Designing and Optimization of Heterogeneous OTN/DWDMNetworks with Intermediate Grooming

Afonso OliveiraIST (METI)

afonso.oliveira@ist.utl.pt

ABSTRACTThe coexistence of channels with different bitrates in thesame optical network OTN/DWDM is a possible scenario asthe technological evolution comes to allow higher bitrates.In this document a study and results are presented after thedevelopment of an optimization framework for OTN net-works. For this framework the intention is to study methodsthat design a cost optimized optical network that supportdifferent services as traffic demands with different bitrates aswell as optical channels with a different bitrate. The use ofintermediate grooming is also be considered where one trafficflow can be regrouped with others at any intermediary nodeof its path. The model considering intermediate groomingproposed yields lower network cost values but needs consid-erably more time to compute. Two heuristic possibilities arecompared having them different behaviors. This work con-siders also the use of different node equipment with differentarchitectures.

KeywordsOTN/DWDM, grooming, ILP, CapEx, intermediate groom-ing, heuristics

1. INTRODUCTIONDue to huge increase in traffic demands resulting from

new services of high bitrate, telecommunications backbonenetworks need to rely on optical solutions like Optical Trans-port Network (OTN). In OTN one optical signal is routedthrough a Dense Wavelength Division Multiplexing (DWDM)network which includes many fibers and optical nodes. Asthese signals are analogue they need to be regenerated inorder to avoid the effects of physical impairments.

In other words it is necessary an electrical-optical-electrical(E/O/E) conversion which is done with the use of Wave-length Division Multiplexing (WDM) transponders. Thesetransponders are devices that can receive and emit opticalsignals. They are currently evolving and their cost and char-acteristics are changing. Each of them will have their ownprice and will offer a different optical reach. Optical reachis the maximum distance an optical signal can travel fromone end in order be received with quality at the other end.Also each transponder only transmits and receives at a givenbitrate.

The optical nodes are usually Reconfigurable Optical Add-Drop Multiplexers (ROADMs) which are equipment belong-ing to the transport layer that have the capability to add ordrop traffic to the infrastructure attached to them in the ser-

vice layer as well as to route traffic in the transport layer.A ROADM has also the ability to route wavelengths, as sooptical signals can be routed without O/E/O conversion.

In the transport layer for nodes with more than two de-grees we need a ROADM Multi-Degree that needs a morecomplex architecture in order to be completely colorless.Some older ROADM do not have the capability to routewavelengths to all directions.

Designing an efficient network requires the use of traf-fic engineering techniques that can adapt the traffic in anoptimized way to have lower costs and work around net-work limitations. One of them is grooming which consistsin aggregating different traffic flows in one optical channelin order to avoid the use of multiple optical channels. Thisgrooming technique can be applied to the traffic at the ex-treme nodes of a communication or at any intermediate nodein the path chosen by the communication. Considering thislast case will be further referred as considering intermediategrooming. The case when only grooming at the source isconsider will be referred as source grooming.

This thesis is the continuation of recent works developedby Santos et al which design and optimize heterogeneousoptical networks with grooming and Virtual Concatenation(VCAT) [7] and provide one alternate heuristic algorithm tothe one considered in [6].

In this work the main objective is to develop a frameworkto design OTN/DWDM networks with the aim of optimiz-ing transponder related Capital Expenditure (CapEx) costs.Transponders can only be located at the nodes. The servicesto be considered will be services with: 1.25, 2.5, 10, 40 and100 Gb/s. Hence referred as 1G25, 2G5, 10G, 40G and 100Gservices, respectively. The optical channels used will haveonly two different bitrates: 40 and 100 Gb/s which are goingto be referred as 40G and 100G transponders.

Three scenarios with different node architectures are tobe considered. The first one considers that all nodes havecolored interfaces. The second considers that there is onlywavelength switching in some directions, as so some direc-tions will need Optical-Electrical-Optical (O/E/O) conver-sion. The last one considers that there is wavelength switch-ing in all directions.

Finally the framework should also be able to design net-works that support intermediate grooming.

This work extends the work [7] by introducing new trafficservices. Although in this thesis work VCAT is not sup-ported, as it is in [7], there are now numerous combinationsof traffic aggregation as different and smaller services areconsidered. Due to this it was created a new ILP formula-

tion with a different approach.This work also extends the work [6] by introducing a differ-

ent heuristic to reduce the computation time of the problemto solve. The new heuristic uses a Lagrangian relaxationapplied to the formulation.

This thesis work will also do a study on the impact ofdifferent node architectures in the network design and opti-mization. Also in this work it is considered the possibility ofrearranging the traffic flows in different channels to reducethe network’s costs.

In Section 2 this document will present works performedin these areas, explaining also the most important conceptsintroduced. After this, in Section 3, the architecture of thework will be presented by describing the formulations andalgorithms introduced. The work’s simulation results arepresented in Section 4. Finally a summary and conclusion ispresented in Section 5 as well as an enumeration of possiblefuture work.

2. RELATED WORKThis chapter presents some considerations about OTN

networks and describes the state of the art in methodolo-gies for designing and optimizing these networks.

2.1 OTNTelecommunication networks can be divided into two net-

works: service network and transport network. The trans-port network provides paths to the service network, as sothe service network can be seen as a client of the transportnetwork. This separation can be observed in Figure 1.

Figure 1: Service and transport network

The OTN layered structure is composed of two main do-mains: electrical domain and optical domain. In the electri-cal domain we can find three different layers Optical channelPayload Unit (OPU), Optical channel Data Unit (ODU) andOptical channel Transport Unit (OTU). These layers adaptthe client signal to fixed throughput units. OPU layer is theresponsible for adapting the signals bitrate. It encapsulatesthe client signal (eg. Synchronous Digital Hierarchy (SDH),Ethernet) and does any rate justification that is needed. TheOPU header in the frame is valid between the source anddestination nodes of the client signal.

ODU’s role is to monitor the connection between the sourceand destination nodes of the client signal. Another role isto establish the data channel between those two nodes andprotect it.

The OTU is responsible for processing the detection and

error correction of an optical transmission. The OTU cre-ates the optical channel until the next colored node.

The optical domain layers relate to the optical channeland have defined important procedures to manage the op-tical signals. The top layer in the electrical domain is theOptical Channel (OCh) which identifies the channel used bya connection between two non-optical ends, for instance twotransponders. The Optical Multiplex Section (OMS) comesnext and is the one responsible for identifying wavelengthsand assigning them to the communication channels. Thebottom layer is the Optical Transport Section (OTS) whichis responsible for managing signal strengthening in order toavoid effects originated by physical impairments.

There are also higher order and lower order OPU andODU so that we can group different traffic demands in oneoptical channel reducing the number of wavelengths needed.After a client signal is mapped indirectly to a lower orderODU, this one can be mapped into an OTU or groupedwith other ODU by being grouped in a Optical channelData Tributary Unit Group (ODTUG) and restarting themapping process but with higher order units.

Traffic grooming is a traffic engineering process that con-sists in aggregating traffic demands so that the bandwidthof an optical channel can be used more efficiently. Differ-ent possibilities of aggregation within the OTN scope canbe found in Figure 2.

Figure 2: Mapping/multiplexing of ODUs intoOTUs. [5]

In an OTN there is a big set of network elements. Thereare two main types that characterize the equipment: colorand colorless equipment. The main difference is that colorequipment has the capability to do optical-electrical conver-sion contrary to colorless equipment.

Even though a node may be colorless some of the traf-fic transiting that node may still need Reamplification, Re-shaping and Retiming (3R) regeneration after some distance(optical reach). Many factors affect the optical reach suchas the launched power of the signal and the modulation for-mat of the signal [2] which are determined by the WDMTansponders on the edge of the communication. In order tooptimize the CapEx of the network we need to know how touse regeneration wisely.

2.2 ROADM ArchitecturesROADM are equipment capable of adding and dropping

traffic to their tributary interfaces. The tributary interfacesare the ones that connect the Transport Layer with the Ser-vice layer. They are connected to the infrastructure in the

Service Layer local to the node. When a ROADM has morethan two degrees there is a need to switch the path of eachwavelength in different directions.

Second generation ROADM used Planner Lightwave Cir-cuit (PLC) technology. The functional technologies of thePLC-based ROADM depend on Arrayed Waveguide Grat-ings (AWG), thermo-optic switches, Variable Optical Atten-uators (VOA) and tap monitors that are used for monitor-ing power in specific channels. PLC-based ROADM haveattracted the most attention because their overall manu-facturing approach is more efficient and simpler [8]. Hencebeing cheaper equipment. Third generation ROADM haveWavelength Selective Switching (WSS) technology. WSS isan advanced optic fiber module that can select individualwavelengths from multiple input fibers and switch these toa common output fiber (Nx1 WSS) [1].

PLC-based, as well as wavelength blocking ROADM donot facilitate true optical branching, in which any wave-length can be directly routed to any desired port withoutthe need to perform optical-electrical conversions. This typeof node architecture will be hence referred as Fixed NodeArchitecture and Flexible Node Architecture to nodes withROADM with WSS technology. These ROADM can be usedas nodes in a mesh network but unnecessary regenerationmay occur.

2.3 Models for Studying OTN/DWDM Net-works

Most of the works use an Integer Linear Programming(ILP) model in order to get the optimal results. In thisarticle only one work will be analyzed which is the one ofthe most importance to this thesis work.

Recently there was a work done by J. Santos et al [7] thatoptimizes the network cost in terms of regenerators. Thenetwork designing framework developed supports only 40Gor 100G equipment as well as 40G and 100G services.

They introduced an ILP model to get the minimum costresults which takes into account grooming and VCAT tech-niques. As the formulation is link-path based there is aneed to pre-calculate paths for each node pair. In this work5 candidate paths per node pair were calculated, computedwith a k-shortest path algorithm aiming to minimize thehop-count.

With the framework developed the authors studied thenetwork regenerators cost varying certain parameters re-lated to the regenerator relative costs and optical reach.The channel capacity was also considered. A study wasmade also about the impact of the use or not of groomingor VCAT techniques.

2.4 Intermediate GroomingIn [10] Zhu and Mukherjee formulate an ILP to reach their

objective which is mainly maximizing the total throughput.The network is already designed and has a fixed numberof equipment. The authors focus in using it in the mostefficient way possible which is different from this thesis work,but the overall architecture of the ILP can be used.

Some works were made on multi-granular networks whichformulations or approaches can be adapted in this work as ithappens in [3]. Instead of having one traffic demand variableper path, the authors have one traffic demand variable perpath and per wavelength used. Which increases the num-ber of variables used but allows to consider a wider set of

scenarios.

2.5 Heuristic AlgorithmsIn order to do an accurate optimization an ILP model is

the best approach. However solving ILP starts to be rathertime consuming when our network gets bigger. In order toreduce the time spent in the ILP solving approximations ortechniques are needed.

One of the methods is presented by Santos, J. et al [6]and Pedro, J. et al [4] in two works also about designing andoptimization of OTN/DWDM networks. They do an LinearProgramming (LP) relaxation that will be solved in a cyclewhere they progressively add constraints to the variablesuntil all the resulting variables are integer. The LP problemformulation is exactly the same as the one developed forthe ILP model previously done. This cyclic strategy, namedLP+R, is depicted in the flowchart of Figure 3.

Figure 3: Flowchart of the LP+R optimization ap-proach. [6]

The strategy consists in solving the LP formulation ineach cycle until the resulting variables are all integer. Thereis a list L which the purpose is to be filled with roundedvalues of the variables in order to add the constraints. Instep 1 while formulating the problem these constraints areadded. After the LP problem solving in step 2 the frame-work checks if all the resulting variables are integer. If theyare the problem was solved, if not the cycle would continueto step 3.

In step 3 the resulting variables are analyzed and a round-ing distance ∆ is calculated. This rounding distance is thedifference between the variable ceiling value and the vari-able value itself. This is calculated so that in step 4 thenon-integer variable with the shortest rounding distance toits ceiling value can be selected. This ceiling value is addedto the list L in order to add a constraint in the next itera-tion. For instance, if variable x is the one selected in step 4with a rounding value a on the next LP formulation therewill be a x ≥ a constraint.

3. ARCHITECTUREThe main architecture of the framework is represented on

Figure 4.

3.1 ILP Model Implementation for Source Groom-ing

Figure 4: Framework architecture.

In order to adapt our traffic demands an OPU0, OPU1,OPU2, OPU3 and OPU4 can be used to map 1G25, 2G5,10G, 40G and 100G, respectively. As in this work the opticalchannels’ bitrates to be considered are 40Gb/s and 100Gb/sall the traffic as to be aggregated either into one OTU3 orone OTU4.

3.1.1 Previous CalculationsFive paths will be calculated using a k-shortest path al-

gorithm minimizing the total path length as each link hasit’s length as weight. The algorithm to use will be Yen’salgorithm presented in [9] which consists in applying succes-sively Dijkstra’s algorithm removing different links in eachiteration.

After choosing the paths the framework will calculate thecost of each path, that is, how may regenerators will it needdepending on the technology used (40G or 100G). In orderto calculate a path’s cost the following parameters regardingregenerators’ characteristics will be used:

• Dmaxch - optical reach of a transponder of the type ch;

• CTxRxch - cost of a regenerator of the type ch.

The algorithm to calculate a path’s cost is represented inAlgorithm 1. In this algorithm the function length returnsthe length of a link, path represents the path k and linkrepresents each of the links of the path considered.

Algorithm 1 Calculate Regsd,kch

length sum← 0reg count← 0for link ∈ path dolength sum← length sum+ length(link)if length sum > Dmax

ch thenreg count← reg count+ 1length sum← length(link)

end ifend forRegsd,kch ← reg count

Also it will calculate how many optical channels will a setof traffic demands of the same source/destination node pairneed in order to calculate a maximum value for a n index(See Formulation 1).

3.1.2 FormulationThe ILP model formulation to solve this problem is de-

scribed in Formulation 1.Equations (2) to (5) represent grooming constraints. In

equations (2) and (3) all the grooming possibilities are con-sidered for each type of channel.

Equation (6) represents the traffic constraints. For eachservice type demand between each node pair the sum ofall the tsdu,ch,n variables should be equal to the respectivetraffic demand value. Finally equation (7) represents thelink capacity.

3.2 HeuristicsAs referred in Section 2 a heuristic called LP+R was de-

veloped to get an approximated value of an ILP problem todesign and optimize an optical network. This heuristic isdescribed in [6]. Another heuristic was implemented in thiswork using as basis the work [3]. This heuristic consists inusing a Lagrangian relaxation in order to calculate a lowerbound of the problem and using the values obtained in therelaxation in an algorithm to calculate an upper bound.

3.2.1 LP+RThe LP+R heuristic was implemented in the same way

as in [6]. For a detailed description of this heuristic pleaseconsult Section 2.

3.2.2 LRHThe final algorithm will be based on running an algorithm

that initially was planed to substitute the upper bound al-gorithm in [3]. After some simulations a conclusion wasreached that the algorithm worked better in the first iter-ation. It produced better results than being iterated withthe Lagrange multipliers. However in order to formulate thealgorithm Lagrangian relaxation theory needs to be appliedto the formulation. So it will be explained.

Constraints (3) and (2) are relaxed and each constraintis associated with the respective λsd,n,ch Lagrange multi-plier also constraints (7) are relaxed and each constraint isassociated with the respective λij multiplier. The objec-tive function to minimize that results from this relaxationis presented in (8).

z =∑ch

∑sd

∑k

∑n

(Csd,k

ch − λsd,n,ch +∑ij

δsd,kch,n,ijλij

)xsd,kch,n+

∑ch

∑sd

∑n

∑opu

(Bopuch λsd,n,ch) topu,ch,n − λijW (8)

In this equation Bopuch represents the division of the bitrate

of a service that is mapped into an OPUopu by a channel’sbitrate ch. This is used to generalize the divisions presentedin (3) and (2). If the channel’s bitrate is bigger than thebitrate of the OPU that carries the traffic this value is zero asthere is no possibility of that channel carrying that service.

As there are no constraints that combine the two types ofvariables there is the possibility of separating this problemin two: Z1 and Z2 as it can be observed in equations (9)to (11). In this formulation Z1 will be restricted to thegrooming constraints that were not relaxed: (4) and (5). Z2

will not be necessary for this implementation.

Formulation 1 ILP formulation considering only sourcegrooming.

Indexes

sd Source and Destination node pair of a traffic demand

ij Link between nodes i and j

ch Bitrate of the channel used ({ch}G)

u Type of service identified by the OPU{u} unit with thesame bitrate

n The nth optical channel which has the same source anddestination going through the same path and using thesame type of regenerators

Input Parameters

T sdu Traffic demands between the node pair sd with the

rate of an OPUu

Csd,kch The total regenerator related costs of a path k between

the node pair sd using a channel of the type ch

W Maximum number of optical channels a link can sup-port

δsd,kij List of values that are 1 if the kth path between thenode pair sd passes through link ij and otherwise

Variables

xsd,kch,n Binary variable which represents the existence or

not of the nth optical channel from node s to noded, that is routed through the kth path of bitrate ch

tsdu,ch,n Integer value which represents how much of a ser-

vice u from node s to node d goes through the nth

channel of type {ch}G (can have a value between 0and the respective T sd

u )

Objective

min:z =∑ch

∑sd

∑k

∑n

[Csd,k

ch xsd,kch,n

](1)

Constraints

∑k

xsd,k100,n ≥1

100.(100tsd4,100,n + 40tsd3,100,n + 10tsd2,100,n+

2.5tsd1,100,n + 1.25tsd0,100,n), ∀sd∀n (2)

∑k

xsd,k40,n ≥1

40.(40tsd3,40,n + 10tsd2,40,n + 2.5tsd1,40,n+

1.25tsd0,40,n), ∀sd∀n (3)

∑k

xsd,kch,n ≤ 1, ∀ch∀sd∀n (4)

xsd,kch,n−1 ≥ xsd,kch,n, ∀k∀ch∀sd∀n\{1} (5)

∑n

(tsdOPU,100,n + tsdOPU,40,n

)= T sd

OPU , ∀sd∀OPU∈{0,1,2,3,4}

(6)

∑sd

∑k

∑n

(xsd,k40,n + xsd,k100,n

).δsd,kij ≤W, ∀ij (7)

z = Z1 + Z2 − λijW. (9)

Z1 =∑ch

∑sd

∑k

∑n

(Csd,k

ch − λsd,n,ch +∑ij

δsd,kch,n,ijλij

)xsd,kch,n

(10)

Z2 =∑ch

∑sd

∑n

∑opu

(Bopuch topu,ch,nλsd,n,ch) (11)

Z1 is easy to solve by an algorithm obtaining the samevalue as solving the respective ILP problem. This can bedone using the coefficient of the xsd,kch,n variable: csd,kch,n (=

Csd,kch − λsd,n,ch +

∑ij δ

sd,kch,n,ijλij).

For variables xsd,kch,n grouped by the same value of sd,chand n, differing only in the path k, the group variable whichas associated the lower final value of csd,kch,n will be 1 and the

others 0 due to constraint (4). There is also the possibility

that for one group all csd,kch,n values are positive. If this isthe case all the variables from the group will be 0 as it isthe set of values that minimizes the objective function. TheAlgorithm 2 describes this process.

The algorithm consists in calculating the csd,kch,n value corre-

sponding to each xsd,kch,n variable. After calculating the value

csd,kch,n for each group of xsd,kch,n variables that differ only in thepath k, we check which as associated the minimum valueof csd,kch,n. This will be the path chosen by the respective

channel unless all csd,kch,n values turn out to be positive. If allvalues for similar variables that differ only in k are positiveall variables should be 0 to minimize Z1.

In order to get all paths between the nodes s, d using chan-nels of bitrate ch it is used the term traffic paths[s, d][ch].Following this notation, to get all the links between twonodes i, j that belong to a path k it is used the termtraffic path[s, d][ch][k].

The upper bound algorithm consists in using the Lagrangemultipliers to fill the traffic in optical channels. Each chan-nel used as an attributed variable xsd,kch,n which minimization

depends on the calculation of csd,kch,n. By organizing thesevalues by ascending order of the total result and associatingeach result to a list of respective variables xsd,kch,n that havethat result we can choose the channels that will be filledwith traffic first.

When calculating Z1 it is stored the value of each csd,kch,n

different result, associating it with the respective xsd,kch,n vari-able. At the end it is obtained the structure c values thatrelate the different values obtained to the list of variableswhich end up with the respective value as different csd,kch,n

expressions can result in equal values.The upper bound algorithm is described in algorithm 3.

The main idea is to iterate the xsd,kch,n variables obtained inthe c values structure. As this structure was ordered thevariables that have associated the lower csd,kch,n values are con-sidered first.

The fill traffic method gathers the traffic demands fromthe node pair sd and aggregates traffic in a total bitrateequal or lower to the channel’s bitrate ch. This methodreturns the sum of traffic bitrate aggregated to the variablefill info, if this variable ends up with the value 0 it means

Algorithm 2 Solve Z1

for all < sd, ch, n >∈ λsd,n,ch[ ] domin← INT MAXall positive← trueminimizer ← −1for all k ∈ traffic paths[s, d][ch] do

z1 ← Csd,kch − λsd,n,ch

for all ij ∈ traffic path[s, d][ch][k] doz1 ← z1 + λij

end forif z1 < 0 thenall positive← false

end ifif z1 < min thenminimizer ← kmin← z1

end ifend forfor all k ∈ traffic paths[s, d][ch] do

if all positive and k == minimizer thenxsd,kch,n ← 1

elsexsd,kch,n ← 0

end ifend for

end for

that there is no more traffic available that fits in the channelof bitrate ch.

If the path k chosen contains links that have more thanW channels passing by, there is a need to find another paththrough the find new path method. In the actual imple-mentation there are more statements such as counting thenumber of channels passing by each link and restrict thevariable attribution so that for similar variables with differ-ent paths only one is selected to have the value 1 in orderto don’t contradict constraint (4).

3.3 Node ArchitecturesAs referred before the framework will design different net-

works each one with different node architectures. In thiswork networks were compared using a fixed node architec-ture, flexible node architecture and non-colorless nodes -digital node architecture.

3.3.1 Flexible Node ArchitectureThe network with flexible node architecture is the default

node type which is the one considered in the previous calcu-lations of the ILP problem with only source grooming. Thecalculations can be observed in Section 3.1.1.

3.3.2 Fixed Node ArchitectureThe more complicated scenario is the network with fixed

node architecture. For each node it is needed to previouslycalculate which of the directions should be the ones that donot need O/E/O conversion, in other words then ones thatcan be optical bypassed.

It was chosen upon calculating the optical bypassed di-rections using the following algorithm. After calculating thepaths for each node pair, each traffic demand is placed inthe path connecting the respective node pair. After that theamount of traffic passing through the different directions is

Algorithm 3 Upper Bound Algorithm

for all xsd,kch,n ∈ c values do

fill info← fill traffic(ch, trafficList[s][d])if fill info 6= 0 thenalternate path← −1for all link ∈ traffic path[s, d][ch][k] do

if is full(link) thenalternate path← find new path(s, d, ch)

end ifif alternate path 6= −1 thenbreak

end ifend forif alternate path == −1 thenxsd,kch,n ← 1

elsek2 ← alternate pathxsd,k2ch,n ← 1

end ifend if

end for

counted. The directions which have greater load for eachnode are the optical bypassed ones.

In order to compare the use or not of an initial algorithm itwas also considered the previous calculations where randomoptical bypassed directions are defined. This way it can beproved that the previous calculation brings advantage. Thiscomparison can be observed in Section 4.

3.3.3 Digital Node ArchitectureIn the network with a non-colorless node architecture there

is a pair of transponders for each wavelength that passesthrough the node. There will always be E/O/E conver-sions and as so the cost of each path will be the cost oftwo transponders for each intermediate node of the pathplus the cost of the source and destination transponders.

3.4 Intermediate GroomingThe formulation constructed is not too different from the

one used for only source grooming (Formulation 1) and isdescribed on Formulation 2. The indexes and parameters arealmost the same with some additions which can be observedin the formulation. Now the variables x correspond to sub-paths, identified by a source/destination pair (a,b) and thepath k that connects those two nodes. These sub-paths areportions of a path that don’t need regeneration and will befurther referred in this document as transparent sub-paths.

For each sub-path one traffic demand can go through dif-ferent channels identified by the channel bitrate ch and anindex n which has the same use of Formulation 1, only nowit refers to ab instead of sd. The maximum value of n foreach ab, k, ch needs to be previously calculated by summingthe values of maximum n related to the traffic demands thathave the possibility of using the subpath ab.

As to the traffic variables t they split into two kinds:

tsd,k,popu and tsd,rab

iopu . Traffic demands tsdopu are identified by

a source/destination pair sd and the OPU necessary to en-capsulate the demand bitrate.

In constraint (15) it is specified that one traffic demandcan go through different paths and within each path it can

have different permutations (p) of regeneration nodes. Hencethe variables tsd,k,popu . We need to separate a traffic demandinto these variables so that we can know which portion of atraffic demand goes through a certain transparent sub-pathab in constraint (16).

4. RESULTSIn this chapter the experiments in order to evaluate the

framework steps are presented and detailed. In each stepthe tests differ as they have different goals.

For all the tests that do not refer the parameters, thedefault values are:

α = 2β = 1,4W = 100Dmax

100 = 2000km

4.1 Testing EnvironmentThe simulations were run on a laptop with an intel pro-

cessor i7 and 4G of RAM running Windows 7 64bits.For the ILP model solving CPLEX v12.2 was used.While measuring computation times non-essential appli-

cations were closed and no interaction was made with thecomputer.

4.2 Testing FrameworkIn order to test the developed framework an to analyze it’s

results there is a need to select networks and traffic demandsto serve as input.

In order to reach good conclusions several traffic demandsshould be considered. For that it was developed a script inPython to fill in the traffic demands.

Also to be easier to make comparisons there should benumeric ordinal values that characterize the traffic demandsfilled. The script developed receives as arguments the net-work topology and two numeric values. The first is the prob-ability of having a traffic demand between two nodes: TrafficDemand Probability (TDP) hence referred as TDP and rep-resented in percentage.

The second number is an index that decides the maximumnumber of different traffic flows belonging to the same ser-vice: Traffic Demand Quantity Index (TDQi) hence referredas TDQi. As different services have a significant differencein bitrate, the maximum possible amount of traffic flows perdemand differ from service to service. In this case 1G25 ser-vices will have the same maximum value as the index passedas argument. For 2G5 services the maximum value is half ofthe index value, for 10G a third, for 40G a forth and 100Ga fifth (using integer division).

The script has also been programmed to generate trafficusing just one parameter: the Total Traffic Volume (TTV)in Gbps. After giving this parameter the script will dis-tribute this total of traffic through the different node pairsand services.

4.3 Step 1 - Source Grooming FrameworkHere some results of the framework with only source groom-

ing are going to be presented.One of the experiments to test this framework was to see

it’s behavior when the traffic volume increased. For that thescript was used to distribute the traffic using the parame-ter TTV between the values 500Gb and 30500Gb with an

Formulation 2 ILP formulation considering intermediategrooming

Extra Indexes

p Identifies a different permutation of the placement ofregenerators on the nodes of a path k

ab Source and Destination node pair of a transparent sub-path

rabi Identifier corresponding to the ith (13) restriction cor-responding to an ab pair

Extra Parameters

δab,kij List of values that are 1 if the kth path between thenode pair ab passes through link ij and 0 otherwise

δsd,uab List of values that are 1 if due the paths and permu-tations calculated the service of type u between thenode pair sd has the possibility of passing throughthe sub-path ab and 0 otherwise

δsd,k,pab List of values that are 1 if the permutation p of thepath k calculated between the node pair sd has thesub-path ab and 0 otherwise

Variables

xsd,kch,n Binary variable which represents the existence or

not of the nth optical channel from node s to noded, that is routed through the kth path of bitrate ch

tsd,k,pu Integer value which represents how much of a ser-vice of type u from node s to node d goes throughthe permutation p of the path k (can have a valuebetween 0 and the respective T sd

u )

tsd,rab

iu Integer value which represents how much of a ser-

vice of type u from node s to node d goes throughthe subpath ab and is also used in restriction rabi(can have a value between 0 and the respective T sd

u )

Objective

min:z =∑ab

∑k

∑n

∑ch

(CTxRx

ch .xab,kch,n

)(12)

Constraints

rabi :∑k

xab,kch,n ≥∑u

∑sd

(Bu

ch.tsd,rab

iu

), ∀ab∀ch∀n (13)

∑k

xab,kch,n ≤ 1, ∀sd∀ch∀n (14)

∑k

∑p

tsd,k,pu = T sdu , ∀sd∀u∈{0,1,2,3,4} (15)

∑sd

∑k

∑p

(tsd,k,pu .δsd,k,pab

)=∑sd

∑rabi

(tsd,rab

iu .δsd,uab

),

∀ab∀u∈{0,1,2,3,4} (16)∑ab

∑k

∑n

∑ch

xab,kch,n.δab,kij ≤W,∀ij (17)

interval of 500Gb. The maximum of 30500Gb is due to thefact that traffic demands with higher traffic volume caused

errors in the framework due to memory limit.Figure 5 represents the computation time needed to solve

the ILP problem depending on the traffic volume variation.Computation time also suffers from the same effect. Al-though it has the tendency to increase if the frameworkreceives traffic demands with higher total bitrate, in somecases the opposite happens. This happens for a set of rea-sons.

From one perspective we have other processes that arerunning in the same machine as the framework and so us-ing it’s resources. From other perspective different trafficdemands with the same amount of traffic yield different for-mulations. Some can have fewer variables and hence theincrease in speed when solving the ILP problem.

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Time (s)

TTV (103xGbps)

Computation Time Varying Traffic Volume

Figure 5: Comparison between the computationtimes for solving the ILP problem varying trafficvolume in EON network.

4.4 Step 2 - HeuristicsHere we compare the values obtained by the implemen-

tation of the ILP Model, the LP+R heuristic and the LRHheuristic.

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30

Cost

TTV (103xGbps)

Network Cost Comparison

ILP

LRH

LP+R

Figure 6: Comparison between implementations’network costs varying traffic volume in EON net-work.

Figures 7 and 6 represent charts comparing computationtimes and the network costs final values, respectively, of thedifferent implementations.

As we can observe LRH has a great computation time witha small growth when the traffic volume as input increases.LP+R has a bigger computation time growth but it is, aswell as LRH, similar to a linear growth. ILP computationtime growth is not linear and is more similar to an expo-nential growth. As so for bigger networks or a bigger traffic

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Time (s)

TTV (103xGbps)

Computaion Time Comparison

ILP

LRH

LP+R

Figure 7: Comparison between implementations’computation times varying traffic volume in EONnetwork.

volume easily the time needed to solve a problem starts tobe too long.

4.5 Step 3 - Node Architecture Study

TDP TDQi Node Arch.Dmax

100 = 1500km

α = 1 α = 1,5

20% 20

Flexible 4068 3616

Fixed 4260 3861,33

R. Fixed 4452 4036

Digital 4804 4320

Table 1: Node Architecture Study for UBN.

TDP TDQi Node Arch.Dmax

100 = 2000km

α = 1 α = 1,5

20% 20

Flexible 2968 2664

Fixed 3640 3296

R. Fixed 3980 3593,33

Digital 4748 4266,67

Table 2: Node Architecture Study for UBN.

Tables 1 and 2 represent the values obtained using thedifferent architectures and different α values in the UBNnetwork. The Fixed architecture line has the final networkcost values using a fixed node architecture and uses the algo-rithm referred in Subsection 3.3.2 to calculate the directionsof a node which are optical bypassed. The Randomly Fixedarchitecture line has the final network cost values using afixed node architecture and selects the optical bypassed di-rections randomly.

By the results it can be observed that, when calculatingthe cost of a fixed node architecture, the algorithm referredbrings advantage when compared to a random selection.In all the calculated values the Fixed architecture returnedlower values than the Randomly Fixed.

Looking at the values it can also be observed that theoptical reach has a smaller impact in networks with digitalnode architecture when comparing to the other node archi-tectures considered. It also has a smaller impact in networks

with a fixed node architecture when comparing to a flexibleone.

4.6 Step 4 - Framework With IntermediateGrooming

Figure 8 is a chart comparing the costs obtained by theframework with and without intermediate grooming. Fromthe chart it can be observed that when using intermediateaggregation the framework yields lower costs.

0

50

100

150

200

250

300

0 250 500 750 1000 1250 1500 1750 2000 2250

Network Cost

TTV (Gbps)

Network Cost Comparison With and Without Intermediate Grooming (IG)

Without IG

With IG

Figure 8: Comparison between step 1 and step 4 im-plementations’ network costs varying traffic volumein EON network.

It can be also observed that the cost calculated usingthe implementation with traffic grooming as a more lineargrowth with traffic volume. By introducing intermediategrooming a wider set of grooming possibilities are consideredwhere the traffic going through a lightpath can be groomedat any node. Due to this fact how the total traffic is or-ganized in the traffic demands has smaller impact in thecalculated network cost.

Figure 9 is a chart comparing the computation times ob-tained by the framework with and without intermediategrooming. As the values observed had a significant differ-ence between them it was opted to present the computationtime values in a logarithmic scale (base 10).

0,001

0,01

0,1

1

10

100

1000

10000

0 250 500 750 1000 1250 1500 1750 2000 2250

Time (s)

TTV (Gbps)

Computation Time Comparison With and Without Intermediate Grooming (IG)

Without IG

With IG

Figure 9: Comparison between step 1 and step 4implementations’ computation times varying trafficvolume in EON network with a logarithmic scale ontime.

As it was expected using the ILP formulation that sup-ports intermediate grooming has a great impact on the timeneeded to solve the problem. By increasing the same amountof traffic the solution with intermediate grooming stepped

from taking around 0,1 seconds to above 1000 seconds (2076,44sto be exact) while the solution with no intermediate groom-ing stepped from taking around 0,01 to around 0,1.

Not only the new formulation takes, in general, longer tocompute but also the difference will be higher and higherwhen raising the total traffic volume to be considered.

5. CONCLUSIONSThis work was separated into different phases. The first

phase was to upgrade the ILP model in order to considerthe 5 different services.

The second was to build a heuristic to reduce the com-putation time of the problem solving. A heuristic was builtbased on the work [3] from Lee et al. called LRH. Thisheuristic consists in an algorithm to calculate an upper boundto the problem and a Lagrangian relaxation to calculate alower bound. The upper bound algorithm depends on theLagrange multipliers which are iterated yielding differentvalues for the lower and upper bound. In this work anotherupper bound algorithm was designed in order to adapt tothe problem. Although it was also based in the Lagrangianrelaxation theory and dependent on the Lagrange multipli-ers, this algorithm proved to yield better results when notiterated.

This solution was then compared to the LP+R solutionintroduced by Joao Santos. For heavier traffic demands,which is when the heuristics bring a great advantage in termsof computation time, LP+R tends to yield more accurateresults and LRH tends to yield results faster.

The impact of a node architecture in the transponder re-lated network cost was also studied and was the third phaseof this work. One of the conclusions was that when de-signing a network with second generation ROADM a goodchoice of the optical bypassed direction is important for alower transponder related network cost. In this work a so-lution is proposed to set these optical bypassed directionswhen the traffic demands are known.

Also the impact of a different node architecture on transpon-der related network cost is higher when the optical reachof the equipment considered is bigger. For instance whenchoosing between second and third generation ROADMS ifthey have equally an optical reach of 1000km the differencein the transponder cost will be smaller than if they had bothan optical reach of 2000km.

Last but not least the final phase was to make the frame-work consider intermediate grooming. By considering inter-mediate grooming lower costs were obtained. Also a moresteady growth of the network cost with the total traffic vol-ume as input can be observed, being this cost a value easierto predict.

5.1 Future workThe study of different node architectures took only into

account the transponder related cost. Second generationROADM are cheaper equipment but require more transpon-ders. Also third generation ROADM costs depend on thenumber of different directions it needs to consider. A studycould complete the third phase of this work where all thisdetails and equipment costs were taken into account.

The ILP model considering intermediate grooming hasa great computation time growth when considering heav-ier traffic demands. The module may require a big mem-ory/storage to return feasible results if the total traffic vol-

ume considered is too high. Also it may require more timethan the one a person or company is willing to wait.

The heuristics proposed are both adaptable to this prob-lem seeing the formulations are similar. However they werenot adapted in this work. A future work can adapt theheuristics used in this work and even compare them with anew one, for instance.

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