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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.
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 2 / 33
Survivability in IP-over-WDM Networks
(a) Logical topology. (b) An unsurvivable mapping.
(c) A survivable mapping.
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 3 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 4 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 5 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 6 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 7 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 8 / 33
Weakly Survivable Routing – MILP Approach
Two-stage approachFirst stage:
Weakly survivable routingMaximize demand satisfaction
Second stage:Minimize maximum unsatisfied demand through rerouting
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 9 / 33
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.
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 10 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 11 / 33
Weakly Survivable Routing – MILP Approach (FirstStage)
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 12 / 33
Weakly Survivable Routing – MILP Approach (FirstStage)
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 13 / 33
Weakly Survivable Routing – MILP Approach (FirstStage)
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 14 / 33
Weakly Survivable Routing – MILP Approach (FirstStage)
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
Weakly Survivable Routing – MILP Approach (FirstStage)
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 16 / 33
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)}
zstk`ij −
∑(`,k)∈EP\{(i,j)}
zst`kij = 1, if s = k , (s, t) ∈ Rij (20)
∑(k,`)∈EP\{(i,j)}
zstk`ij −
∑(`,k)∈EP\{(i,j)}
zst`kij = −1, if t = k , (s, t) ∈ Rij (21)
∑(k,`)∈EP\{(i,j)}
zstk`ij −
∑(`,k)∈EP\{(i,j)}
zst`kij = 0, otherwise, (s, t) ∈ Rij (22)
finds alternative lightpath for disrupted logical link (s, t)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 17 / 33
Weakly Survivable Routing – MILP Approach (SecondStage)
Residual capacity constraint: For all (i , j) ∈ EP∑(s,t)∈Rij
(xstk`ij + xst
`kij) ≤ ck` −∑
(u,v)∈EL\Rij
ρ∗uv yuv∗k` , (k , `) ∈ EP \ {(i , j)} (23)
xstk`ij ≤ Mzst
k`ij , (s, t) ∈ Rij , (k , `) ∈ EP \ {(i , j)} (24)
λstij ≥ xst
k`ij , (s, t) ∈ Rij , (k , `) ∈ EP \ {(i , j)} (25)
λstij ≤ xst
k`ij + M(1− zstk`ij), (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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 18 / 33
Weakly Survivable Routing – MILP Approach (SecondStage)
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 19 / 33
Weakly Survivable Routing – MILP Approach (SecondStage)
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 20 / 33
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 21 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 22 / 33
INCIDENCE-SMART: An Example
(a) (b) Logical topology GL, v4 is the da-tum vertex.
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 23 / 33
INCIDENCE-SMART: An Example
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 24 / 33
INCIDENCE-SMART: An Example
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 25 / 33
INCIDENCE-SMART: An Example
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)
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 26 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 27 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 28 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 29 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 31 / 33
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
T. Lin, Z. Zhou, K. Thulasiraman (OU, IBM) DRCN 10/10/2011 33 / 33