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Attack-aware Lightpath Provisioning in Elastic

Optical Networks with Trafﬁc Demand Variations

Konstantinos Manousakis1, Tania Panayiotou1, Panayiotis Kolios1, Ioannis Tomkos2and Georgios Ellinas1

1KIOS Research and Innovation Center of Excellence, Department of Electrical and Computer Engineering,

University of Cyprus, 1678 Nicosia, Cyprus

{manouso, panayiotou.tania, pkolios, gellinas}@ucy.ac.cy

2Athens Information Technology, Marousi, 15125 Athens, Greece

itom@ait.gr

Abstract—This work considers lightpath provisioning in elastic

optical networks with trafﬁc demand variations while accounting

for the impact of jamming attacks. Trafﬁc requests are modeled

based on their variation in trafﬁc and a number of network trafﬁc

scenarios are pre-computed. Variations in trafﬁc are used in

order to design the network with improved resilience to jamming

attacks in the general case, without considering a speciﬁc trafﬁc

matrix. The mathematical formulation and heuristic algorithms

proposed in this work jointly consider the routing and spectrum

allocation problem for the pre-computed network scenarios,

aiming to minimize the required lightpath reallocations and

the number of wavelength selective switches (WSSs) placed at

speciﬁc network nodes/ports so as to minimize the impact of

jamming attacks. Performance results demonstrate the beneﬁts

of this approach in terms of required lightpath reallocations,

number of WSSs, as well as computational time required for

dynamically reconﬁguring the network when considering trafﬁc

demand variations.

I. INTRODUCTION

The ever increasing trafﬁc demand of core networks is

expected to be supported by elastic optical networks (EONs),

as in EONs the spectrum is more efﬁciently utilized, using

ﬁner slot granularity, compared to wavelength division multi-

plexed (WDM) networks. In addition to the increasing trafﬁc

demands, a big challenge for the network operators is to cope

with trafﬁc demand variations and guarantee network availabil-

ity for the requested connections. For example, trafﬁc demand

variations can occur due to several bandwidth consuming

applications/services (e.g., 3D video, cloud computing) as well

as popular events (e.g., Olympic Games, World Cup) and will

necessitate more frequent network reconﬁgurations so as to

satisfy the user demands and manage the network resources

more efﬁciently [1].

Usually, in order to satisfy the network requests, network

operators overprovision the network, leading to a waste of

resources and increased operational and capital expenditures

(opex/capex). For this reason, several other approaches have

been proposed in the literature that reconﬁgure the network

so that it closely follows the trafﬁc demand variations [2]–[5].

Generally, proactive network optimization is initially required

prior to the demand requests, followed, in real time, by

network reconﬁguration. With the right network design and

real-time support, network operators can handle the expected

trafﬁc demand, even during popular events [6].

Further, for establishing a connection in EONs, the routing

and spectrum allocation (RSA) problem must be solved, satis-

fying the spectrum continuity, contiguity, and non-overlapping

constraints [7]. In addition to the aforementioned constraints,

the crosstalk effect must also be taken into account when

provisioning a new connection (both for the new connections

as well as the already established ones), since crosstalk not

only degrades the signal quality [8] but it can also be used

to spread a jamming attack throughout the network [9], [10].

These attacks can have an even more devastating effect during

popular events, as they can cause signiﬁcant service disruption

and affect a large part of the telecommunication network.

A. Previous Work

The concept of attack-aware algorithms in WDM networks

to solve the routing and wavelength assignment (RWA) prob-

lem was presented in [11]–[13] having as an objective the

minimization of the impact of high-power jamming attacks.

In these works, apart from the attack-aware RWA problem,

equalizer placement [14], monitor placement [15], and dedi-

cated path protection [16] were also considered. The concept

of jamming attacks in EONs has been considered in [17]–[20].

Authors in [17] address the problem of physical-layer security

in multi-domain ﬂexible grid optical networks, proposing

to differentiate the routing and spectrum allocation (RSA)

schemes of intra- and inter-domain requests with security con-

siderations. Authors in [18] solve the problem of attack-aware

service provisioning in one domain of multi-domain EONs

to improve network scalability using game theory techniques.

Further, authors in [19] propose an Integer Linear Program

(ILP) for the crosstalk-aware RSA problem, while in [20], they

propose a crosstalk-aware RSA together with a wavelength

selective switch (WSS) placement technique to eliminate intra-

band crosstalk. In that work, initially, all network nodes (re-

conﬁgurable add/drop multiplexers - ROADMs) are assumed

to have a broadcast-and-select (BS) architecture, with splitters

and WSSs at the input and output ports, respectively. The

algorithm decides on the replacement of some of the splitters

with WSSs at the input stage of the BS-based architecture

in order to compensate for the in-band crosstalk interactions

among lightpaths. In fact, the algorithm tries to achieve zero

crosstalk interactions and in the cases where it is not possible,

WSSs are placed to compensate for these interactions.

In the aforementioned works, the authors assume that the

trafﬁc demand is static and that it can be known a priori.

Therefore, none of these works considers trafﬁc demand

variations and lightpath reallocations that are required for such

trafﬁc, while at the same time considering the impact of intra-

band jamming attacks, which is precisely the focus of this

work.

Further, it is also important to note that there exist several

works in the literature that reallocate the lightpaths considering

dynamic trafﬁc or variations in trafﬁc [24]–[26]. However,

none of these works considers how one network conﬁguration

can affect the other conﬁgurations, nor do they consider the

crosstalk effect, thus, the proposed solutions can result in high

network blocking probabilities.

B. Our Contribution

In this work, the attack-aware (Aa)-RSA and WSS place-

ment problems in EONs (with the WSS placement problem

following the procedure described above [20]) are solved for

satisfying jointly several sets of connection requests (demand

scenarios). A demand scenario is deﬁned as a possible demand

state that can be found based on trafﬁc demand variations (by

considering the stochastic nature of the trafﬁc that varies with

time [21], [22]). The proposed algorithms use models that take

advantage of the fact that probability distributions governing

the trafﬁc demands are known or can be estimated. Therefore,

the trafﬁc is modeled in order to precompute a number of

possible conﬁgurations that have high probability to appear in

the network.

The output of the problem solution is a set of network

conﬁgurations, where a network conﬁguration is a RSA so-

lution and the WSS placement for each demand scenario. The

network conﬁgurations are computed ofﬂine and can be used

online for dynamic reconﬁguration of the network in order

to meet the trafﬁc demand variations. One of the problem

objectives is to minimize the required lightpath reallocations

between different network conﬁgurations. Another objective

of the problem is to minimize the number of required WSSs

for all the possible demand scenarios in order to compensate

for the crosstalk effect and therefore to minimize the impact

of jamming attacks.

The novelty of this work is the design of optimization as

well as heuristic algorithms that jointly consider the crosstalk-

aware RSA problem with WSS placement and the lightpath

reallocations between different demand scenarios. Thus, the

solutions consider the network conﬁgurations jointly in order

to avoid lightpath reallocations. In addition, the WSS place-

ment considers the variations in trafﬁc and places the WSSs

not only at speciﬁc nodes but also decides in which node

ports to place the WSSs in order to satisfy jointly the network

conﬁgurations, for every possible trafﬁc demand scenario.

Consequently, the algorithms reduce both the capex, by

minimizing the required number of WSSs, and the opex, by

minimizing the number of lightpath reallocations and thus

reducing the computational complexity and time required in

the path computation element (PCE) for reconﬁguring the

network upon variations in the trafﬁc demand.

The reader should note that in this work the term reconﬁgu-

ration is used to denote the change between one conﬁguration

of the network to another (in terms of established lightpaths),

while the term reallocation is used to denote the tear-down

and the setup of a lightpath (leading to service disruption) in

order to meet the variation in trafﬁc.

The rest of the paper is organized as follows. Section II

presents the trafﬁc demand modeling, while Section III

presents the concept of jamming attacks and WSS placement.

Section IV provides the mathematical formulation of the

problem. Section V presents the proposed attack-aware RSA

heuristic algorithms, while performance results are discussed

in Section VI. Finally, Section VII offers some concluding

remarks and avenues for future work.

II. MODELING TR AFFI C DEM AN DS

In this work, without loss of generality, during normal

network operation, we assume trafﬁc that is log-normally

distributed and each connection is described by its own

distribution as described in [21], [22] (note that any other

trafﬁc distribution can also be applied in this work). Further,

regarding trafﬁc modeling during popular events, we assume

that each connection is described by its expected bandwidth

demand during the occurrence of the speciﬁc event. On this

basis, the trafﬁc demand for each connection nduring normal

network operation is described by Zn∼LN(µn, σ2

n)and

during popular events is described by a ﬁxed value ei

n, where

ei

ndenotes the expected bandwidth demand of connection n

during the occurrence of the ith event.

For normal network operation, we ﬁnd the distribution

describing the probability of the network being at a particular

state (demand scenario) s={dn}N

n=1, where Nis the

number of connections in scenario s, and dnis the bandwidth

demand of connection n. For ﬁnding such a distribution,

Monte Carlo simulations are performed, by sampling the

discretized {Zn}N

n=1 distributions. Regarding popular events,

the assumption is that these events are known in advance and

occur with certainty at particular time intervals. Their related

states (demand scenarios) can be easily found by the {ei

n}N

i=1

values. Upon the occurrence of such events, the network

switches to some pre-computed network conﬁgurations.

Finding the discretized distribution allows us to ﬁnd the

possible trafﬁc demand scenarios of the network and accord-

ingly to solve the crosstalk-aware RSA problem for different

network conﬁgurations. Each distribution is a function of the

bandwidth demand that is measured according to the requested

number of spectrum slots. Even though the requested number

of spectrum slots depends on several factors, such as the trans-

mission distance, the modulation format, and the quality-of-

transmission (QoT) requirements, for simplicity, and without

loss of generality, we assume that the distributions directly

reﬂect the requested number of spectrum slots; an assumption

that does not affect the scope of this work. As the number

of possible scenarios may render the crosstalk-aware RSA

problem computationally intractable, the scenarios that rarely

appear, are not considered while solving this problem. These

scenarios, if they appear, can be handled dynamically.

III. JAMMING ATTACKS AND WSS PLAC EM EN T IN EONS

In-band crosstalk in optical networks is the result of power

leakage between two signals on the same wavelength crossing

an optical node. In-band crosstalk must be addressed in optical

networks, as it not only causes optical signal degradation

but it can be potentially used to launch high-power in-band

jamming attacks in the network (an attacker injects a high-

power signal at an optical node on the same wavelength as

the information carrying signal). A high-power jamming signal

can cause signiﬁcant leakage inside the switches between

lightpaths that are on the same wavelength as the attacking

signal, resulting in lightpath signals that cannot be recovered

at their respective receivers. It is further important to note that

these affected lightpaths become secondary attackers, affecting

other lightpaths on the same wavelength that they encounter

at other switching nodes along their path, and so on. Thus, the

high-power jamming attack can potentially spread through the

network affecting a large number of lightpaths [13]. Several

of the works mentioned in Section I tried to address this

problem by solving the RWA/RSA problems in WDM/EON

networks respectively in such a way that if an attack happens

the propagation effect is minimized [11]–[13], [19].

To address such an attack, other works [20] proposed algo-

rithms that initially aim to minimize the crosstalk interactions

among lightpaths as much as possible (through crosstalk-

aware RSA), trying to achieve zero interactions. If this is not

possible, then splitters are replaced by WSSs at the input stage

of the ROADMs where there are lightpath interactions through

in-band crosstalk (utilizing the minimum required number)

in order to further compensate for the crosstalk effect and

minimize the impact of a jamming attack. The replacement of

a few splitters with WSSs at speciﬁc locations of the network

will maintain the network cost low while at the same time the

crosstalk effect will be decreased with the use of the WSSs.

Therefore, the impact of jamming attacks will be minimized.

In this work, the problem of the placement of WSSs is

further explored in order to cover a set of demand scenarios.

In this case, each of the demand scenarios must be satisﬁed,

while the WSSs must be placed in positions that also satisfy

all the different demand scenarios. Thus, the RSA solution of

each set must be taken into account by the other demand sets in

order for the total number of required WSSs to be minimized.

IV. ATTAC K-AWARE RSA AND WSS PLACEMENT

FORMULATION

A mathematical formulation is presented in this section

for the efﬁcient establishment of connections in EONs with

trafﬁc demand variations. To capture the uncertainties in

the trafﬁc demand, mathematical optimization is employed

through scenario construction, where the number of required

lightpath reallocations as well as the number of WSSs are

minimized for the sum of deterministic equivalent instances.

Note that the in-band crosstalk interactions are minimized per

scenario, whereas the minimum number and the placement of

WSSs are chosen in order to satisfy all demand scenarios.

In particular, the attack-aware RSA and WSS placement

problem is solved having as an objective to minimize spectrum

utilization, the number of lightpath reallocations, and also the

number of required WSSs. The proposed algorithm consists of

two phases; in the ﬁrst phase, kcandidate paths are identiﬁed

for each source-destination pair by employing a k-shortest

path algorithm [23], while in the second phase the problem

is formulated taking as input the output of the ﬁrst phase (i.e.,

the set of kcandidate paths). Its parameters, variables, and

objective/constraints are shown below:

Parameters:

•(d, s)∈Ds: a demand dfor scenario s

•f∈F: a spectrum slot over the available spectrum slots

•p∈P: a candidate path

•l∈E: a network link

•Fs

d: required number of slots for demand dof scenario s

•S: set of all scenarios

•Pd: set of candidate paths to serve demand d

•πs: probability for scenario sto occur

•B,M: large constants that are used to activate/deactivate

a constraint, where MB

Variables:

•xs

pf : Boolean variable for the sth realization, equal to 1

if path pand frequency slot fare used to serve demand

dand equal to 0otherwise.

•ypf Boolean variable, equal to 1if frequency slot fis the

starting spectrum slot of a contiguous spectrum to serve

demand dover path pand equal to 0otherwise.

•zl: Boolean variable, equal to 1if there exists a WSS at

the end of link land equal to 0otherwise.

Objective:Minimize :

X

s

πsX

p

X

f

c1·xs

pf +X

l

c2·zl+X

p

X

f

c3·ypf (1)

Subject to the following constraints:

•Demand constraint

X

p∈Pd

X

f

xs

pf =Fs

d,∀(d, s)∈Ds,∀s∈S(2)

•Contiguity constraint

xs

pf −xs

p(f−1) ≤ypf ,∀p∈P, ∀f∈F, ∀s∈S(3)

Case: f= 1, then, xs

p(f−1) = 0,∀s∈S

•Non-overlapping spectrum

X

p|l∈p

xs

pf ≤1,∀l∈E, ∀f∈F, ∀s∈S(4)

•Jamming interactions and WSS placement

X

{p0|m∈p,p0}

xs

p0f+B·xs

pf −M·zl≤B, (5)

∀l∈p, ∀p∈P, ∀f∈F, ∀s∈S

The objective function, (Eq. 1) accounts for (i) the number

of required frequency slots, (ii) the number of required WSSs,

and (iii) the number of required reallocations. Each coefﬁcient

ci(i= 1,2,3), declares the relative impact of each term of the

objective. The frequency slot minimization is considered based

on the probability πsassociated with a particular scenario.

This means that a scenario that is more probable to happen

will have a higher impact on the objective function.

In addition, a number of xs

pf Boolean variables are activated

to satisfy the different scenarios. Hence, a number of path-slot

pairs are assigned for each source-destination request, that are

jointly optimized to minimize the objective function. Note that

the assignment for each demand scenario sis decided based

on the assignment for every other scenario, thus the path-slot

pairs are chosen in such a way so as to minimize the overall

cost indicated in the objective function.

Constraint 1(Eq. 2) ensures that all lightpaths have a

total capacity equal to the requested demand for each of the

realizations and thus all incoming trafﬁc is satisﬁed. Constraint

2(Eq. 3) ensures that each demand is assigned contiguous

spectrum on all the ﬁbers of each path. Speciﬁcally, this

constraint counts the transitions from zero to one. In this

way, variable ypf keeps track of the starting frequency slot to

serve a demand. Variable ypf is the same for all the different

scenario realizations. Therefore, taking into account the ob-

jective and this constraint the spectrum and path reallocations

are minimized as much as possible. Constraint 3(Eq. 4)

is the non-overlapping spectrum constraint and ensures that

each spectrum slot is used at most once on each ﬁber for

each scenario realization. Note that the spectrum continuity

constraint (each demand is assigned the same spectrum along

all the edges of the path) in this formulation is taken into

account via the deﬁnition of the xs

pf variable. Finally, Con-

straint 4(Eq. 5) is included in order to account for the in-

band jamming interactions and to minimize the number of

required WSSs. In Constraint 4,Band Mare constants (taking

large values), where MB. The reason for introducing

constant Bis to take into account only the constraints for the

lightpaths that will be used from all the candidate lightpaths

(activate/deactivate the constraint). Additionally, the reason

for introducing constant Mis to account for the replacement

of splitters with WSSs (activate/deactivate the constraint). In

Constraint 4,P{p0|m∈p,p0}xs

p0fis the total number of in-

band crosstalk interfering sources that affect the signal of

lightpath (p, f )at node mfor the sth scenario, while variable

zlspeciﬁes where to place the required WSSs. Note that node

nin Constraint 4is the end-node of link l. Based on the

objective function, the WSSs are placed at speciﬁc locations

inside the network nodes in order to satisfy all the different

scenarios under consideration.

V. ATTACK -AWARE EXPANSION/REDUCTION RSA

HEURISTIC ALGORITHM

To solve the problem utilizing an algorithmic approach,

we propose the attack-aware expansion/reduction RSA (Aa-

ER-RSA) heuristic algorithm that aims at ﬁnding a set of

network conﬁgurations that (i) supports all possible trafﬁc

demand scenarios, (ii) minimizes the number of WSSs re-

quired for handling the crosstalk effect, and (iii) minimizes the

service interruptions that may occur during switching between

sequential (in time) conﬁgurations (including conﬁgurations

that support popular events). To achieve this, the proposed

algorithm ﬁnds a set of network conﬁgurations that are similar

(as much as possible) in their lightpaths (routing paths and

allocated spectrum) and support the possible future demand

when appropriately expanding/reducing [24] the allocated

spectrum of each lightpath. By doing so, we aim to reduce

the number of WSSs required for supporting all the possible

network conﬁgurations and minimizing the service disruptions

that may occur during switching between sequential (in time)

network conﬁgurations.

The Aa-ER-RSA algorithm is compared to a complete reallo-

cation attack-aware RSA algorithm (Aa-REC-RSA) that solves

the provisioning problem for each scenario without consid-

ering the conﬁgurations found in previous scenarios (only

the WSSs found from previous network conﬁgurations are

considered). Thus, a compete lightpath reallocation takes place

for each scenario, aiming to minimize the number of WSSs

required for supporting all the possible demand scenarios.

In general, with the usage of the expansion/reduction policy,

trafﬁc interruptions can be avoided [25] but the resources may

not be efﬁciently utilized amongst the established connections.

Compared to the expansion/reduction policy, the complete

reallocation policy requires higher computational complexity

and complex algorithms in the PCE for minimizing trafﬁc

interruptions [26]. Both the Aa-ER-RSA and Aa-REC-RSA

heuristics are described in Algorithm 1, while the expan-

sion/reduction (ER) procedure of the Aa-ER-RSA heuristic is

described in Algorithm 2.

Algorithm 1 Aa-x-RSA Heuristic Algorithm

Input: The set S={si}D

i=1, where siis a demand scenario with

πsi> p. Set Sis sorted in descending order with the scenario

demanding the maximum cumulative spectrum placed ﬁrst on the

list.

Output: The sets Wand {Csi}D

i=1, where Wis the set of WSSs

and Csiis the set of established lightpaths for demand scenario si.

1: W→ ∅

2: Csi→ ∅ ∀si∈S

3: for i= 1 to Ddo

4: if i= 1 OR x= Rec then

5: Solve the Aa-REC-RSA problem for all connections in si

6: Update sets Csiand W

7: else

8: Solve Algorithm 2

9: Update sets Csiand W(updates in Wmay occur only

from the reallocated connections)

10: end if

11: end for

12: Return sets Csi∀si∈S, and W

In general, both heuristics (Algorithm 1) start from the

trafﬁc demand scenario sdemanding the maximum cumulative

bandwidth and continue to scenario s0with a cumulative

Algorithm 2 ER Algorithm

1: Identify in sithe connections that remain unchanged, need to be

reduced or expanded in their spectrum when compared to their

allocated spectrum at s(i−1).

2: From Cs(i−1) add in Csithe lightpaths that remain unchanged

or need to be reduced in their spectrum.

3: In Csiupdate the information regarding the allocated spectrum

of the lightpaths that need to be reduced in their spectrum

(by removing the necessary number of slots, starting from the

rightmost slot, and shifting the central frequency accordingly).

4: In Csiadd from Cs(i−1) the lightpaths where expansion is

feasible and update in Csiinformation regarding their allocated

spectrum (by adding the necessary number of slots, starting from

the rightmost slot, and shifting the central frequency accord-

ingly).

5: For each connection in sithat its expansion is not feasible, solve

the Aa-RSA problem (reallocate).

bandwidth that is closer to that of the previous scenario.

Speciﬁcally, the Aa-x-RSA problem is solved for each sce-

nario, s, by taking into account the previous WSS placement.

For the ﬁrst scenario (s) on the sorted list or when reallocation

is needed (i.e., when the REC procedure is followed (x=REC)

or when connection expansion is not feasible in the ER

procedure (x=ER)), the heuristic solves the Aa-RSA problem

as follows: For the routing procedure, it calculates k-shortest

paths and for each one of the kpaths the spectrum allocation is

solved according to the ﬁrst-ﬁt scheme. Among the candidate

lightpaths, the one that yields the minimum crosstalk penalty is

chosen, where the crosstalk penalty, rj, for the jth lightpath is

deﬁned as the number of nodes the jth lightpath overlaps (on

its allocated spectrum) with the already established lightpaths.

If the minimum crosstalk penalty is not zero, WSSs are placed

at the necessary network nodes’ input ports for eliminating the

crosstalk effect among the overlapping connections.

The reader should note that as the number of possible

scenarios may render the problem computationally intractable,

the scenarios that rarely appear are not be considered during

Aa-x-RSA. Speciﬁcally, in this work, the heuristics are solved

for all scenarios swith πs> p, where pis a probability

threshold used so as not to consider the scenarios that rarely

occur. These rare scenarios can be handled online given the

placement of the WSSs.

VI. PERFORMANCE RE SU LTS

To evaluate the performance of the proposed optimization

and heuristic algorithms, a small network with 6nodes and 9

links, and the generic Deutsche Telekom (DT) network with

14 nodes and 23 links (Fig. 1), were considered, and each

spectrum slot was assumed to occupy 12.5GHz. For solving

the mathematical formulation, the Gurobi library was used [27]

and a PC with Core i5−2400@3.1GHz and 16GB memory was

used for the simulation environment. The proposed algorithms

are investigated and compared for different metrics; number of

required WSSs, number of lightpath reallocations, and running

times. In this work, it is assumed that the network has some

trafﬁc demands that vary over time based on a log-normal

distribution (other distributions can be considered as well)

and some ﬁxed connections, where their bandwidth demand

was set to be constant for all the different scenarios (the

requested number of slots was chosen uniformly between 0

and 5). For all connections, the source destination pairs were

chosen randomly. Further, ten (10) executions corresponding to

different trafﬁc instances for each trafﬁc load were performed

and for all simulations the network resources were enough to

establish all connections (i.e., the blocking probability was set

to zero in order to fairly compare all approaches in terms of

the investigated metrics). The mathematical formulation and

the Aa-ER-RSA heuristic algorithm are compared with the

Aa-REC-RSA heuristic algorithm to illustrate the beneﬁts to

network planning and operation when jointly considering the

crosstalk-aware RSA problem with WSS placement and the

lightpath reallocations between different demand scenarios. It

is noted that the coefﬁcients ciof the objective functions (Eq.

1) were set equal to one (ci= 1), since it is assumed that all

the terms equally contribute to the objective function. Different

values for these coefﬁcients can be used when the monetary

cost of using a spectrum slot, reallocating a connection and

the cost of the WSS is determined.

Fig. 1. (a) 6-node network, and (b) DT network topology.

A. Results for the 6-node Network

For the 6-node network, six of the connections follow the

log-normal distribution, whereas the rest are set to be static.

We assume that the 6-node network supports 30 slots per link.

Each connection’s bandwidth demand was assumed to take

values between 2and 10 slots (increasing by 2slots between

sequential intervals). Monte Carlo simulations returned 23

scenarios with probability p≥10−2. The mean numbers

of requested slots (static and log-normal) per scenario are

shown in Table I. This table depicts a comparison of the pro-

posed mathematical formulation and the heuristic algorithms

for the requested connections with respect to the objective

performance and the required running time for different mean

numbers of requested slots per scenario.

The Aa-REC-RSA algorithm is used as a benchmark for

lightpath reallocations. In this case, the required number of

reallocations is high compared to the rest of the algorithms that

have as an objective the minimization of the lightpath reallo-

cations. Speciﬁcally, it is shown that the Aa-ER-RSA heuristic

TABLE I

6-NOD E NET WOR K RESU LTS (W:NUMBER OF WSSS, R : NUMBER OF

REALLOCATIONS,T:RUNNING TIME )

Mean slot

requests

Formulation Aa-ER-RSA Aa-REC-RSA

W R T W R T W R T

33 0 0 2.7m 0 0 0.55s 0 95 10s

47 0 0 25h 5 0 1.86s 6 329 38s

59 0 0 48h 10 0 2.5s 10 380 46s

75 4 0 48h 11 0 2.5s 15 483 53s

85 4 1 48h 11 0 2.55s 18 502 1m

100 7 2 48h 14 0 2.77s 18 512 1m

algorithm requires no lightpath reallocations for all cases under

consideration and has better performance compared to the

mathematical formulation, since the optimization algorithm re-

quires 1−2reallocations for the examined scenarios. However,

the mathematical formulation requires less number of WSSs

to compensate for the crosstalk-related interactions among

lightpaths compared to the Aa-ER-RSA heuristic algorithm.

This occurs due to the fact that the Aa-ER-RSA heuristic

algorithm has as a primary objective the minimization of the

number of lightpath reallocations and as a secondary objective

the minimization of WSSs, whereas the optimization algorithm

tries to jointly optimize the number of required frequency slots,

the number of lightpath reallocations, as well as the number

of required WSSs.

The mathematical formulation found the best bound (op-

timal solution) for the ﬁrst two cases in 3minutes and 25

hours, respectively. For the rest of the cases, the optimal

solution cannot be found and the algorithm terminated due

to the time limit that was set to 48 hours, as the running

time of the mathematical formulation increases exponentially

with the trafﬁc load. On the other hand, the Aa-ER-RSA

heuristic required less than 3minutes of running time for

all the cases under consideration. The reader should note

that this time period is just for planning purposes and that

the online adaptation can be performed on the order of

seconds or even milliseconds [28]. It must also be noted that

the performance of crosstalk-unaware algorithms exhibit high

number of lightpath interactions irrespective of the number of

scenarios considered (one or more scenarios) and thus require

a high number of WSSs [20].

B. Results for the DT Network

For the DT network, 10 of the connections follow the

log-normal distribution, whereas the rest are set to be static.

The DT network is assumed to support 300 slots per link.

Each connection’s bandwidth demand was assumed to take

values between 2and 10 slots (increasing by 2slots between

sequential intervals). Monte Carlo simulations returned 707

scenarios with probability p≥10−2. In this scenario, only the

heuristics are implemented and compared as the mathematical

formulation cannot be implemented due to the large network

size.

As can be seen from Figs. 2 - 4, the Aa-ER-RSA algo-

rithm signiﬁcantly outperforms Aa-REC-RSA for all metrics

considered. Note that due to the high running time (62 hours)

Fig. 2. Running time vs. mean requested number of slots per scenario.

required by Aa-REC-RSA for the case of 832 requested slots

(Fig. 2), we have chosen not to examine any other scenario

requesting a larger number of slots. Also, note that Aa-ER-

RSA, even for the case of 832 requested slots, ran in only a

few minutes, as it does not need to recompute the lightpaths

for every scenario and for every connection within each

scenario, since it follows an expansion/reduction policy for

adjusting the spectrum of the already established connections.

On the contrary, Aa-REC-RSA recomputes the lightpaths for

every scenario and for every connection within each scenario,

leading to both an increased computational time (Fig. 2)

and an increased number of reallocations (Fig. 4) and as a

consequence an increased number of service interruptions.

Fig. 3. Number of WSSs vs. mean requested number of slots per scenario.

Regarding the number of WSSs, Aa-ER-RSA requires signif-

icantly fewer WSSs than Aa-REC-RSA as can be seen in Fig. 3.

This is due to the fact that Aa-ER-RSA ﬁnds a set of network

conﬁgurations that are similar in their computed lightpaths and

for which the crosstalk effect can be mitigated by “almost”

the same set of WSSs. In contrast, Aa-REC-RSA has to ﬁnd

a new network conﬁguration for each scenario without taking

into account the WSSs that are already placed in the network.

VII. CONCLUSIONS

This work proposed attack-aware RSA optimization and

heuristic algorithms in EONs, that consider a set of different

scenarios representing demands with uncertainty that vary

Fig. 4. Number of reallocations vs. mean requested number of slots per

scenario.

over time. The aim of these algorithms is to minimize the

number of WSSs, placed at the input ports of speciﬁc network

nodes, required to mitigate the crosstalk effect, and thus the

spread of an attack, as well as to minimize the required light-

path reallocations between different trafﬁc scenarios. Thus,

the proposed technique reduces both the network capex and

opex, by minimizing the required number of WSSs and the

number of lightpath reallocations upon variations in the trafﬁc

demand. Performance results demonstrate the effectiveness of

the heuristic algorithm in terms of computational time, as

the proposed heuristic performs close to the results of the

mathematical formulation, while outperforming the complete

reallocation policy.

Future works will explore decomposition techniques for

the mathematical formulation so as to address larger network

problems. In addition, online reconﬁgurability of the network

with samples from the distributions of the connections will be

examined.

ACKNOWLEDGMENT

This work has been partially supported by the European

Union’s Horizon 2020 research and innovation programme

under grant agreement No 739551 (KIOS CoE) and from the

Government of the Republic of Cyprus through the Directorate

General for European Programmes, Coordination and Devel-

opment. It was also partially supported by the Cyprus Research

and Innovation Foundation under project CULTURE/AWARD-

YR/0418/0014. This article is based upon work from COST

Action CA15127 (Resilient communication services protecting

end-user applications from disaster-based failures RECODIS)

supported by COST (European Cooperation in Science and

Technology).

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