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Despite this, however, SOA technology also entails some non-desirable effects such as power consumption, noise and non-linearity that must be taken into account during the node design process. Hence, this modified TAS node architecture depicted in Fig. T-OBS node architecture . After the combiner stage, an EDFA booster amplifier provides the signal with enough power to cope with the losses of the first fiber span.
It is worth mentioning that since the output of the WC-SOA is handled by the OBS node controller, all wavelengths from all input ports have the same privileges when requesting a regenerator, and, thus, fairness in the access to the regenerator pool is provided by this architecture.
We also point out that our offline planning approach requires that a burst, whenever sent on a path, will be regenerated only at the nodes that are specified as regenerative sites for this particular path.
To signalize these sites, source nodes include in the BCPs the information regarding the set of nodes where their corresponding data burst has to be regenerated. In the following subsections, we evaluate the performance of the proposed node architecture by means of an OSNR model. In the literature, OSNR is generally defined as the ratio between the signal channel power and the power of the ASE noise in a specified bandwidth e. Thus, all bursts arriving at the destination node with an accumulated OSNR value lower than a predefined quality threshold T osnr cannot be read correctly, and, thus, are discarded.
Although ASE noise is commonly considered as the most severe impairment limiting the reach and capacity of optical systems, in OBS networks, non-linear impairments arising both from its inherent ON OFF switching nature and from dynamic power fluctuations generated by gain changes in amplifiers may strongly impact system performance.
Indeed, these fast ON OFF transitions cause sudden power variations in every single channel, resulting in a variety of non-linear phenomena degrading the optical signal, for instance, cross-phase modulation XPM -induced crosstalk in a burst caused by neighboring bursts co-propagating simultaneously over several common links.
We assume that T osnr pen is configured by the network operator according to the transmitted signal bitrate, modulation format, etc. Note that in systems where non-linear impairments are dominant either larger values of T osnr pen should be set up with a possible impact on the network performance or more accurate and computationally efficient analytical models to capture dynamic PLIs have to be developed. Similarly, to minimize the ASE effect caused by the internal node amplifiers, gain values should be designed such that each node presents an OSNR level as high as possible.
The expression that we use to compute N osnr is equal to the one that we have defined for AS osnr ; however, due to the presence of several components e. In the next subsection, we provide specific values for all these parameters by considering performance values obtained from datasheets of commercially available or lab trial devices see, e. Component specifications are provided in Table I and the power constraints for this analysis are the output power of the node i.
From Eq. In Fig. See Appendix A for the simulation details. All network paths are computed making use of the routing algorithm presented in Section V. One can observe that, with the exception of the German topology, the length, and thus the number of amplifier spans, have a strong impact on the received OSNR. In the German network, which is characterized by much shorter links and by a high number of nodes see Appendix A , by contrast, it is the number of intermediate nodes that has the greater impact on the OSNR figure.
The objective of our offline RRPD problem is to find, for a given set of traffic demands, 1 the set of explicit paths to be used to route bursts through the network, the placement of regenerator sites in selected nodes on those paths having unacceptable OSNR at the receiving end and 3 the number of such regenerators in each node in order to guarantee a given target burst loss probability. Path length km Fig. Their gain values must be carefully designed so that both equivalent figures are minimized and the power constraints are respected.
In order to minimize F eq, it can be deduced from Eq. In this way, the impact of the M ASE powers is reduced.
In order to reduce this complexity, in our approach we decouple the routing problem from the RPD problem. The main reason supporting this decision is the fact that in OBS networks routing must be carefully engineered since the main source of performance degradation is the contention between bursts that arise due to both the lack of optical buffering and the generally considered one-way resource reservation scheme. Hence, given a set of traffic demands, we first find a proper routing that minimizes burst losses due to congestion in bottleneck network links.
Afterward, this routing solution is used as input information to solve the RPD problem which eventually aims at minimizing the number of regenerators deployed in the network. Let P denote the set of predefined candidate paths between source s and termination t nodes, s, t V and s t.
Each path p P is identified with a subset of network links, that is, p E. Adequately, subset P e P denotes all paths that go through link e. Let s p and t p denote the source and termination nodes of p.
Let D denote the set of demands, where each demand corresponds to a pair of source termination nodes.
Each subset P d comprises a small number of paths, for example, k shortest paths. To be precise, the presented algorithm consists in solving, sequentially, two MILP models in order to find a solution to the routing problem. The objective is to distribute the traffic over a set of candidate paths so that congestion in network bottleneck links is reduced. The network applies source routing, and hence the source node determines the path that a burst must follow in the network.
Let variable y represent the average traffic load on the bottleneck link. Despite minimizing the average traffic load on the bottleneck link, many solutions to this problem may exist and most of them exploit unnecessary resources in the network i. RMILP1 , the one that entails the minimum increase of the average traffic load offered to the remaining network links. For this purpose, let us denote y as an optimal solution of Eq.
Note that, in constraint 8 , we ensure that the maximum average traffic load on the bottleneck link is bounded by the solution of Eq. These MILP models, if sequentially solved, determine the path p that will be in charge of carrying the traffic for each demand d. Hence, only one path p d P d is selected as the valid path to be followed by all bursts belonging to demand d. This implies that only a given small enough ratio of bursts cannot be regenerated due the fair competitive statistical multiplexing access to the regenerators and consequently are lost.
Let P o Q denote the subset of paths for which the OSNR level at receiver t is non-compliant with the QoT requirements, and, thus, paths p P o that require regeneration at some node v V p. For each path p, there may exist many different options on how to build an end-to-end OSNR compliant path, composed by its transparent segments, since the node or group of nodes where the regeneration can be performed is generally not a unique solution.
S p and S p depends on the length of the transparent segments in path p. B as the QoT constraint. To illustrate this concept by means of an example, let us consider an OSNR non-compliant path p o between source node 1 and destination node 5 crossing intermediate nodes, 3 and 4.
In p o, the precomputation phase may find three different regenerator allocation options e. In the following subsections, we propose four different offline heuristic RPD algorithms. For the sake of clarity, we consider an objective function denoted by g which accounts for the calculation of the number of regenerators required.
This is achieved by calling the dimensioning function whose pseudo-code is shown in Procedure 5 in Subsection VI. Although this procedure may be called several times within the RPD heuristics next presented, the solutions of Procedure 5 are precomputed only once at the very beginning of the algorithm and stored in an ordered array, thereby substantially reducing the time complexity see details in Subsection VI.
Hence, we do not include this factor in the complexity analysis of the heuristic RPD algorithms presented below. In this algorithm, we assume a neighboring solution is achieved by means of a flip operation which consists of a permutation of the regeneration sites for a specific set of demands. The pseudo-code of the KLS algorithm is shown in Procedure 1. Then, let R o be an initial randomly selected solution to the problem where constraints 9a and 9b are met for each z p, p P o.
Similarly, let R tb, R i and R b denote, respectively, the global best solution obtained so far, the best solution of a whole iteration and one of the solutions of the iteration in progress.
Between lines 5 and 13, starting from solution R b, we iteratively take, for each p P o, vector z p R b, and then we set it to z p, which is the solution for vector z p that minimizes the number of regenerators to be deployed taking into account the current solutions for all other paths, that is, solutions in the current R b.
Once a choice is made for p, then it remains fixed until the loop is initiated again. It is also worth noticing that in line 1, an update of the current solution is performed even if it entails worsening R b.
Procedure 1 does this in order to increase the probabilities of escaping from the local optima and in the hope that some neighboring solution generated during an iteration will turn out better than the current global best solution R tb. Regenerator Grouping RG Algorithm The RG method LCR in  aims at selecting those regenerator sites which lead to solutions having the smallest possible number of nodes equipped with regenerators.
The idea is that, since the access to the regenerators is subject to statistical multiplexing, grouping regenerators in few sites instead of spreading them throughout the network thus having few regenerators in many sites may increase its effectiveness.
In this particular algorithm, in contrast to the others, we do not make use of the precomputed set of regeneration options S p, p P o, but instead the OSNR level of each candidate transparent segment is evaluated see lines 13 and 19 in Procedure. Hence, let K p denote the node or set of nodes where the regeneration is performed for path p.
Then, Procedure is executed. Procedure iteratively processes each path p P o with the aim of ensuring that the OSNR signal level meets the predefined T osnr threshold at each node v N p. To 11 12 J. Once Procedure finishes, the set of nodes K where the regeneration has to be performed is obtained. Note that in line 7, set K is mapped into set R so that we can apply the objective function g r Procedure 5 in Subsection VI.
Such an operation is performed once per path p P o, and, hence, P o. ACO was introduced in the early s as a nature-inspired meta-heuristic for solving hard combinatorial optimization problems. ACO methods try to mimic the behavior of real ants in their task of foraging for food. Initially, an ant explores the area surrounding its nest, and when a food source is found, it evaluates the quantity and quality of its finding.
Based on this measurement, the ant on its way back to the nest will deposit more or less quantity of a chemical pheromone, thereby creating a so-called pheromone trail which will subsequently help other ants to find the best possible food source. If these other ants also find food, they will reinforce the same trail by depositing more pheromone. However, if the quantity or quality of the food found decreases, the pheromone trails will tend to evaporate over time, thereby reducing the trail attractiveness.
Once an assignment for each path is performed, a feasible solution for the RPD problem is obtained. Note that we are dealing with an unconstrained problem, and, thus, each path can take any s S p independently of the decision taken by other paths.
Finally, let us also call the combination of a path p i with a regeneration option s j a solution component which we denote by c j. Hence, we define the set of possible solution i components for path p i as C i. Eventually, we denote the whole set of pheromone trail parameters by T. Then, over a number of global iterations, a number of ants are generated to construct, independently, a solution to the problem by selecting, for each path p P o, a solution component according to a state transition rule.
Hence, each ant performs the complete set of variable instantiations. Since the order in which paths are processed does have impact on the goodness of the solution, each ant has a different, randomly generated order for processing the paths in P o.
In our ACO heuristic, we rely on two different pheromone updates, namely, a local and a global update. Whilst the former tries to bias the ant toward regeneration options which contain nodes with its own pheromone i.
The state transition rule and both types of pheromone updates are next described.
It is worth mentioning that some of the mathematical expressions here presented are borrowed from  and .
State Transition Rule: This rule is responsible for selecting the next solution component regeneration option in the ant regenerator allocation process see line 10 in Procedure 3.
To be precise, the transition is based on a pseudo-random-proportional rule aimed at balancing the exploration and exploitation abilities of the algorithm. The main objective of this rule is to bias the ant toward nodes it has already visited during the construction of the solution with the aim of aggregating regenerators across the network. The aim of this rule is to guide the next group of ants toward high quality solution components.
Finally, the exponential factor favors the deposit of pheromone on those regeneration nodes belonging to the best solutions obtained by each group of ants. In most cases, this meta-heuristic is characterized by being able to obtain high quality solutions in very short times.
In addition, each gene is assigned a value, called an allele, in the real interval [0, 1]. Each chromosome encodes a solution of the problem and a fitness level i. Like any other GA algorithm, BRKGA evolves a set of p individuals, called a population, over a number of generations until a stopping criterion is met 13 14 J.
The subsequent generations consist of individuals which are created by means of 1 a mating process two chromosomes of the current population are combined , a set of high quality chromosomes of the current generation called elite set p e , which are copied unchanged, and 3 a set of new randomly generated chromosomes called mutants p m, which should help the algorithm escape from local optima.
To produce offspring through the mating process, two chromosomes of the current population one elite and another non-elite are selected at random and then combined.
In order to compute the fitness of each chromosome, a deterministic algorithm, called a decoder, is used. The decoder is the only problem-dependent part of the BRKGA algorithm, and, hence, is the only part that needs to be specifically developed to solve the RPD problem.
The pseudo-code of our decoder algorithm is shown in Procedure 4. We select the option s S p which minimizes the cost in terms of that metric.
Oznacza to jednak, e stale musisz by podczony do sieci. WA4 jest dostpny w ksigarniach.
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