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Optics Communications 270 (2007) 247–254

Physical layer impairment aware wavelength routing algorithmsbased on analytically calculated constraints

Vasilis Anagnostopoulos a,*, Christina (Tanya) Politi b, Chris Matrakidis b, A. Stavdas b

a School of Electrical and Computer Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zographou, 15773, Athens, Greeceb Department of Telecommunications Science and Technology, University of Peloponnese, Tripolis, Greece

Received 1 March 2006; received in revised form 6 September 2006; accepted 8 September 2006

Abstract

A quality-of-service (QoS)-aware routing engine for a transparent optical network that accounts for physical layer impairments (PLI)is presented. PLI are studied collectively by means of Q-factor. The latter is calculated by analytical methods that speed up the calcu-lation and allow application in a dynamic network. Two path establishment algorithms are deployed: the shortest-path and the shortest

widest path. The impact of PLI awareness on the QoS is measured in terms of blocking probability and load balance. Any of the physicalparameters can be used as an optimization variable in order to assess their effect on performance degradation at system and networklevel. The impact of the path establishment algorithm on the optimization parameter is analysed.� 2006 Elsevier B.V. All rights reserved.

1. Introduction

Core wavelength division multiplexing (WDM) net-works are expected to migrate from point-to-point linksto intelligent, multi-hop and transparent optical networks,in order to fully exploit the advantages offered by a wave-length routed network [1]. Quality-of-service (QoS)provisioning associated with service guarantees, is animportant asset for developing highly scalable ‘‘on-demand’’ networks. To provide acceptable QoS, wave-length routing algorithms (WRA) should associate effectiverouting algorithms with awareness of physical layer prop-erties, taking under consideration physical layer impair-ments (PLI). In the literature, many papers are involvedwith either defining a constraint-based routing algorithmwhere the constraint is PLI related, e.g. [2,3] or anapproach where a check on a PLI related parameter is per-formed before the lightpath establishment e.g. [4,5]. As faras the transmission effects that are modelled are concerned,

0030-4018/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2006.09.063

* Corresponding author. Tel.: +30 210 7723940; fax: +30 210 7722534.E-mail addresses: vanag@telecom.ntua.gr (V. Anagnostopoulos),

tpoliti@uop.gr (Christina (Tanya) Politi), cmatraki@uop.gr (C. Matraki-dis), astavdas@uop.gr (A. Stavdas).

there is a plethora of specific phenomena that have beenconsidered independently from each other like polarisationmode dispersion [2], self-phase modulation [6], four-wavemixing (FWM) [7], combination of crosstalk and AmplifiedSpontaneous Emission (ASE) [8] or a numerically pre-cal-culated combination like in [9].

In this work, a PLI-aware WRA is developed toaddress QoS. Its effectiveness is assessed by means ofblocking probability (BP) and load balance (LB) for differ-ent path establishment algorithms. In terms of PLI recei-ver noise, ASE accumulation, cross-phase modulation(XPM) and FWM are taken into account and their collec-tive impact on system performance is studied. This is eval-uated via analytically calculating their combined effects onthe Q-factor of the signal, for the first time to the best ofour knowledge. Analytical methods are fast and allowapplication in a dynamic network. They are also upgrade-able and can be used in a scalable network. Moreover, dueto the flexibility of the algorithm, any of the physicalparameters can be used as an optimization variable inorder to assess its impact in performance degradation atsystem and network level. This is proven here by meansof an example, where BP versus power per channel is cal-culated. Finally, two path establishment algorithms are

248 V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254

used for that purpose and their performance is comparedto that respect.

2. Formulation of the constraint based routing algorithm

The Pan European Network is modeled as a unidirec-tional graph with one fiber per edge, G = (V,E) where V

is the set of nodes with cardinality jVj and E is the set ofedges, E � V · V, with cardinality jEj. We also assume L

wavelengths per (fiber) edge [10]. This number is assumedto be the same for every edge e. We associate each edge e

with a cost function l which plays the role of a generalizedlength. This function maps the set of edges to non-negativereal numbers, l : E! R. We define the availability matrixM = (Me,k) with dimensions jEj · L and the specification

Me;k ¼1 if wavelength k; in edge e is free

0 otherwise

�

A path is represented as a vector X with jEj componentswith definition

X e ¼1 if the path passes from edge e

0 otherwise

�

We will also need the well-known adjacency matrix fromgraph theory A = (Ai,e) which is an jVj · jEj matrix withentries

Ai;e ¼1 if edge e leaves from node i

�1 if edge e arrives at node i

0 otherwise

8><>:

No wavelength conversion can be performed in the net-work hence the wavelength continuity constraint must beapplied. In order to formulate the routing problem, let usconsider a unidirectional request for a connection betweensource node s and destination node d served by one wave-length, in other words its bandwidth requirements areequal to the capacity provided by one channel. Let B bea vector with jVj components like this

Bi ¼1 if i ¼ s

�1 if i ¼ d

0 otherwise

8><>:

For each wavelength a path X might exist that satisfies thisparticular request. For a specific wavelength we considerthe existence of such path as equivalent to the existenceof a path of shortest generalized distance. In practice, thegeneralized distance is actually the length of the edge, di-rectly related to the physical properties of the medium. Inother cases, the generalized distance of the path is the num-ber of hops and hence related to the network resources. Inorder to formulate the ‘‘shortest-path’’ (S-P) problem, weassume that for fixed k, a suitable X is required that fulfilsthe minimization

minXEj j

e¼1

X e‘ðeÞ( )

: 8k and X compatible with the constraints

Simultaneously the following constraints should hold:

Constraint 1: The path starts from s and ends at d:AX = B if X(k) 5 0.Constraint 2: Wavelength continuity: XeMe,k = Xe "e.Constraint 3: We implicitly assume under the definitionof X that its entries are either 0 or 1.

There might be multiple solutions for the above problemfor each k. In order to solve the problem the ‘‘Bellman–Ford’’ algorithm is used that runs in polynomial time.

For the shortest widest path problem, (SWP for short)the formulation differs. A path X common for every k issought, indicate by the lack of k superscript. The SWPproblem takes the following form.

SWP problemFind suitable X in the minimization

maxXL

k¼1

Ye:Xe¼1

Me;k

( ): 8k and X compatible with the constraints

Constraint 1: The path starts from s and ends at d:AX = B if X 5 0.

Constraint 2: We implicitly assume under the definitionof X that its entries are either 0 or 1.

Here, the wavelength continuity condition is automaticallysatisfied. The solutions to the above problem are not cyclefree. Hence, the solutions with the least number of hops arekept. Note that SWP provides load balancing. SWP cannotbe solved in polynomial time. Therefore we resort to a sim-ple heuristic based on Banach’s fixed point algorithm. Weemploy an iterative scheme inspired by successive approxi-mations in mathematical analysis. For each node i in thenetwork, we define a vector X(i) with L components takingvalues 0 or 1. We use the notation X(i)(t) to denote the vec-tor X(i) at step t of the algorithm. We also define a stack foreach node Stack(i). For notational convenience we denotethe componentwise product of two vectors, with binaryentries of the same dimension as (A�B)k = AkBk and thenumber of ones in a vector with binary entries X as jXj.For the request represented as (s,d), our algorithm can beformulated as follows:

Initialization, t = 0

X ðiÞð0Þ ¼ 0 for i 2 f1; . . . ; jV jg � fsgStackðiÞðtÞ ¼£ for i 2 f1; . . . ; jV jg � fsg

and

XðsÞk ð0Þ ¼ 1 for k 2 f1; . . . ; LgStackðiÞð0Þ ¼ fsg

Iterative step t + 1

V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254 249

From the set of solutions of the minimization problem

maxj:ðj;iÞ2E

jX ðjÞðtÞ �Me;�j

select randomly a jo, such that the length of Stack(j0)(t) isminimal.

If jX(j0)(t) �Me,Æj > jX(i)(t)j, i.e. we have an improvement,we make the update X(i)(t + 1) = X(j0)(t) �Me,Æ

And Stack(i)(t + 1) = [Stack(j0)(t), j0]. If no improvementis possible, X(i)(t + 1) = X(i)(t).

Check for repeating the iterative step

There is at least one improvement.The above iterative procedure converges, a situation

that is easy to verify. Keep in mind that the number of onesin the vector X(i) increase or remain the same in successivesteps of the algorithm and this number is bounded by L. Sothis sequence X(i)(t) converges when t!1.

When PLI are included things vary slightly. Some extradefinitions are required. Consider an edge e having L wave-lengths. Consider as Pl,e the noise power of a specific wave-length l at a specific edge e, which can be identified exactlyas the standard deviation r2 involved in the Q-factor calcu-lation of Section 4. If we use the notation, M ðeÞ

k ¼ Me;k, thenPl,e = Pl,e(M(e)). A reservation of a path X = (Xe) on wave-length k, transforms the noise linearly

P l;e M ðeÞ �X e dk;:

� �¼ P l;e M ðeÞ� �

þX eSkl;e M ðeÞ� �

with Skl;e P 0

For an existing path Y on wavelength l a reservation of X

on wavelength k may transform its noise power toXe

Y eP l;e M ðeÞ� �!X

e

Y eP l;e M ðeÞ� �þX

e

Y eSkl;e M ðeÞ� �

in the last term lies the influence of X on Y. For the prob-lem at hand, the purpose is to maximize the physical layermerit function for performance assessment which is the Q-factor of a particular lightpath. This depends on the wave-length, length and noise power of a path as a function.When searching for a particular lightpath, its wavelengthis not known in advance. For a particular lightpath X re-served on wavelength k, the Q-factor is a non-linear func-tion of X. An empirical rule is that the shorter the paththe better the physical performance, which is not alwaysthe case, hence a PLI aware algorithm should check theQ-factor of the path (see next section) Furthermore, reser-vation of a path can affect the performance of other estab-lished paths in terms of the Q-factor. This simulations haveshown that effect cannot be neglected. It is necessary tomake this check (the Q-factor of the reserved paths)although it incurs high computational cost. Note that sincethese paths have a fixed length, the reservation of a newpath affects only the noise power induced on them. In thiscase, the influence of the new path is linear and a bound onQ-factor can be transformed to a bound on the noisepower, which in turn can be specified as a bound (T) onthe influence of a newly reserved path to an existing path

and an approximate linear problem is formulated thatcan be solved in polynomial time.

PLI aware SP problem: Suppose that we are given a net-work with pre established paths Y(n) on wavelength kn. Forfixed k find a suitable X

minX

e

X e‘ðeÞ( )

: 8X compatible with the constraints

Constraint 1: The path starts from s and ends at d:AX = B if X(k) 5 0.Constraint 2: Wavelength continuity: Xe Me,k = Xe

"e.Constraint 3: We implicitly assume under the definitionof X that its entries are either 0 or 1.Constraint 4: For every candidate check that the Q-fac-tor is higher than threshold Q 0 (the algorithm gives a setof candidate lightpaths per wavelength).Constraint 5: We respect the pre-established pathsX

e

Y ðnÞe P kn;e M ðeÞ� �þX

e

Y ðnÞe X eSkkn;e M ðeÞ� �

6 T n

We also provide an SWP variant

PLI aware SWP problemFind suitable X in the maximization

maxXL

k¼1

Ye:X e¼1

Me;k

( ): 8k and X compatible with the constraints

Constraint 1: The path starts from s and ends at d:AX = B if X 5 0.Constraint 2: We implicitly assume under the definitionof X that its entries are either 0 or 1.Constraint 3: Feasibility condition for Q (check that it ishigher than threshold Q 0).Constraint 4: We respect the pre-established paths.

Xe

Y ðnÞe P kn;e M ðeÞ� �þX

e

Y ðnÞe X eSkkn;e M ðeÞ� �

6 T n

Even in this simplified form, the problem exhibits complex-ity, since for every existing path a linear inequality has tobe checked. Simulations have shown that this contributionreduces the complexity of the problem since for high block-ing probability it is not necessary to check all the existingpaths. The more our network is saturated, the more prob-able is for a new path to drop the Q-factor of an existingpath below its threshold.

3. Lightpath establishment

The structure of the routing algorithm is shown inFig. 1. Connection requests are dynamic and the generatedtraffic is related to a service with constant service time offour units and inter-arrival times that follow a uniform dis-tribution with mean time of 10 units. Each connection

250 V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254

request is supposed to require bandwidth equal to thecapacity provided by one wavelength.

As reference network, the Pan-European Network isused that has N = 16 nodes and K = 23 links [12] and isconsidered to be transparent with L = 40 WDM channelswithout any regeneration or wavelength conversion. Fur-thermore no protection is assumed. It is noted that no spe-cial effort was made to dimension the reference networkthat was used as in the IST Nobel project. It would beappropriate to investigate two network plans that are suit-able for each of the SP and the SWP algorithms takingunder consideration the traffic matrix for each case. How-ever the scope of this paper is to investigate the qualitativeperformance of the algorithm when PLI constraints areapplied with respect to the case when no constraints areused. The QoS metrics to assess network performanceare BP and LB. The latter is defined as the standard devi-ation of the lightpath occupancy in the network.

The path establishment process is based either on the‘shortest-path’ (SP) or the ‘shortest widest path’ (SWP)routing principle. With SP, when a request for connectingany two nodes appears, the shortest-path is calculated [1].SWP seeks the path that has maximum continuous (adja-cent) available wavelengths and thus is least congested.The routing engine searches for the path with the lowestcost. For the case for SP: for each wavelength k, it findsthe shortest-path with continuous wavelengths that con-nects the two nodes that request connection. It then keepsonly those that are available so then returns the set ofunused paths that fulfill the wavelength continuity con-

Find available p

For each of the pos

PLI?

Yesreturn k(

Yes=PLI on No=PLI off

Cho

Calculate Q-factor of

Q >QA

Calculate minimum Q-factor of affected lightpaths after reservation of

Q >QB

For each candidate lightpath P=1..k(

Nodrop lightpath

No

drop lightpath

Put into the table of acceptable lightpaths

Yes

Yes

Find available p

For each of the pos

PLI?

Yesreturn k(λ) lightpaths

Yes=PLI on No=PLI off

Cho

Calculate Q-factor of P

Q >QA

Calculate minimum Q-factor of affected lightpaths after reservation of P

Q >QB

For each candidate lightpath P=1..k(λ)

Nodrop lightpath

No

drop lightpath

Put into the table of acceptable lightpaths

Yes

Yes

Fig. 1. The routing engine developed for

straint. For the case for SWP: the path wavelengths thathas maximum continuous (adjacent) available betweentwo nodes is found. If the engine is PLI aware, for eachof the available lightpaths it calculates a merit function thatdesignates physical layer performance, here the Q-factor[13,14]. The engine compares the Q-factor values with athreshold Q 0 and rejects the lightpaths having a lower Q-factor. In the next step, the potential impact of the candi-date channel on the established lightpaths is evaluated.The engine probes the system with each of the candidatelightpaths. If any of the candidate lightpaths affects irre-versibly the connected ones, i.e. the Q-factor of any affectedlightpath drops below threshold Q 0, the candidate lightpathis rejected. A set of candidate lightpaths is finally returned.In the final step, one path is selected with the assistance ofthe first fit (FF) wavelength assignment algorithm, whichconsiders a lower numbered lightpath before a higher-num-bered one [1].

4. Physical layer design

The fiber links are considered to comprise fully disper-sion compensated fiber spans with single mode fiber(SMF) segments followed by dispersion compensating fiber(DCF) segments, like shown in Fig. 2. Fiber parameters areshown in Table 1. Span losses are exactly compensated byan erbium doped fiber amplifier at the end of each span.The physical layer is not OSNR limited, i.e. it has beendesigned in a way that approximately 90% of all possiblelightpaths perform sufficiently at full load.

ath that minimises cost

sible wavelengths =1…

Noblock request

Available?

Assign one wavelength from this table with

BF, RF or FF

Return a table with acceptable lightpaths

ose COST

ath that minimises cost

sible wavelengths λ=1…N

Noblock request

Available?

Assign one wavelength from this table with

BF, RF or FF

Return a table with acceptable lightpaths

ose COST

PLI aware WRA as described in text.

Table 1Fiber physical parameters

SMF DCF

Attenuation coefficient 0.23 dB/km 0.5 dB/kmDispersion coefficient 17 ps/nm km �85 ps/nm kmDispersion slope 0.085 ps/nm2 km 0.3 ps/nm2 kmEffective area 65 lm2 22 lm2

Non-linear refractive index 2.6 · 10�20 m2 W�1 3.4 · 10�20 m2 W�1

Span length 40 km 8 km

V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254 251

The impact of the transmission channel on the signal Q-factor degradation is modeled analytically as in [15] for asystem with 50 GHz channel spacing. In our studies, powerper channel Ps,M is taken equal to +3 dBm unless otherwisestated. The Q-factor is given by: Q � RP s;M= r0 þ r1½ �where r0 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2

th þ 2qRP chASE;M þ r2

spon–spon

qand

r1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2

th þ r2shot þ r2

sign–spon þ r2spon–spon þ r2

XPM þ r2FWM

qwhere rth is the thermal and rshot the shot noise of thereceiver. The ASE related spontaneous–spontaneousrspon–spon noise and signal–spontaneous rsign–spon noiseare calculated as in [13] for the whole amplifier chain. rXPM

and rFWM are the standard deviations of the XPM andFWM generated fluctuations respectively.

Here the receiver is a PIN diode and it gives shot andthermal noise [15]

r2th ¼ ðNEP � RÞ2Be;

r2sh ¼ 2qRP ch

out;M Be:

Here the ASE related noise spontaneous–spontaneous andsignal–spontaneous [15]

r2sign–spon;M ¼ M2R2P ch

s P chASEBe=Bo; r2

spon–spon;M

¼ M2R2ðP chASE;MÞ

2ðwBo � BeÞBe=B2o

And the noise from non-linearities is briefly described here.The total XPM-induced crosstalk on the test channel i

due to channel k is obtained by adding up the contributionsfrom all fibre sections and is given by [16]

P XPM;ik xð Þ

¼ 2P k xð Þ exp �ixX2M

l¼1

LðlÞ

vðlÞgi

" #X2M

l¼1

cðlÞi

� exp ixXl�1

n¼1

dðnÞik LðnÞ" #

P ðnÞi

� aðlÞik sinðBl�1i �QðlÞk Þ � ðb

ðlÞik þ qðlÞk Þ cosðBl�1

i �QðlÞk ÞðaðlÞik Þ

2 þ ðbðlÞi � qðlÞk Þ2

(

þ ½aðlÞik sinðQðlþ1Þ

k �BðlÞi Þ þ ðbðlÞi þ qðlÞk Þ cosðQðlþ1Þ

i �BðlÞi Þ�e�aðlÞik LðlÞ

ðaðlÞik Þ2 þ ðbðlÞi þ qðlÞk Þ

2

þ aðlÞik sinðBðl�1Þi þQðlÞk Þ � ðb

ðlÞi � qðlÞk Þ cosðBðl�1Þ

i þQðlÞk ÞðaðlÞik Þ

2 þ ðbðlÞi � qðlÞk Þ2

� ½aðlÞik sinðQðlþ1Þ

k þBðlÞi Þ � ðbðlÞi � qðlÞk Þ cosðQðlþ1Þ

k þBðlÞi Þ�e�aðlÞik LðlÞ

ðaðlÞik Þ2 þ ðbðlÞi � qðlÞk Þ

2

)

where QðlÞk ¼ x2k2k

Pl�1n¼1LðnÞDðnÞk =ð4pcÞ; bðlÞi ¼ x2DðlÞi k2

i =

ð4pcÞ; qðlÞk ¼ x2DðlÞk k2k=ð4pcÞ; and BðlÞi ¼ x2k2

i

PNn¼lþ1

LðnÞDðnÞi =ð4pcÞ Furthermore, aðlÞik ¼ aðlÞ � jxdðlÞik with dðlÞik

…

SMF DCF EDFA SMF DCF EDFAOXC OX C

span link

…

SMF DCF EDFA SMF DCF EDFAOXC OX C

span link

Fig. 2. Block diagram of the physical layer design.

being the walk-off parameter between channels i and k inthe fibre segment given by dðlÞik ðv

ðlÞgi Þ�1 � ðvðlÞgk Þ

�1 and P ðnÞi

is the power level of channel i entering the nth fibre. Oddnumbered fibre segments are SMF and even numberedare DCF.

The standard deviation of the fluctuation due to XPM isgiven by

r2XPM ¼

Xk 6¼i

R2

Z þ1

�1P XPM;ikðxÞj j2 � H elecðxÞj j2 dx

with Helec(x) the transfer function of the electrical filter atthe receiver.

In a WDM system with N channels with equal channelspacing, the total time averaged FWM power generatedat channel n (with frequency fn) at the end of the Mth link,assuming that the input power per channel is Ps,M = P forall channels, can be written as follows [17]:

r2FWM ¼

1

9c2 � P 4

Xfn¼fiþfj�fk

pijknijkd2ijk

�sin2 M DbSMF

ijk ðknÞLSMF þ DbDCFijk knð ÞLDCF

� �.2

h isin2 DbSMF

ijk ðknÞLSMF þ DbDCFijk knð ÞLDCF

� �.2

h in; i; j; k ¼ 1; 2; . . . ; Lð Þ

where M is the number of links, that is the number ofamplifiers. The summation is over all relevant channelcombinations satisfying the relationship fn = fi + fj � fk

(k 5 j) and (k 5 i). c is the non-linear coefficient, dijk isthe degeneracy factor that takes a value of 3 (for i = j) or6 (for i 5 j), pijk the probability of all wavelength beingat the ‘‘1’’ level simultaneously and gijk the FWM factor de-fined by

gijk ¼1� e� a1�iDbSMF

ijkð ÞLSMF

aSMF � iDbDCFijk

þ e� a1�iDbSMFijkð ÞLSMF

1� e� a2�iDbDCFijkð ÞLDCF

aDCF � iDbDCFijk

����������2

where Dbijk ¼ bn þ bk � bj � bi represents the propagationconstant difference (phase mismatch) between the carriers.

5. BP and LB

The routing engine is used for two different cases withand without PLI awareness, and the BP versus offered traf-fic load (by means of traffic scaling factor – Erlang) is cal-culated and plotted in Fig. 3. BP is greatly affected by thePLI awareness. While traffic load is low, blocking is negli-

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

0 10 15 20 25 30

offered traffic load

BP

SP,w/o PLI SP, w PLI, Q'=10SP, w PLI, Q'=8SP,Worst Case Analysis, Q'=10

5

Fig. 3. BP with respect to the offered traffic load when Q 0 = 0 (w/o PLI)and when Q 0 = 8 and 10, (w PLI) have been used. BP is calculated atsteady state and the confidence level of the measurements is 97.5% . Theconfidence interval for all measurements is of the order of 1.5–2.5% andhence cannot be illustrated on the plot.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 10 20 30

offered traffic load

BP

SP, w/oPLI SP, -1.5 dBm SP, 4.5 dBmSWP, -1.5 dBmSWP, 4.5 dBmSWP, 7.5 dBmSP, 7.5 dBmSWP, w/oPLI

Fig. 5. BP versus traffic scale factor for two different algorithms (SP andSWP) and different power per channel.

252 V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254

gible for both Q 0 = 0 and Q 0 5 0. When traffic load is low,the main source of degradation is the ASE and not the non-linearities. Since for this network ASE noise alone is not alimiting factor, for the specific PS,M, the physical perfor-mance is acceptable for all lightpaths. When the traffic loadstarts growing, the fiber links start getting populated bylightpaths and hence fiber non-linearities start affectingthe performance. As the traffic load grows further, block-ing is mainly imposed by the network resource limitations.Hence, longest paths that are more likely to suffer fromnon-linearities are blocked anyway. This result necessitatesthe introduction of PLI awareness in the WRA, since, forthe cases with poor physical performance, resources arewasted for signals that have unacceptable quality.

It is evident that blocking is quite pronounced for thespecific network even when PLI awareness is turned on.For comparison purposes however, and in order to ensurethat the algorithms assist in efficiently utilising theresources of the network, the results are directly comparedto the case where the algorithm assumes that the perfor-mance of a specific lightpath is the worst possible, i.e.Worst Case Analysis as indicated in Fig. 3. In this case,

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30

offered traffic load

LB

SP, w/o PLI

SP, w PLI, Q'=10

Fig. 4. LB versus offered traffic load using the engine of Fig. 1 for Q 0 = 0and 10.

for the calculation of the Q-factor the network is consid-ered fully loaded and hence the under-performing light-paths are blocked.

The other QoS metric is the LB and is plotted in Fig. 4.The deviation of the occupancy is higher when PLI aware-ness is off. This means that the network resources are dis-tributed more evenly when the PLI aware algorithm isdeployed.

6. The impact of the physical layer

The blocking performance of the SP and SWP algo-rithms for the PLI-blind and PLI-aware cases are shownin Fig. 5 for different values of the channel power PS,M.For the PLI blind cases (w/o PLI in the figure) the twoalgorithms perform in a similar manner and the power levelhas no effect. When PLI awareness is turned on and PS,M isequal to (or less than) �1.5 dBm the network becomes ASElimited and, as a result, the engine blocks most of the light-paths. As power per channel grows, the physical perfor-mance is better and this is reflected in the overallblocking performance. The two algorithms no longer per-form similarly. For low traffic the SP algorithm outper-forms the SWP one. As traffic grows, non-linearitybecomes considerable. Now SWP performs better as itsinherent characteristic, to find the least occupied link, helpstowards relieving the blocking performance. For higherpower levels both algorithms perform similarly. All thecases tend to the same BP value when scale factor grows,since for high scale factors, limitations are imposed by lackof network resources. Comparison of the algorithms is sta-tistically valid as the error bars of the graphs below is in theorder of 1.5–2.5% of the values (see Appendix).

A general comment for all figures is that the BP is quitehigh and this is because no special consideration has beentaken with respect to the traffic matrix and hence blockingis high.

To compare the two algorithms the number of steps per-formed should be discussed. For the specific network theSP algorithm required L*O(N2) operations to computethe path and M = O(L*N2) operations to check the affectedpaths. The SWP algorithm uses only O(N2) operations to

V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254 253

compute the path while checking the affected paths incursM = O(L*N2 ) complexity too.

The Q-factor depends on many parameters, for examplethe number of channels, channel spacing, fiber type andparameters (dispersion, attenuation, non-linearity), bit-rate, power etc [18]. Evidently, each of these parameterscan be used as an optimization variable in order to assessits impact on performance degradation, at system and con-sequently at network level. This is clearly manifested inFig. 5. There, the BP is calculated for different values ofpower per channel PS,M, for both SP and SWP and forthe specific case, where traffic is scaled by a factor of 20.The BP is calculated for different values of power per chan-nel. The Q-factor of the lightpaths is affected directly by thepower of each channel, through the ASE and non-lineari-ties and the blocking is increased for lower values of theQ-factor. Such a curve can be used to collectively evaluatethe impact of the power per channel on the network andphysical performance, as well as to evaluate the impact ofthe path establishment algorithm. Note that for the PLIblind case, the BP is 0.01. So in the case of the specific net-work the system designer can either use an average powerof 0 dBm combined with the SP WRA or a +4 dBm aver-age power per channel with the SWP WRA. The latter out-performs the former in terms of calculation speed. Hence, amajor conclusion from the above is that the decision on thetype of WRA to be used on the network for specific trafficdirectly depends on the physical layer plant and vice versa(see Fig. 6).

7. Conclusions

In this work, QoS metrics like BP and LB are used tomeasure the effectiveness of a routing engine, that inte-grates routing algorithms and PLI. For the first time, twopath establishment algorithms, the SP and the SWP, wereconsidered using this engine. In addition the engine incor-porates other novel features, such as the fact that it takesinto account the impact of ASE, XPM and FWM on theQ-factor, using analytical models and guarantees that

0

0.1

0.2

0.0

0.4

0.5

0.6

0.7

0.8

0.9

-4 -2 0 4 10

power per channel (dBm)

BP

_20

SWPSP

2 6 8

Fig. 6. BP versus power per channel when PLI aware routing algorithm isperformed for SP and SWP when traffic scale factor is 20 (i.e. BP_20).

resources are not wasted on substandard lightpaths. It isshown that such a routing engine not only assists in QoS-aware networking but it can also be used as a tool for find-ing the optimum physical parameters for different pathestablishment algorithms. Conclusively, the choice of therouting algorithm and QoS parameters strongly dependson the physical layer parameters.

Acknowledgements

The authors would like to acknowledge the IST NobelProject for partially funding this work. Furthermore thereviewers are greatly acknowledged for their valuablefeedback.

Appendix

In this section the methodology for the measurements ispresented. In order to simulate the traffic of the networkbetween every node pair of the form (s,d) we make theassumptions that: (a) between successive requests of thesame form we choose an inter-arrival time that is exponen-tially distributed with mean value Tinter-arrival(s,d), and that(b) each request has a life-time (time that keeps resourcesreserved) that is also exponentially distributed with meanvalue Tlife-time(s,d). Since we use discrete time we generatethese random variables with the help of Bernoulli trials.The load contributed by each pair is defined as

Loadðs; dÞ ¼ T life-timeðs; dÞT inter-arrivalðs; dÞ

For measurement of the blocking probability per N re-quests arriving at the route computation module (RCM)we measure the number of failures defined as the numberof requests dropped due to lack of resources. This numberis defined as Nfailure. Since we tried to be as accurate as pos-sible we also include the possibility that at the time we mea-sure the number of requests because of the non-zeroprobability of zero inter-arrival time N cannot be kept fixedbut it has a small variation. So while sampling we check thecondition N > N0. This signifies a measurement event. Inorder to compute the blocking probability BP we sampledfor m0 events to find the blocking probability pi defined aspi = Nfailure,i/Ni for the ith event. We make the assumptionthat for large N0, Nfailure,i are independent, with boundedcommon variation, and mean value N0 BP, so we use awell-known statistical test. From the central limit theorem,Nfailure,I must follow a normal distribution and for this rea-son we can make the Student test for Nfailure,i with m0�1 de-grees of freedom. In these tests we chose N = 10000,m0 = 100 and decision threshold 0.95. So, for the randomvariable X = Nfailure we know that � Sffiffiffiffi

m0p tm0�1;0:475þ

�X 6 N 0BP 6 Sffiffiffiffim0p tm0�1;0:475 þ �X is the test for the BP. How-

ever we need to skip the transient state of our network inorder to keep N0 reasonable. This is done via thetest 1

i

Pik¼1P k � 1

iþ1

Piþ1k¼1P k

��� ��� < A 1i

Pik¼1P k. After the i that

254 V. Anagnostopoulos et al. / Optics Communications 270 (2007) 247–254

satisfies this condition, we take m0 measurements in orderto make the statistical test. Note that the above measure-ments are considered asymptotic so the error bars equalfive times the confidence interval.

References

[1] H. Zang, J.P. Jue, B. Mukherjee, Opt. Net. Mag. 1 (January) (2000).[2] J. Strand, A.L. Chiu, R. Tkach, IEEE Commun. Mag. 39 (2) (2001) 81.[3] S. Herbst, H. Lucken, C. Furst, S. Merialdo, J.-P. Elbers, C.

Glingener, Routing Criterion For XPM-Limited Transmission InTransparent Optical Networks, WE2.4.4, ECOC 2003, Rimini, Italy.

[4] A. Levandovsky, Wavelength routing based on physical impairments,OFC, 2, 2001, TuG7.

[5] R. Sabella et al., J. Lightwave Technol. 16 (November) (1998) 1965–1972.

[6] I. Cerutti, A. Fumagalli, M.J. Potasek, Photon Technol. Lett. 14(2002) 411.

[7] I.E. Fonseca, M.R.N. Ribeiro, R.C. Almeida Jr., H. Waldman,Electron. Lett. 40 (5) (2004) 191.

[8] B. Ramamurthy, D. Datta, H. Feng, J.P. Heritage, B. Mukherjee, J.Lightwave Technol 17 (10) (1999).

[9] R. Cardillo, V. Curri, M. Mellia, Considering Transmission Impair-ments in Wavelength Routed Networks. ONDM 2005, February 7–9,2005, Milan, Italy.

[10] D. Banerjee, B. Mukherjee, IEEE J. Select. Areas Commun. 14 (5)(1996) 903.

[12] IST Project LION: Deliverable D19 Multilayer resilient networkplanning and evaluation: intermediate results.

[13] A. Stavdas, S. Sygletos, M. O’Mahoney, H.L. Lee, C. Matrakidis, A.Dupas, J. Lightwave Technol. 21 (February) (2003) 372.

[14] E.A. Golovchenko, A.N. Pilipetskii, N.S. Bergano, C.R. Davidson,F.I. Khatri, R.M. Kimball, V.J. Mazurczyk, J. Select. AreasCommun. 6 (March–April) (2000) 337.

[15] R. Ramaswani, K.N. Sivarajan, Optical Networks: A PracticalPerspective, Morgan Kaufmann Publishers, Inc., San Franciso,USA, 1998.

[16] A.V.T. Cartaxo, J. Lightwave Technol. 17 (2) (1999) 178.[17] W. Zeiler et al., J. Lightwave Technol. 14 (9) (1996) 1933.[18] N. Antoniades, A. Boskovic, I. Tomkos, N. Madamopoulos, M. Lee,

I. Roudas, D. Pastel, M. Sharma, M.J. Yadlowsky, IEEE J. Select.Areas Commun. 20 (1) (2002) 149.