Logical Topology Survivability in IP-over-WDM Networks - DRCN 2011

Logical Topology Survivability in IP-over-WDMNetworks: Survivable Lightpath Routing for

Maximum Logical Topology Capacity and MinimumSpare Capacity Requirements

Tachun Lin1 Zhili Zhou2 Krishnaiyan Thulasiraman1

1School of Computer Science, University of OklahomaOklahoma, USA

2IBM T. J. Watson Research CenterNew York, USA

T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 1 / 33

IP-over-WDM Network

Two-layer networkIP (logical) networkWDM (physical) network

Concept of lightpath

(a) A logical link (IP link) (b) A lightpath corresponding to the logical link(1,4) in physical topology.


Survivability in IP-over-WDM Networks

(a) Logical topology. (b) An unsurvivable mapping.

(c) A survivable mapping.


Capacitated IP-over-WDM Networks

a

b c

2

1

2

a

b

c 2

2

3

1

2 2 3

3

a

b

c 2

2

3

1

2 2 3

3

(a) Logical topology (b) Physical topology

a

b

c 2

2

3

1

2 2 3

3 (c) Survivable and all demands are satisfied (d) Survivable and (a,c) demand is not satisfied

a

b

c 2

2

3

1

2 2 3

3 (e) Not survivable but all demands are satisfied


Pioneer Works

Modiano and Narula-Tam, “Survivable routing of logical topologiesin WDM networks”, INFOCOM 2001

Propose ILP formulation to solve the survivable routing problemRequired to enumerate ALL CUTSETS in the topology

Kurant and Thiran, “Survivable mapping algorithm by ring trimming(SMART) for large IP-over-WDM networks”, BroadNets, 2004

Propose structural approach based on piecewise survivability andheuristics

Thulasiraman et al., “Circuits/Cutsets duality and a unifiedalgorithms framework for survivable logical topology design inIP-over-WDM optical networks”, INFOCOM 2009

Study and extend the structural approach using circuits/dualityPropose CITCUIT-SMART, CUTSET-SMART, andINCIDENCE-SMART algorithms


Definitions

DefinitionWeakly survivable routing: a lightpath routing that guarantees thelogical topology remains connected after a single physical link failure

DefinitionStrongly survivable routing: a weakly survivable routing thatguarantees all logical demands are satisfied

DefinitionSpare capacity: additional capacity added to physical links to satisfylogical demands


Problem Description

Problem 1:Given a capacitated IP-over-WDM network with demands onlogical linksFind a weakly survivable routing for the logical topology withdifferent optimization criteria

Maximize total logical demand satisfiedMaximize demand satisfaction on one logical link

Rerouting after a physical link failure to achieve maximum demandsatisfaction


Problem Description

Problem 2:Given a capacitated IP-over-WDM network with demands onlogical linksFind a strongly survivable routing for the logical topology whichrequires minimum spare capacity


Weakly Survivable Routing – MILP Approach

Two-stage approachFirst stage:

Weakly survivable routingMaximize demand satisfaction

Second stage:Minimize maximum unsatisfied demand through rerouting


Weakly Survivable Routing – MILP Approach

Variables used in MILP formulation

Variable Description Info.yst

ij binary variable indicates whether the logical link(s, t) ∈ EL is routed through the physical link(i, j) ∈ EP . If yes, yst

ij = 1, otherwise, ystij = 0.

first stage for Problem 1.

f stij flow on physical link (i, j) due to lightpath (s, t) first stage for Problem 1.

r ijst fractional variable for connectivity constraints. first stage for Problem 1.ρst the capacity for the logical link (s, t), where ρst

is the smallest capacity of links in the lightpath.first stage for Problem 1.

θ variable for max single logical link capacity. first stage for Problem 1.cij capacity on the physical link (i, j). given.dst demand for the logical link (s, t). given.uij link utilization request on the physical link (i, j) given.λst

ij maximal flow for logical link (s, t) after a physicallink failure and re-routing

second stage for Problem 1.

xstk`ij rerouted flow on (k, `) which can be maintained

after the physical link (i, j) failure and re-routing.second stage for Problem 1.

zstk`ij binary variable indicates whether (s, t) re-route

through (k, `) after (i, j) failure.second stage for Problem 1.

ηij amount of spare capacity required on the physi-cal link (i, j) to satisfy strong survivability

second stage of Problem 2.

M a large positive number Problem 1.


Weakly Survivable Routing – MILP Approach (FirstStage)

Lightpath constraint:∑(i,j)∈EP

ystij −

∑(j,i)∈EP

ystji = 1, if s = i , (s, t) ∈ EL (1)

∑(i,j)∈EP

ystij −

∑(j,i)∈EP

ystji = −1, if t = i , (s, t) ∈ EL (2)

∑(i,j)∈EP

ystij −

∑(j,i)∈EP

ystji = 0, otherwise, (s, t) ∈ EL (3)

ystij + yst

ji ≤ 1, (i , j) ∈ EP , (s, t) ∈ EL (4)

selects a lightpath for each logical link



Flow equivalent constraint:

f stk` + M(yst

k` − 1) ≤ f stpq + M(1− yst

pq), (5)

(s, t) ∈ EL, (k , `), (p,q) ∈ EP , (k , `) 6= (p,q)

guarantees that the flow on each selected lightpath is the same for everyphysical link in the lightpath



Flow conservation constraint:∑(i,j)∈EP

f stij −

∑(j,i)∈EP

f stji = ρst , if s = i, (s, t) ∈ EL (6)

∑(i,j)∈EP

f stij −

∑(j,i)∈EP

f stji = −ρst , if t = i, (s, t) ∈ EL (7)

∑(i,j)∈EP

f stij −

∑(j,i)∈EP

f stji = 0, otherwise, (s, t) ∈ EL (8)

ρst ≤ dst , (s, t) ∈ EL (9)

requires the flow on each selected lightpath to be less than or equal to thelogical demandBounded flow constraint:

(f stij + f st

ji ) ≤ My stij , (i, j) ∈ EP , (s, t) ∈ EL (10)

assures that each physical link carries flow only if the lightpath(s) route throughthe physical link



Capacity constraint:∑(s,t)∈EL

(f stij + f st

ji ) ≤ cij , (i , j) ∈ EP (11)

guarantees that the flow on a physical link will not exceed the capacity ofthe physical link

Congestion constraint (optional):∑(s,t)∈EL

(ystij + yst

ji ) ≤ uij , (i , j) ∈ EP , (12)



Idea: if there exists a logical spanning tree after any physical link failure, therouting is survivable (based upon Q. Deng et al., “Survivable IP over WDM: amathematical programming problem formulation,” Allerton Conference onCommunication, Control and Computing, 2002)For each physical link (i, j), the set of logical links (s, t) for which r ij

st 6= 0 mustform a spanning tree in the logical topology this guarantees that unfailed logicallinks form a connected graphSurvivability constraint:∑

(s,t)∈EL

r ijst −

∑(t,s)∈EL

r ijts = −1, if s = v1, (i, j) ∈ EP , (13)

∑(s,t)∈EL

r ijst −

∑(t,s)∈EL

r ijts =

1|VL| − 1

, otherwise, (i, j) ∈ EP , (14)

0 ≤ r ijst ≤ 1− (y st

ij + y stji ), (i, j) ∈ EP , (s, t) ∈ EL, (15)

0 ≤ r ijts ≤ 1− (y st

ij + y stji ), (i, j) ∈ EP , (s, t) ∈ EL (16)

Benefit: do not need to enumerate all cutsetsT. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 15 / 33


Objective: maximize total logical link demands:

max∑

(s,t)∈EL

ρst (17)

s.t . Constraint (1)–(11), (13)–(16),

ystij ∈ {0,1}, r st

ij ≥ 0, f stij ≥ 0, ρst ≥ 0 (i , j) ∈ EP , (s, t) ∈ EL (18)

Objective: maximize the minimum demand satisfaction on a singlelogical link:

max θs.t. θ ≤ ρst (19)


Weakly Survivable Routing – MILP Approach (SecondStage)

Rij : a set of logical links which is disconnected due to the failure ofphysical link (i , j)

Re-routing constraint: For all (i , j) ∈ EP∑(k,`)∈EP\{(i,j)}

zstkìj −

∑(`,k)∈EP\{(i,j)}

zst`kij = 1, if s = k , (s, t) ∈ Rij (20)

∑(k,`)∈EP\{(i,j)}

zstkìj −

∑(`,k)∈EP\{(i,j)}

zst`kij = −1, if t = k , (s, t) ∈ Rij (21)

∑(k,`)∈EP\{(i,j)}

zstkìj −

∑(`,k)∈EP\{(i,j)}

zst`kij = 0, otherwise, (s, t) ∈ Rij (22)

finds alternative lightpath for disrupted logical link (s, t)



Residual capacity constraint: For all (i , j) ∈ EP∑(s,t)∈Rij

(xstkìj + xst

`kij) ≤ ck` −∑

(u,v)∈EL\Rij

ρ∗uv yuv∗k` , (k , `) ∈ EP \ {(i , j)} (23)

xstkìj ≤ Mzst

kìj , (s, t) ∈ Rij , (k , `) ∈ EP \ {(i , j)} (24)

λstij ≥ xst

kìj , (s, t) ∈ Rij , (k , `) ∈ EP \ {(i , j)} (25)

λstij ≤ xst

kìj + M(1− zstkìj), (s, t) ∈ Rij , (k , `) ∈ EP \ {(i , j)} (26)

assures that each physical link on alternative lightpath for disruptedlogical link carry flow up to its capacity



Flow equivalence constraint:

xstk`ij + M(zst

k`ij − 1) ≤ xstpqij + M(1− zst

pqij), (27)

(s, t) ∈ Rij , (k , `), (p,q) ∈ EP \ {(i , j)}

guarantees that the flow on physical links of alternative lightpath will beequivalent



Objective: maximum demand satisfaction

max∑

(s,t)∈EL

∑(i,j)∈EP

λstij (28)

s.t . Constraints (20) to (27),

zstk`ij ∈ {0,1}, λst

ij , xstk`ij ≥ 0,

(i , j) ∈ EP , (s, t) ∈ EL, (k , `) ∈ EP \ {(i , j)} (29)


Strongly Survivable Routing – MILP Approach

First stageWeakly survivable routing

max∑

(s,t)∈EL

ρst (30)

s.t . Constraint (1)–(10), (12)–(15)

Second stageMinimize spare capacity required to satisfy all demands after failure

min∑

(i,j)∈EP

ηij (31)

s.t . Constraints (19) to (21), (23) to (26),∑(s,t)∈Rij

dst(zstk`ij + zst

`kij) ≤ ck` −∑

(s,t)∈EL\Rij

ρ∗styst∗k` + ηk`, (22

′)

(i , j) ∈ EP , (k , `) ∈ EP \ (i , j)


Weakly Survivable Heuristics – First Stage

Assumption: all demands can be satisfied by physical link capacityINCIDENCE-SMART+Augmentation

Identify datum node 4 (logical node with the highest degree)

If there exists a logical node v with degree ≥ 2

Find edge-disjoint lightpaths for any two adjacent edges of vRemove v and all adjacent edges of v

If there exists a logical node v with degree = 1 (logical edge (u, v))

Augment (u, v) with a parallel edge (u′, v

′)

Find edge-disjoint lightpaths for (u, v) and (u′, v

′)

Remove (u, v)

If there exists a logical node v with degree = 0 (individual node)

Add two parallel edges connecting (v ,4)Find two edge-disjoint lightpaths for (v ,4)Remove v


INCIDENCE-SMART: An Example

(a) (b) Logical topology GL, v4 is the da-tum vertex.



INC(v1), INC(v2), INC(v3), INC(v5) is an INC-sequence of lengthk = 4Iteration 1:

Pick v1, Degree v1 ≥ 2 in the current graph. Map at most two edgesincident on v1({e1,e5}) into disjoint lightpathsDelete {e1,e5,e6,e7} from the graph

(a) (b) (c)



Iteration 2:Pick v2, Degree v2 ≥ 2 in the current graph. Map at most two edgesincident on v2 {e2,e8} into disjoint lightpathsDelete {e2,e8,e9} from the graph

(a) (b) (c)



Iteration 3:Pick v3, Degree v3 = 2 in the current graph. Map the two edgesincident on v3 {e3,e10} into disjoint lightpathsDelete {e3,e10} from the graph

Iteration 4:Pick v5, Degree v5 = 1 in the current graphProvide a protection edge eMap e and e4 into disjoint lightpathsDelete {e,e4} from the graph

(a) (b) (c)


Solution in General Case

K. Thulasiraman, Muhammad Javed, Tachun Lin, Guoliang (Larry)Xue, “Logical topology augmentation for guaranteed survivabilityunder multiple failures in IP-over-WDM optical networks”, IEEEANTS, 2009K. Thulasiraman, Tachun Lin, Muhammad Javed, Guoliang (Larry)Xue, “Logical topology augmentation for guaranteed survivabilityunder multiple failures in IP-over-WDM optical networks”, OpticalSwitching and Networking, 2010


Weakly Survivable Heuristics – Second Stage

For each physical link (i , j)Find out a set of logical links Rij which will be disconnected if (i , j)failsCalculate the residual capacity on each physical link after (i , j) failsFor each logical link in Rij

Find an alternative lightpath which avoids (i, j) and has maximalresidual capacity along the pathCalculate the demand which can be satisfied with the alternativelightpathSubtract the satisfied demands from the specified demands


Strongly Survivable Heuristics – Second Stage

For each physical link (i , j)Find out a set of logical links Rij which will be disconnected if (i , j)failsCalculate the residual capacity on each physical link after (i , j) failsFor each logical link in Rij

Find an alternative lightpath which avoids (i, j) and has maximalresidual capacity along the pathCalculate the (extra) capacity required to satisfy with the alternativelightpath

Calculate the total extra capacity to be added to physical links tosatisfy all logical demands after any single physical link failure


Simulation Results

Tested physical topologies

1 2

3 4

(a) SMALL (b) G3 (c) G6

(d) EURO 1 (e) EURO 2T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 30 / 33

Simulation Results

Table 1: Comparison of MILP and heuristic results on demand satisfactionafter failure (weakly survivable)

SMALL G3 G6 EURO 1 EURO 2 RANDMILP 0/28 38/38 69/71 17/17 45/47 361/387Ratio 0% 100% 97% 100% 96% 93%

Heuristic 0/28 32/36 44/62 10/17 41/47 317/372Ratio 0% 89% 71% 59% 87% 85%

Table 2: Comparison of MILP and heuristic results on minimum sparecapacity (strongly survivable)

SMALL G3 G6 EURO 1 EURO 2 RANDMILP 26 3 17 10 6 2

Heuristic 26 3 21 12 6 18


State of the Art

Where we are


Conclusions

Introduce the weakly and strongly survivable concept incapacitated IP-over-WDM networksProvide MILP formulation and heuristics for weakly and stronglysurvivable problem in capacitated IP-over-WDM networksFuture works

Load-balancing on logical demand satisfactionAugmentation in logical network to guarantee survivability in MILPformulationSurvivable routing for multiple failure scenario


Logical Topology Survivability in IP-over-WDM Networks - DRCN 2011

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