Optimal Traffic Re-Grooming Model for Heterogeneous Carrier Ethernet Services over WDM Optical Network.

— This paper proposes three novel integer linear programming (ILP) formulations, where the first model deals with the Grooming, Routing, Wavelength Assignment, and Carrier Ethernet Interface Allocation Problem (GRWA-I); the second to Traffic Re-Grooming Problem (TRGP) to accommodate demand changes in a GRWA-I network scenarios; and the third to Traffic Re-Grooming demands in case of failures. The traffic re-grooming problem consists basically in assigning demands change in a working network, without affect others requests. In addition, in this work, it problem is formulated for the first time using ILP model. As TRGP needs a configured network scenario as input parameter, the first model proposed accomplish this task for the first network scenario. In numerical results, it was used a 14-node network (NSFnet) and 6 traffic matrix. Moreover, the models proposed were compared with a shortest path (SP) routing method. Results show the difference for network cost between an optimal method and a heuristic design over time, as well as the importance of an initial optimal configuration for future network growth.

I. INTRODUCTION Optical network has been well established as the technology to support the traffic demand in backbones, due to its capacity to support more than a hundred of channels by meaning of Wavelength Division Multiplexing (WDM), where each wavelength can transmit 100Gb/s. This technology has permitted the development of different corporative and domestic services, such as, Video on Demand (VoD), Cloud Services, Data Center, etc. The classical configuration problem in WDM optical networks supporting electronic processing is called traffic grooming, routing and wavelength assignment problem (GRWA). Because of its complexity to generate a good network configuration, this problem is frequently divided in smaller parts where the main goal is the optimization of resources [1]- [3]. The division for GRWA problem is made according these following sub-problems: Virtual Topology Design (VTD); Routing and Wavelength Assignment (RWA); and Traffic Grooming Problem (TGP) [1].
While WDM optical network has been consolidated as backbone physical layer, the data layer has a set of technological alternatives. Based in circuit switched paradigms, SONET/SDH was the earlier technological choice offering static, reliable, and bandwidth aggregated circuits. However, now, was proposed an Integer Liner Programming (ILP) model to assign the Carrier Ethernet interfaces considering the traffic grooming problem and regenerators cost.
Besides of network design models, a recent important issue is how to keep the cost-effective network over time. The main idea on this question is developing strategies to accommodate the traffic evolution, where the most important constraint is to allocate new demands without interfere on the rest of previously set up requests. If a network has the traffic grooming functionality, such as optical network, it is called Traffic Re-Grooming Problem (TRGP). There are few investigations dealing with this issue [9]- [11], and then it still is considered a new problem in the literature. The three cited works propose heuristics for accommodate new demands minimizing the network cost, where a new request cannot affect the previously assigned demands.
Since the author has not found works presenting an ILP model dealing with TRGP, this work proposes the first ILP model to TRGP to Carrier Ethernet over WDM optical network. To test the model proposed it is necessary a network configuration where will be accommodate the new demands. Furthermore, there is also proposed another model with the task of configuring the Carrier Ethernet interfaces on an optical network, considering an initial traffic matrix. To both models, the objective function used is minimizing the number of Carrier Ethernet interfaces. The functionality of keep previous demand and optimize a network change may offer plenty kind of reconfigurations tests.
In addition, it was proposed a modification in Re-Grooming ILP model to reassign demands or the traffic engineering to reconfiguration for predicted failures. As study case, the traffic re-grooming model proposed was compared with a routing method using the shortest path strategy, and computational experiments are accomplished with 6 increasing traffic matrices on a 14-node network. The remainder of this paper is as follows. The next section presents characteristics of network scenarios considered and models proposed, one formulation to generate the optimal network configuration, one to TRGP for traffic evolution, and a model to TRGP minimizing the number demands that can not be reassigned in case of failure. Section III shows the numerical results achieved by models, and as a comparison, it is presented results achieved by configuration accomplished by shortest path process. It process is widely used as routing strategy in commercial devices and protocols. In addition, the results simulate the growth of demands by mean of 6 traffic matrices. The

A. ILP Model to Grooming, Routing, Wavelength, and Client interfaces assignment (GRWA-I)
The first model presents as result an optimal network configuration containing the routes, wavelength and interfaces used by each demand. As following shown, this model is used to generate the input parameters to re-grooming formulation. In addition, its objective function is to minimize the network CapEx, represented by number of Carrier Ethernet interfaces. Fig. 1 illustrates the functionality offered by a considered node.  Fig. 1 An illustration for traffic grooming [12] Fig. 1 shows the optical channel Transport Unit capacity considered, OTU4, that can support until 100 Gb/s Carrier Ethernet services. As mentioned, each signal is electronic processed and must keep the same kind of interface along with the path. On wavelength 1 is illustrated a set of 10xODU2, where part is processed in the represented node and part is added and dropped at node. To illustrate the grooming capacity, wavelengths 2 and 3 show some possibilities, such as: in 2, 5xODU2 is dropped and 1xODU3 is electronically processed; in 3, 1xODU3 is added and dropped, and ODU2s are added, dropped, and electronically processed; moreover, in 2 and 3 is illustrated a demand that offered a wavelength conversion, by mean of electronic processing.
The following notation is used in our mathematical model:   : Link-Path indicator. It is a binary that is set in case link ij is used in route r to meet demand sd, and zeroed otherwise. It is provided by the Yen's Algorithm.

Variables:
: is the amount of traffic in wavelength w and interface k using route r from source s to destination d. It is illustrated in Fig. 1.

Description:
Expression (2) ensures that all the traffic between each pair of node sd will be assigned. In addition, this constraint allows that a demand can be carried by multiple routes and channels, however it limits this division must occur only in the source node. Expression (3) restrains the quantity of traffic in an interface to its capacity.
Expression (4) shows that X ij,w is equals the sum of every Carrier Ethernet Interface assigned in this channel. It represents the grooming of Carrier Ethernet Interface on Optical Network. Expression (5) has two goals, first to create a relation between variables X ij,w and XB ij,w , and second assuring that the quantity of traffic on a wavelength never exceed its capacity. In addition, the variable XB ij,w can be used to count the number of transceivers in the optical layer, and employed as objective function. Nevertheless, this goal is out of this work's scope.

B. ILP model to Traffic Re-Grooming Problem (TRGP)
This model has as input a working network scenario and the traffic (or network) alterations. It must be highlighted that it is the first ILP model that consider a working network state as an input problem.
Since the idea of network optimization is kept in TRGP, every parameter and constraint employed in GRWA-I model also will be used here. Moreover, TRGP requires adding the following parameters and constraints.

Parameters:
R: set of new demands that most be assigned. Description: Expression (6)

C. Optimal Recovering-Oriented Configuration Design
This model is constrained by the available (deployed minus faulty) resources and aims at traffic engineering protection set-ups with the largest amount of recovered traffic. Besides parameters and constraints presented in Subsections A and B, to this model requires adding the following parameters and variables.

Parameters:
F: contains the demands sd in need of rerouting (e.g. due to node, link, or wavelength failure) that will be dealt with by the traffic engineering protection arrangements.

Variables:
sd D : is a slack variable with the traffic sd that can not be reassigned. sd S : is the fraction of traffic sd that can be reassigned. k w ij IB , : is a binary 1 if the interface k on wavelength w at link ij was not affected by the failure, and zero otherwise.
Objective Function: As the network is configured, the goal is minimize the unattended demands. Min:

Descriptions:
Expression (9) is similar to (6), where the difference is that in (6) R contains the new demands while F is a set of demands that must reassigned.
Expression (2) in GRWA-I model is here replaced by (10) and (11). Expression (10) divide a demand of traffic in two parts, the reassigned demands, sd S , and the demands that can not be reassigned, However, due to complexity reduction in TRGP model, the new traffic demands were optimal allocated in 10 minutes to every traffic increase.
The initial traffic scenario was generated with a full traffic matrix and demands between 10Gb/s and 100Gb/s, uniformly distributed, considering 10Gb/s as traffic granularity. To analyze the demands evolution, from the initial matrix, 5 others were interactively generated. From initial matrix, 5% of demands are selected to duplicate their traffic requests. It process was repeated 5 times, always under the last matrix generated.  layer; second, to find the optimal re-grooming where the foremost characteristic is keeping unchanged the working demands; and third, an optimal re-grooming approach to recover the maximal demands lost in case of failure. The TRGP was thought to bear any kind of network change, but in spite of the TRGP flexibility, the numerical experiments it was focused on traffic growth to compare with another re-grooming process found in the literature, shortest path. In addition, Carrier Ethernet Interfaces minimization was used as objective function, different from number of transceivers that is frequently found in literature. Due to TRGP model flexibility, it was adapted for a model to design the traffic reassignment on failure cases or in any other network disturb. Different from two models before presented, instead of minimize the cost with interfaces here it number is kept and it was minimized the quantity of demands unattended after a failure.
In numerical experiments it was used a 14-node network (NSFnet) and 6 traffic matrix, analyzing the traffic growth on the network. From an initial traffic matrix, the next traffic matrix is generated duplicating 5% of traffic requests, which were randomically selected. This experiment shown that for two iteration of traffic chance, optimal and heuristic strategies can obtain similar results for both initial scenarios, however to next iterations is observed the difference between these two methods, highlighting the TRGP effectiveness. For the second experiment, the TRGP was applied to two initial scenarios, generated by GRWA-I and SP, showing the difficulty of TRGP equalize these two scenarios. This experiment demonstrates the importance of a well designed initial scenario for the future network evolution. As shown in Fig. 4, even an optimal approach cannot mitigate the cost difference between an optimal (GRWA-I) and a rough (SP) initial scenario. In addition, as expected, due to relative cost used, it was observed a predominance of 100Gbs interfaces for both methods, however the shortest path routing strategy tends to produce an underused network scenarios.