogical topologies shown in Fig. 2(a) and (b). The lightpaths inthe logical topology are routed over the physical topology intwo different ways in Fig. 2(c) and (d). In Fig. 2(c), a failureof physical fiber (1, 5) would cause lightpaths (1, 5) and (3, 5)to fail. Consequently, node 5 will be disconnected from othernodes in the logical topology. On the other hand, in Fig. 2(d),the logical topology will remain connected even if one of thefibers fails. The above example demonstrates that in a multilayernetwork, a physical link failure can result in multiple logical linkfailures, and that the routing of the logical links on the physicaltopology has a big impact on the connectivity of the multilayernetwork.

In contrast to the simplified example of Fig. 2, real-life net-works are highly intertwined and layered. However, due to thelack of general understanding of the issues in cross-layer sur-vivability, most existing protection and restoration mechanismsare based on principles that are applicable only to single-layer

1063-6692/$26.00 © 2010 IEEE

IP-over-WDM layered network

3

Lightpath routing

Layer Elements

▶ logical topology is defined by a set of nodes and lightpathsconnecting the nodes

▶ physical topology is defined by a (possibly different) set of nodesand the fibers connecting them

Request (logical layer)(1, 2)

Routes (physical layer){(1, 3, 4, 2), (1, 5, 6, 2),

(1, 3, 5, 6, 2), ...}

v1 v2

v3 v4

v5 v6

v1 v2

4

Graph Theory Review

Cut C(s, t)

the set of edges (links) whose removal disconnects node s and t

Menger’s theorem

The size of the minimum edge cut for |C(s, t)| is equal to the maximumnumber of pairwise edge disjoint paths from node s to t

C(v1, v2)1. {e(v1, v5), e(v1, v3)}2. {e(v3, v4), e(v3, v6), e(v5, v6)}

v1 v2

v3 v4

v5 v6

① ②

5

Survivability in single network

Edge-connectivity χ(G)

the minimum number of edges (links) whose removal separate aconnected graph G to two or more components († the size of minimumcut)

C(v1, v2), C(v2, v3), ...

χ(G) = 2v1 v2

v3 v4

v5 v6

① ②

6

Research objective

How to extend the concept of connectivity (cut-set) in single layernetworks to the context of layered networks?

1. disjoint paths in cross layer routing

2. s-t cut problem in layered networks

3. connectivity of layered networks based on the s-t cut

7

References

1. disjoint paths in cross layer routing

2. s-t cut problem in layered networks

3. connectivity of layered networks based on the s-t cut

E. Modiano and A. Narula-Tam, “Survivable lightpath routing: a new approach tothe design of wdm-based networks,” IEEE Journal on Selected Areas inCommunications, vol. 20, pp. 800 - 809, May 2002.

K. Lee, E. Modiano, and H. W. Lee, “Cross-layer survivability in wdm-basednetworks,” IEEE/ACM Transactions on Networking, vol. 19, pp. 1000 -1013, Aug2011.

8

1. Survivable routing

Survivable Routing problem

▶ Physical and logical networks, GP = (VP , EP ) and GL = (VL, EL)

▶ Routing defined by a |EL| × |EP | matrix F whose elementfstij ∈ {0, 1}

▶ E(s, t) = {(i, j) | fstij = 1}.

▶ Is there a routing matrix F that satisfies∩(s,t)∈C(S,S)

E(s, t) = ∅ ∀S ⊂ NL

9

1. Survivable routing e.g.

Given GP = (VP , EP ) and GL =(VL, EL),Is there a routing matrix F thatsatisfies∩(s,t)∈C(S,S)

E(s, t) ̸= ∅ ∀S ⊂ NL

s1

s2

t2

t1

S

s1 t1

s2t2

10

1. Survivable routing e.g.

Given GP = (VP , EP ) and GL =(VL, EL),Is there a routing matrix F thatsatisfies∩(s,t)∈C(S,S)

E(s, t) = ∅ ∀S ⊂ NL

s1

s2

t2

t1

S

s1 t1

s2t2

11

2. Cross Layer s-t MinCut

MinCut for logical node pair s-t

Minimize∑

(i,j)∈EP

yij

subject to∑

(i,j)∈L(p)

yij ≥ 1 ∀p ∈ Pst

yij ∈ {0, 1} ∀(i, j) ∈ EP

L(p) :={(i, j)

∣∣ fstij = 1

}When yij = 1, link (i, j) is an element of a cut.

12

2. Cross Layer s-t MinCut e.g.

Minimize∑

(i,j)∈EP

yij

subject to∑

(i,j)∈L(p)

yij ≥ 1 ∀p ∈ Pst

yij ∈ {0, 1} ∀(i, j) ∈ EP

L(p) :={(i, j)

∣∣ fstij = 1

}

s1 t1

s1 t1

i j

13

2. Cross Layer s-t MinCut

▶ NP-hardness is proved from the reduction to Minimum Set Coverproblem

Minimum Set Cover

Given Set E, family of subsets of E: F = {f1, f2, ..., fm},Find minimum sub-family F∗ that satisfies

∪f∈F∗ f = E

MinCut Reduction

Given Logical link set EL = {ei}, family of subsets of EL (Use ofphysical fibers by logical links): F = {f1, f2, ..., f|EP |},Find minimum sub-family F∗ that satisfies

∪f∈F∗ f = EL

▶ inapproximability result follows from the inapproximability ofMinimum Set Cover problem: there does not exit O(log n)-factorapproximation algorithm for this problem.

14

3. Connectivity of layered networks

Minimum Cross Layer Cut (MCLC)

MCLC = minS⊂VL

HS , (1)

where S is a subset of logical node set VL, and HS is the minimumnumber of physical fibers in EP needed for disconnecting all links in cutC(S, S)

▶ Maximize MCLC (= connectivity maximization in single layernetwork)

▶ NP-hardness is proved because it contains s-t MinCut

15

Routing for MCLC Maximization

The size of minimum cut (MCLC = minS⊂VL HS) depends on light pathrouting.MCLC + lightpath routing = MFC

Routing for MCLC Maximization

▶ F : set of all possible lightpath routings

▶ MFC(f, S): the minimum number of fibers whose removaldisconnects all logical links in the cut set C(S, S) given thelightpath routing f ∈ F

maxf∈F

minS⊂VL

MFC(f, S) (2)

▶ No simple way to express MCLC using linear programming

16

Approximate MCLC

Algorithms

▶ Simple Multi-commodity Flow Formulation MCFw

▶ identity weight function widentity

▶ MinCut weight function wMinCut

▶ Enhanced Multi-commodity Flow Formulation MCFLF

Existing algorithm (for comparison)

▶ Survivable Lightpath Routing formulation (SURVIVE), whichcomputes the lightpath routing that minimizes the total fiber hops,subject to the constraint that the MCLC must be at least 2.

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Preliminary

Multi-commodity Flow Problem

Minimize χ(f)

subject to fstij ∈ {0, 1}{(i, j) ∈ EP

∣∣ fstij = 1

}forms an (s, t)-path ∀(s, t) ∈ EL

if we have wavelength continuity constraint, any wavelength λ on aphysical fiber is used by at most one lightpath{

(i, j) ∈ EP

∣∣ fstijλ = 1

}forms an (s, t)-path on wl λ ∀(s, t) ∈ EL∑

(s,t)∈EL

fstijλ ≤ 1 ∀(i, j) ∈ EP , ∀λ

18

Simple Multi-cmdity Flow MCFw

Attempt

the multi-commodity flow formulation will try to spread the weight of thelightpaths across multiple fibers, thereby minimizing the impact of anysingle fiber failure.

The objective function ρw measures the maximum load of the fibers,where the load is defined to be the total lightpath weight carried by thefiber.

Minimize ρw

subject to ρw ≥∑

(s,t)∈EL

w(s, t)fstij ∀(i, j) ∈ EP

fstij ∈ {0, 1}{(i, j) ∈ EP

∣∣ fstij = 1


19


s1

s2

t2

t1

S

s1 t1

s2t2

s1

s2

t2

t1

S

s1 t1

s2t2

20


Minimize ρw


(s,t)∈EL


fstij ∈ {0, 1}{(i, j) ∈ EP

∣∣ fstij = 1


weight w(s, t)

▶ widentity = 1: minimize the number of lightpaths traversing thesame fiber

▶ wMinCut =1

|CL(s, t)|, where CL(s, t) is minimum s-t cut in logical

layer. if an edge (s, t) belongs to a smaller cut (more fragile), it willbe assigned a higher weight. The algorithm will try to avoid puttingthese small cut edges (fragile pairs) on the same fiber.

21


widentity = 1: minimize the number of lightpaths traversing the samefiber

s1 t1

s1 t1

i j

1 1 1

0

0 0

0

22


widentity = 1: minimize the number of lightpaths traversing the samefiber

s1 t1

s1 t1

i j

1 1 + 1 1

0

0 0

0

s2 t2

s2

t2

23


wMinCut =1

|CL(s,t)| , where CL(s, t) is minimum s-t cut in logical layer. if

an edge (s, t) belongs to a smaller cut (more fragile), it will be assigned ahigher weight. The algorithm will try to avoid putting these small cutedges (fragile pairs) on the same fiber.

s1 t1

s1 t1

i j

1/3 1/3 1/3

0

0 0

0

the connection btwn s1 and t1 can be sustained even after link (s1, t1) fails.

24


wMinCut =1

|CL(s,t)| , where CL(s, t) is minimum s-t cut in logical layer. if

an edge (s, t) belongs to a smaller cut (more fragile), it will be assigned ahigher weight. The algorithm will try to avoid putting these small cutedges (fragile pairs) on the same fiber.

s1 t1

s1 t1

i j

1/1 1/1 1/1

0

0 0

0

link (i, j) is critical to sustain the connection btwn s1 and t1.

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Enhanced Multi-cmdity Flow MCFLF

Attempt

the multi-commodity flow formulation will try to spread the weight of thelightpaths across multiple fibers, thereby minimizing the impact of anysingle fiber failure.

γ means that given logical cut C(S, S), how much percent of logicalconnections between S and S depends on physical fiber (i, j)?

Minimize γ

subject to γ∣∣C(S, S)

∣∣ ≥ ∑(s,t)∈C(S,S)

fstij ∀(i, j) ∈ EP , S ⊂ VL

fstij ∈ {0, 1}{(i, j) ∈ EP

∣∣ fstij = 1


26


γ∣∣C(S, S)

∣∣ ≥ ∑(s,t)∈C(S,S) f

stij ∀(i, j) ∈ EP , S ⊂ VL

s1

s2

t2

t1

S

s1 t1

s2t2

ji

1/2

1/2

2/2

1/2

1/2

27


γ∣∣C(S, S)

∣∣ ≥ ∑(s,t)∈C(S,S) f

stij ∀(i, j) ∈ EP , S ⊂ VL

s1

s2

t2

t1

S

s1 t1

s2t2

ji

1/2

1/2

1/2

1/21/2

1/228

Difference btwn MCFw and MCFLF

MCFw

Minimize ρw


(s,t)∈EL


MCFLF

Minimize γ

subject to γ∣∣C(S, S)

∣∣ ≥ ∑(s,t)∈C(S,S)

fstij ∀(i, j) ∈ EP , S ⊂ VL

C(S, S) ⊂ EL

Theorem

ρw ≥ γ 29

Simulation

Settings

▶ NSFNET for physical topology (amended so that it has connectivity4)

▶ 350 random logical topologies with connectivity at least 4 and sizeranging from 6 to 12 nodes

1008 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 19, NO. 4, AUGUST 2011

Fig. 4. Augmented NSFNET. The dashed lines are the new links.

Fig. 5. MCLC performance of randomized rounding versus ILP.

TABLE IAVERAGE RUNNING TIME OF AND

which is less than a minute. In fact, our simulation on largernetworks shows that the algorithm often fails to terminatewithin a day when the network size goes beyond 12 nodes. Onthe other hand, the algorithm for is able toterminate consistently within 2 h for very large instances with a100-node physical topology and 50-node logical topology. Thisshows that the randomized approach is a much more scalablesolution to compute survivable lightpath routings.

In Fig. 5, the survivability performance of the randomized al-gorithm is compared with its ILP counterpart. Each data point inthe figure is the MCLC average of 50 random instances with thegiven logical network size. As our result shows, the lightpathroutings produced by have higher MCLC valuesthan solving the ILP optimally. This is because the objectivevalue for ILP is a lower bound on MCLC. As we willsee in Section V-A.3, this lower bound is often not tight enoughto accurately reflect the MCLC value, and the optimal solu-tion to the ILP does not necessarily yield a lightpath routingwith maximum MCLC. On the other hand, the randomized al-gorithm generates lightpath routings nondeterministically basedon the optimal fractional solution of . Therefore, it ap-proximates the lightpath routing given by the ILP, with an ad-ditional randomization component to explore better solutions.

Fig. 6. Augmented USIP network. The dashed lines are the new links.

When the randomized rounding process is repeated many times,the algorithm often encounters a solution that is even better thanthe one given by the ILP.

To sum up, randomized rounding provides an efficient alter-native to solving integer programs without observable qualitydegradation. This allows us to experiment with more complexformulations in larger networks where solving the integerprograms optimally is infeasible. In the next section, we willcompare the different formulations introduced in Section IV-A,using randomized rounding to compute the lightpath routings.

2) Lightpath Routing With Different Formulations: In thisexperiment, we study the survivability performance of thelightpath routings generated by the formulations introducedin Section IV. We use the 24-node USIP network (Fig. 6),augmented to have connectivity 4, as the physical topology.We generate 500 random graphs with connectivity 4 and sizeranging from 6 to 15 nodes as logical topologies.

We compare the MCLC performance of the lightpathroutings generated by the randomized rounding algorithm,

, on the following formulations:1) Multicommodity Flow , with the identity weight

function, i.e., for all ;2) Multicommodity Flow , with the weight function

introduced in Section IV-A ;3) Enhanced Multicommodity Flow .For comparison, we also run randomized rounding on the Sur-

vivable Lightpath Routing formulation , introducedin [7], which computes the lightpath routing that minimizes thetotal fiber hops, subject to the constraint that the MCLC mustbe at least 2.

Fig. 7 compares the average MCLC values of the lightpathroutings computed by the four different algorithms. Overall,the formulations introduced in this paper achieve better surviv-ability than . This is because these formulations tryto maximize the MCLC in their objective functions, whereas

minimizes the physical hops. Therefore, eventhough does well in finding a survivable routing(i.e., ), the new formulations are able to achieveeven higher MCLC values, which allow more physical failuresto be tolerated.

To further verify the survivability performance of the light-path routings from a different perspective, for each lightpathrouting, we simulated the scenario where each physical linkfails independently with probability 0.01. Fig. 8 shows the

NSFNET (amended).

30

SimulationLEE et al.: CROSS-LAYER SURVIVABILITY IN WDM-BASED NETWORKS 1009

Fig. 7. MCLC performance of different formulations.

Fig. 8. Probability that logical topology becomes disconnected if physical linksfail independently with probability 0.01.

average probability that the logical topology becomes discon-nected under this scenario. The result is consistent with Fig. 7,as lightpath routings with higher MCLC values can toleratemore physical failures, and the logical topologies are thus morelikely to stay connected.

The quality of the lightpath routing also depends on thegraph structures captured by the formulations. Compared to

, the formulation uses a weight functionthat captures the connectivity structure of the logical topology.As a result, the algorithm will try to avoid putting edges thatbelong to smaller cuts onto the same physical link, therebyminimizing the impact of a physical link failure on thesecritical edges. This allows the algorithm to producelightpath routings with higher MCLC values than .

As the number of logical links increases with the size of thelogical topology, the maximum fiber link load becomes less ef-fective in capturing the impact of fiber failures for the logicalcuts. As a result, the performance of the simple multicommodityformulations degrades somewhat rapidly. On the other hand, theenhanced formulation captures the connectivity struc-ture of the logical topology in much greater detail by having aconstraint to describe the impact of a physical link failure toeach logic cut. Therefore, this formulation is able to providelightpath routings with the highest MCLC values. This observa-tion is supported by Theorem 9, which states that the objectivemaximized by is closer to the actual MCLC value.

3) Lower Bound Comparison: In Theorem 9, we establishdifferent lower bounds for the MCLC. In this experiment, we

Fig. 9. Comparison among Min Cross Layer Cut (MCLC), Weighted LoadFactor (WLF), and the optimal values of and .

measure these lower bound values for 500 different lightpathroutings and compare them to the actual MCLC values.

As Fig. 9 shows, the Weighted Load Factor is a veryclose approximation of the Min Cross Layer Cut. Among the500 routings being investigated, the two metrics are identicalin 368 cases. This suggests a tight connection between thetwo metrics, which also justifies the choice of such metrics assurvivability measures.

The figure also reveals a strong correlation between theMCLC performance and the tightness of the lower bounds givenby the multicommodity flow formulations in Section IV-A.Compared to , the formulation provides anobjective value that is closer to the actual MCLC value of thelightpath routing. This translates to better lightpath routings,as we saw in Fig. 7. Since there is still a large gap betweenthe objective value and the MCLC value, this suggestsroom for further improvement with a formulation that gives abetter MCLC lower bound.

To summarize this section, a good formulation that properlycaptures the cross-layer connectivity structure is essential forgenerating lightpath routings with high survivability. Combinedwith randomized rounding, it gives a powerful tool for designinghighly survivable layered networks.

VI. CONCLUSION

In this paper, we introduce the problem of maximizing theconnectivity of layered networks. We show that survivabilitymetrics in multilayer networks have significantly differentmeaning than their single-layer counterparts. We proposetwo survivability metrics, the Min Cross Layer Cut and theWeighted Load Factor, that measure the connectivity of a mul-tilayer network and develop linear and integer formulations tocompute these metrics. In addition, we use the metric Min CrossLayer Cut as the objective for the survivable lightpath routingproblem and develop multicommodity flow formulations toapproximate this objective. We show, through simulations, thatour algorithms produce lightpath routings with significantlybetter Min Cross Layer Cut values than existing survivablelightpath routing algorithm.

Our simulation shows that a good formulation, combinedwith the randomized rounding technique, provides a powerfultool for generating highly survivable layered networks. There-fore, an important direction for future research is to establish

MCLC performance of different formulations.

31

Simulation

LEE et al.: CROSS-LAYER SURVIVABILITY IN WDM-BASED NETWORKS 1009

Fig. 7. MCLC performance of different formulations.

Fig. 8. Probability that logical topology becomes disconnected if physical linksfail independently with probability 0.01.

average probability that the logical topology becomes discon-nected under this scenario. The result is consistent with Fig. 7,as lightpath routings with higher MCLC values can toleratemore physical failures, and the logical topologies are thus morelikely to stay connected.

The quality of the lightpath routing also depends on thegraph structures captured by the formulations. Compared to

, the formulation uses a weight functionthat captures the connectivity structure of the logical topology.As a result, the algorithm will try to avoid putting edges thatbelong to smaller cuts onto the same physical link, therebyminimizing the impact of a physical link failure on thesecritical edges. This allows the algorithm to producelightpath routings with higher MCLC values than .

As the number of logical links increases with the size of thelogical topology, the maximum fiber link load becomes less ef-fective in capturing the impact of fiber failures for the logicalcuts. As a result, the performance of the simple multicommodityformulations degrades somewhat rapidly. On the other hand, theenhanced formulation captures the connectivity struc-ture of the logical topology in much greater detail by having aconstraint to describe the impact of a physical link failure toeach logic cut. Therefore, this formulation is able to providelightpath routings with the highest MCLC values. This observa-tion is supported by Theorem 9, which states that the objectivemaximized by is closer to the actual MCLC value.

3) Lower Bound Comparison: In Theorem 9, we establishdifferent lower bounds for the MCLC. In this experiment, we

Fig. 9. Comparison among Min Cross Layer Cut (MCLC), Weighted LoadFactor (WLF), and the optimal values of and .

measure these lower bound values for 500 different lightpathroutings and compare them to the actual MCLC values.

As Fig. 9 shows, the Weighted Load Factor is a veryclose approximation of the Min Cross Layer Cut. Among the500 routings being investigated, the two metrics are identicalin 368 cases. This suggests a tight connection between thetwo metrics, which also justifies the choice of such metrics assurvivability measures.

The figure also reveals a strong correlation between theMCLC performance and the tightness of the lower bounds givenby the multicommodity flow formulations in Section IV-A.Compared to , the formulation provides anobjective value that is closer to the actual MCLC value of thelightpath routing. This translates to better lightpath routings,as we saw in Fig. 7. Since there is still a large gap betweenthe objective value and the MCLC value, this suggestsroom for further improvement with a formulation that gives abetter MCLC lower bound.

To summarize this section, a good formulation that properlycaptures the cross-layer connectivity structure is essential forgenerating lightpath routings with high survivability. Combinedwith randomized rounding, it gives a powerful tool for designinghighly survivable layered networks.

VI. CONCLUSION

In this paper, we introduce the problem of maximizing theconnectivity of layered networks. We show that survivabilitymetrics in multilayer networks have significantly differentmeaning than their single-layer counterparts. We proposetwo survivability metrics, the Min Cross Layer Cut and theWeighted Load Factor, that measure the connectivity of a mul-tilayer network and develop linear and integer formulations tocompute these metrics. In addition, we use the metric Min CrossLayer Cut as the objective for the survivable lightpath routingproblem and develop multicommodity flow formulations toapproximate this objective. We show, through simulations, thatour algorithms produce lightpath routings with significantlybetter Min Cross Layer Cut values than existing survivablelightpath routing algorithm.

Our simulation shows that a good formulation, combinedwith the randomized rounding technique, provides a powerfultool for generating highly survivable layered networks. There-fore, an important direction for future research is to establish

Probability that logical topology becomes disconnected if physical links failindependently with probability 0.01.

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Summary

▶ Survivability in single layer networks▶ Cross layer Survivability

▶ disjoint paths in layered networks (SURVIVE routing)▶ s-t cut (s-t MinCut)▶ edge-connectivity of layered networks (MCLC)

▶ Approximation algorithms▶ Simple Multi-commodity flow based▶ Enhanced Multi-commodity flow based

▶ SimulationEnhanced approximation algorithm demonstrating itsbetter performance in MCLC maximization

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Publication Review: Cross-layer survivability in WDM-based networks

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