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Abstract
The quality of transmission (QoT) of a light-tree is influenced by a variety of physical impairments including attenuation, dispersion, amplified spontaneous emission (ASE), nonlinear effect, light-splitting, etc. Moreover, a light-tree has multiple destinations that have different distances away from the source node so that the QoT of the received optical signal at each destination is different from each other. Since the optical network is a living network, the real-time network state is difficult to obtain. Therefore, it is difficult to accurately and rapidly determine the QoT or availability of a light-tree. However, the QoT or availability of a light-tree obtained in advance not only guarantees the quality of service (QoS) but also helps to network optimization design. This paper studies the problems of the optical signal-to-noise ratio (OSNR) and availability predictions for multicast light-trees while leveraging deep neural network (DNN) in optical WDM networks. The DNN based OSNR and availability prediction methods are developed and implemented. Numerical results show that the DNN based OSNR prediction method reaches an accuracy of about 95%. And the DNN based availability prediction method reaches a high accuracy greater than 98%. These two methods provide a fast decision approach for light-tree construction.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, a range of new industries such as data center, cloud computing, big data, 5G, artificial intelligence (AI), have gained a high-speed development. Among those industries, AI is becoming increasingly important and many countries have taken it as the future research focus in the next few years. On Jul. 20, 2017 the State Council of China issued the New Generation of Artificial Intelligence Development Plan, which was identified as the national development strategy [1]. On June 30, 2018, the Beijing White Paper on the Development of Artificial Intelligence Industry was published [2]. Beijing has become the gathering place and innovation highland for the development of AI in China. AI is a collective name, covering a variety of individual technologies such as decision tree, association rules, support vector machine (SVM), artificial neural networks (ANN), Bayesian networks, genetic algorithms, etc. Among these technologies, ANN inspired by biological neural networks has a powerful nonlinear modeling ability when introducing hidden layers. An ANN that contains many hidden layers is also designated as deep neural network (DNN) or deep learning. The most famous one is the DNN used in AlphaGo [3]. It contains up to 14 hidden layers. AI has a very wide range of applications and has been applied in vast fields such as general game playing, Internet fraud detection, medical diagnosis, natural language understanding, machine translation, pilotless driving, etc. In the field of operation, administration and maintenance (OAM) of optical networks, AI also has a significant guiding and application value [4]. It decreases the complexity and improves the implementation efficiency of the OAM of optical networks, and helps to optical network optimization design.
With the development of new industries, multicast services such as data backup, scientific computing, ultra-high-definition TV delivery, are gaining popularity and momentum [5]. Optical networks which take advantages of large capacity, high speed and low energy have been widely applied for interconnection and interworking. In this way, how to accommodate multicast services in optical networks has become an important research focus. In [6], the authors compared the performance of the light-path scheme with that of the light-tree scheme in minimizing network blocking probability for dynamic multicast traffic grooming in WDM networks. In [7], the authors proposed a distributed sub-tree (DST) scheme that used multiple distributed sub-trees to jointly serve one multicast service. In [8], the authors conducted on-demand routing, modulation level and spectrum allocation for multicast service aggregation in elastic optical networks. The light-tree scheme provides a spectrum-efficient method to accommodate multicast services in optical networks. However, considering practical deployment, the quality of transmission (QoT) of a light-tree is influenced by a variety of physical layer impairments including attenuation, dispersion, amplified spontaneous emission (ASE), crosstalk, etc. A light-tree is usually implemented by multiple light-splitters which decrease the optical signal power. To ensure the acceptable optical signal power at the receiving side, optical amplifiers need to be deployed at the optical fiber line or the receiving side. Since a light-tree has multiple destinations which have different distances away from source node, the optical signal transmitted along different branch is attenuated and amplified through different types (attenuation distance, light-splitting times, magnification, and amplification times). Then, the QoT of the received optical signal at each destination is different with each other. There also exist several approaches for the modeling of physical layer such as Q-factor, Monte Carlo simulations, etc. These modeling methods can be used to calculate the QoT of a light-tree. However, these approaches are usually complicated and time-consuming. Moreover, since the optical network is a living network, these approaches are valuable merely at the engineering and performance evaluation stages [9]. Typically, it is difficult to accurately obtain the QoT of a light-tree in advance. The accurate calculation of the QoT of a light-tree in advance can not only guarantee the quality of service (QoS) of multicast services but also help to network optimization design. On the one hand, since a light-tree can be deployed in the physical layer or not is known beforehand, the success rate of multicast service accommodation can be improved. On the other hand, the adopted modulation level and routing of a light-tree can be optimized until the QoT of the received optical signal at each destination does not satisfy the detection requirement. Therefore, it is essential and significative to accurately obtain the QoT of a light-tree in advance.
In this paper, we study the problems of optical signal-to-noise ratio (OSNR) prediction and availability prediction for multicast light-trees while leveraging DNN in optical WDM networks. The DNN models are designed for the OSNR prediction and the availability prediction respectively. The DNN is implemented and trained through the platform of TensorFlow and the optical WDM network is simulated through VPI Transmission Maker. The rest of this paper is organized as follows. Section II discusses related works. Section III gives problem description. Section IV elaborates the proposed DNN based OSNR and availability prediction methods. Simulation testbed is described in Section V. Numerical results are presented and analyzed in Section VI. Finally, Section VII concludes this paper.
2. Related research
In this section, we summarize the current research progress in the AI-assisted optical network design and optimization. Among these researches, the QoT estimation is focused on. Besides, the contributions of this paper are summarized.
2.1 AI-assisted optical network design and optimization
AI has been applied in many aspects of optical networks. In [4], the authors gave an overview of the application of machine learning into optical communications and networking. In [10], the authors reviewed and employed the machine learning techniques relevant for nonlinearity mitigation, carrier recovery, and nanoscale device characterization. In [11], the authors reviewed machine learning concepts tailored to the optical networking industry and discussed algorithm choices, data and model management strategies, and integration into existing optical network control and management tools. To sum up, the current researches involve failure localization and anomaly detection [12–15], routing and resource allocation [16–21], modulation level recognition [22], optical interconnection [23,24], network control and management [25–27], and the QoT estimation [28–37], etc. Among all AI-assisted applications, the QoT estimation is an important one. It not only guarantees the quality of service (QoS) for unicast and multicast services but also helps to network optimization design. However, the current researches mainly focus on the QoT estimation of light-paths and few studies involve the QoT estimation of light-tree. In [28], the authors investigated two machine learning approaches to formulate the QoT estimation for light-paths, i.e., analytical physical layer model (APLM) and machine learning model (MLM). In [29], the authors used the machine learning techniques to estimate the QoT of light-paths in coherent uncompensated WDM links. In [30], the authors developed a machine learning classifier that predicts whether the bit error rate of unestablished light-paths meets the required system threshold based on traffic volume, desired route, and modulation format. In [31], the authors investigated a machine-learning technique that predicts whether the bit-error rate of unestablished light-paths meets the required threshold based on traffic volume, desired route and modulation format. In [32], the authors evaluated the effectiveness of various machine learning models when used to predict the quality of transmission (QoT) of an unestablished light-path, speeding up the process of light-path provisioning. The considered models are: K-nearest neighbors, logistic regression, support vector machines, and artificial neural networks. In [33], the authors realized quality of transmission (QoT) prediction for light-paths using machine learning for dynamic operation of optical WDM networks. In [34], the authors proposed three frameworks to acquire meaningful data that is used to train machine learning models for light-path validation in a SDN-controlled optical network. The above research mainly focuses on the QoT prediction for light-paths. In [35,36], the authors used the QoT data of previous unicast and multicast connection requests to accurately decide the QoT of newly arriving connections. In [37], we proposed the DNN based OSNR prediction method for light-trees. However, these methods do not consider the availability prediction for multicast light-trees and the measured performance parameter is relatively simple.
2.2 Our contributions
In this paper, we use light-trees to accommodate emerging multicast services in optical networks. Since the QoT of a light-tree is influenced by a variety of physical impairments, the conventional modeling method is complicated and time-consuming. Moreover, the optical network is a living network and the network state is changed with the time. It is difficult to accurately obtain the QoT of a light-tree. To successfully establish light-trees for multicast services, we use the DNN to predict the OSNR and availability of light-trees in advance. The contributions of this paper consist of three aspects.
- 1) The DNN models are designed for the OSNR prediction and the availability prediction respectively. The DNN model includes features, output, hidden layers, error function, and training algorithm.
- 2) The DNN based OSNR prediction method and the DNN based availability prediction method for light-trees are developed. The framework and operation process of these two methods are elaborated in detail.
- 3) A DNN testbed is built where the DNN is implemented and trained through TensorFlow. An optical WDM network is implemented through Transmission Maker 8.5. All samples are obtained from the simulated optical WDM network. The proposed DNN based OSNR prediction method and the DNN based availability prediction method are evaluated in the DNN testbed.
3. Problem description
In this section, we first elaborate the characteristic of “living” of optical networks. Then, the conventional method which is used to estimate the transmission reach of a light-tree is introduced. Finally, we analyze the advantages of the OSNR prediction instead of the BER prediction for multicast light-trees.
3.1 “Living” optical network
Likes human beings, the optical network consists of multiple parts that cooperate with each other. It can provide data transmission and communication services only when each part works well and coordinated. Moreover, it is vulnerable to environment, fault, and usage time. The characteristic of living mainly reflects in the following four aspects.
- (1) The optical network is comprised of a series of equipment including laser, multiplexer, demultiplexer, reconfigurable optical add-drop multiplexer (ROADM), optical cross-connect (OXC), wavelength selective switch (WSS), fiber, light-splitter, optical amplifier, attenuator, filter, etc. As time goes by, all these equipment would gradually age and deteriorate. This will influence the QoT of a light-path or a light-tree, and then decrease the traffic capacity of optical networks. However, in a short period of time, the impact is relatively small.
- (2) All parts of the optical network should be cooperated with each other. For example in transmission plane, the type of optical fiber must be suitable for the emission wavelength of the laser. In the control plane, the light-path or light-tree calculated by routing modular can be realized in the transmission plane. Uncooperative work will lead to low efficiency and high cost.
- (3) The traffic accommodated by optical networks changes by time. Often, the traffic is very heavy during the day and the traffic is relatively low during the night. The performance of the optical network will decrease when the traffic is very heavy. Besides, the network size and network type will be upgraded according to the planning and optimization strategies.
- (4) The optical network can be easily destroyed. To reduce the cost and facilitate the construction, the optical network is usually deployed in wild, unsafe areas. Moreover, it usually spans multiple provinces and municipalities. The frequently occurred natural disasters such as earthquakes, hurricanes, tsunamis, and human-made intentional attacks can easily destroy the connectivity of the optical network and lead to severe business disruption.
3.2 Transmission reach of a light-tree
Since the state of an optical network is difficult to be obtained accurately in real-time, the state is always assumed to be stable in a short period of time. Thus, the transmission reach of a light-path or a light-tree is assumed to be unchanged. For a light-path, the adopted modulation level is often used to determine its maximum transmission distance. In [38], the authors listed the maximum transmission distance of a light-path which adopts modulation levels BPSK, QPSK, QAM. Typically, the transmission reaches of modulation levels BPSK, QPSK, and 8QAM are 5000 km, 2500 km, and 1250 km, respectively. For a light-tree, the light-splitting will reduce the transmission reach of the adopted modulation level. In [39], Eq. (1) is used to describe the relationship among the adopted modulation level, the maximum transmission distance of its branch, and the total number of destination nodes.
In Eq. (1), Sm,n denotes the transmission distance of the longest branch of a light-tree that adopts modulation level m and has n destination nodes, and dm denotes the maximum transmission distance of modulation level m. Equation (1) indicates that the influence of light-splitting is expressed by the total number of destination nodes. However, the total number of destination nodes cannot completely reflect the influence of light-splitting. For example in Fig. 1, the total number of destination nodes of these two light-trees T1 and T2 are same. But, the optical power at node j of light-tree T1 in Fig. 1(a) is larger than that of light-tree T2 in Fig. 1(b). Therefore, the transmission length of the longest branch of light-tree T1 will be longer than that of light-tree T2. This example shows that Eq. (1) is only an approximate model and cannot accurately determine the transmission reach of a light-tree. Therefore, a simple method which can quickly and accurately determine the maximum transmission reach of a light-tree is expected.
3.3 OSNR and availability predictions
Besides using Eq. (1) to estimate the maximum transmission reach of a light-tree, some detection instruments can be used to measure the QoT of the optical signal terminated at each destination node. The OSNR and BER are two important metrics to evaluate the QoT of an optical signal. The OSNR is defined as the ratio of optical signal power to the noise power, often expressed in decibels. The BER is the number of bit errors per unit time. It is equal to the number of bit errors divided by the total number of transferred bits during a studied time interval. The BER is the main judgment basis to measure the reliability of a digital system, and the BER measurement is after signal decoding. The OSNR and BER have corresponding relationship where the OSNR measurement is widely used to estimate BER [23,24]. The higher the OSNR, the lower the BER is. It is quite easy to measure OSNR using an optical spectrum analyzer (OSA). At present, many existing detection instruments are based on the measurement of analog indicators. Therefore, it is easy to conduct the OSNR detection rather than the BER measurement, especially when a large number of multicast light-trees need to be evaluated. In addition, the OSNR is usually used to determine if a calculated light-tree can be realized in the physical layer. Based on this, the availability determination can be conducted directly instead of the OSNR measurement. Machine learning performs unexpectedly and exceptionally well when the underlying physics and mathematics are difficult to analyze or impossible to describe explicitly. In this paper, we focus on the OSNR prediction and availability prediction for light-trees in optical WDM networks.
4. DNN based OSNR and availability prediction methods
In this section, we first elaborate the designed features of the DNN models for light-trees. Then, the DNN based OSNR prediction method and the DNN based availability prediction method are elaborated in detail.
4.1 Designed features for light-trees
The OSNR value of the received optical signal at each destination node of a light-tree can be predicted by a trained DNN. Before that, a large number of samples should be collected and used to train the DNN. Each sample is modeled by a vector <X, Y>, where X is the feature vector which can uniquely represents a light-tree, and Y is the label vector. For the OSNR prediction, Y contains all measured OSNR values at each destination node of a light-tree. For the availability prediction, Y contains a binary value which denotes if a light-tree can be realized in the transmission plane or not. Figure 2 presents the light-tree based design principles of optical networks. The transmission reach, the number of destinations, and the transmission rate are important transmission requirements of a light-tree. The number of destinations determines the type and the number of light-splitters, and also influences the type and the number of amplifiers. Besides, the transmission reach also influences the type and the number of amplifiers. The transmission rate determines the bandwidth and launch power. The amplifiers will introduce ASE noise. Bandwidth and launch power will introduce crosstalk. The ASE noise and crosstalk both will decrease the OSNR. Besides, the attenuation will also decrease the OSNR. The OSNR in turn determines the highest available modulation level. It can be seen that the number of destinations, light-splitter type, light-splitter number, the transmission reach, transmission rate, modulation level, bandwidth, launch power, amplifier type, and amplifier number all determine the OSNR of a light-tree.
Based on above analysis, the features need to be designed to represent the influence factor of the OSNR of a light-tree. The factors of transmission rate, modulation level, bandwidth, and launch power can be easily expressed by explicit values. The amplifier type and the amplifier number are fixed values for a given network. In this paper, we do not consider dynamically increasing or decreasing the amplifier number, or changing the magnification of an amplifier for a given optical network. In simulations, each fiber link will be deployed with an amplifier which is used to compensate the attenuated optical power. In [31], the modulation level, transmitting power, transmission rate, and the number of links are regarded as the features of a light-path. For a multicast light-tree, all those features can also be adopted.
Table 1 lists all features of a multicast light-tree, x1 is the wavelength allocated to the multicast optical signal. x2 is the modulation format adopted by the light-tree, x3 is the launch power of the multicast signal, x4 is the transmission rate of the multicast signal, x5 is the number of destination nodes of the light-tree, x6 is the number of branches in the light-tree, x7 is the length of the longest branch of the light-tree, x8 is the total length of all links in the light-tree, and x9 is the maximum number of links in one branch of a light-tree. The characteristics of the light-tree are expressed by features x5, x6, x7, x8, and x9. Since we assume that the amplifier type and the amplifier number are fixed values for a given network, the introduced ASE is hidden in the relationship between inputs and outputs.
Table 1. All Features of a Light-Tree
4.2 DNN based OSNR prediction method
A DNN contains one input layer, one output layer and multiple hidden layers. At presents, there exist several types of DNN including convolution neural network (CNN), recurrent neural network (RNN), fully-connected neural network (FCNN), etc. The connection relationship between hidden layers determines the type of DNN. A type of DNN is designed for one specific application area. The CNN is usually used to image recognition. The RNN is usually used to speech recognition. The FCNN is usually used to value prediction. In this paper, we use the FCNN to conduct OSNR prediction for multicast light-trees.
Figure 3 presents the framework of the DNN based OSNR prediction method. In input layer, the number of neurons is equal to the number of features of a multicast light-tree. Since all optical nodes of a network may be the destination nodes of a multicast light-tree, the number of neurons in output layer is equal to the total number of optical nodes in this network. Then, the measured OSNR value at each optical node is regarded as labels and stored in Y. A label in Y corresponds to an optical node. If the value of one label in Y is 0, it means the corresponding optical node is not the destination node of the light-tree. The number of hidden layers and neurons in each hidden layer are determined by the trial and error method during the training process. The weights of interconnections between adjacent layers neurons are adjusted by iterative training through optimization algorithms, i.e. back propagation (BP) algorithm. Figure 4 shows the process of DNN training. The process can be divided into two steps. The first step is using training samples to train the DNN. In simulation, 80% samples are regarded as training samples. The remaining 20% samples are regarded as testing samples. The second step is using testing samples to evaluate the DNN. The error values between the OSNR predicted results and the real results at all the destination nodes of a light-tree constitute an error vector denoted by E. When each value in E is less than the set threshold, the prediction value is acceptable. At each iteration, all parameters (e.g., the number of hidden layers and neurons in each hidden layer, learning rate, training times, batch size, etc.) will be adjusted through optimization algorithms until the accuracy meets the requirements. When the accuracy meets the requirement, the training process will be terminated, and then the eventually obtained DNN can be used to conduct the OSNR prediction for incoming light-trees.
Figure 5 shows the process of light-tree establishment. The process can be divided into three steps. The first step is pre-calculating a multicast light-tree for each multicast service. The shortest-path tree algorithm can be used to conduct routing calculation and the First-Fit algorithm can be used to conduct wavelength allocation. The second step is conducting OSNR prediction for each destination node of the pre-calculated multicast light-tree using the trained DNN. The third step is determining whether the light-tree can be established according to predicted OSNR values.
4.3 DNN based availability prediction method
For a multicast light-tree, when the OSNR values at any destination node are larger than the set threshold, this light-tree is available and can be configured in the physical layer. Therefore, a new DNN can be designed to directly determine whether the light-tree is available without the OSNR prediction for all destination nodes of a multicast light-tree. For this new designed DNN, the label of all samples needs to updated. Then, each sample is modeled as < X, y>, where y a binary value. The value of y is determined according to the OSNR values of all destination nodes of a light-tree.
The value of y is set to 1, when the OSNR measurement values of all destination nodes of the corresponding light-tree are larger than the set threshold. Otherwise, the value of y is set to 0. Then, the problem of light-tree establishment is transformed into a binary classification problem. Figure 6 presents the framework of the DNN based light-tree availability prediction method. There is only one neuron in output layer of the neural network model. Figure 7 shows the process of light-tree establishment with binary classification. The first step is pre-calculating a multicast light-tree for each multicast service. The second step is determining whether the light-tree is available or not. This method avoids the OSNR prediction for each destination node of a light-tree.
5. Simulation platform
The topology of the WDM optical network is shown in Fig. 8, which consists of 14 nodes and 13 links [37]. The node S is the source, and other nodes are all optional destination nodes. The routing of a light-tree is calculated by the shortest-path tree algorithm which uses the path length in km as the metric. The shortest-path tree algorithm calculates the shortest path for each destination node of a multicast service and all these shortest paths form a light-tree after deleting duplicate links. The optical WDM network is built using VPI Transmission Maker 8.5. Figure 9 presents a multicast light-tree, which connects source node S to destination nodes i, j, and k. A multicast optical signal is split at node d into three copies. The copies are routed to nodes i, j, and k.
Table 2. Available Wavelengths
For the DNN training, each sample is randomly generated. Firstly, the number of destination nodes of each light-tree is obtained at random. Then, the corresponding locations of destination nodes are also randomly selected. In simulations, the number of destination nodes of each light-tree is set randomly to one value from 1 to 9 and each node in user set {“1”, “2”, “3”, “4”, “5”, “6”, “7”, “8”, “9”} has the same probability to be the destination node. The destination nodes of one multicast service are randomly selected from set {“1”, “2”, “3”, “4”, “5”, “6”, “7”, “8”, “9”, “10”, “11”, “12”, “13”}. The transmission rate of each multicast demand is randomly set to {10 Gbps, 40 Gbps, 80 Gbps}. For a light-tree, the modulation levels of BPSK, QPSK, and 8QAM are optional. The launch power for each light-tree at the transmitter is set to 0 dB and 10 dB. As presented in Table 2, there are 8 wavelengths from 1546.92nm to 1552.52nm in 100GHz grid can be adopted by a light-tree.
A wavelength selective switch (WSS) is comprised of a wavelength division demultiplexer and a switch, which is installed at the output end of the source node. The wavelength is a 3 bit sequence encoding a number between 1 and 8. It specifies the input port where optical signal is routed to the output port. Under the wavelength continuity constraint, all links of a multicast light-tree can only be assigned with a common wavelength. Gauss white noise is added to simulate the actual impairments. Light-splitters are employed to support optical multicasting, which is configured at each intermediate node of a light-tree. At present, there exist multiple frameworks to implement DNN such as Caffe, MXNet, Torch, Theano, TensorFlow, etc. TensorFlow was developed by Google Brain team for internal Google use. It is an open-source software library for dataflow programming across a range of tasks. We use TensorFlow to implement and train the DNN. The code mainly contains five parts, i.e. import sample dataset, initialize parameters and set interlayer connections, initialize DNN, train DNN and prediction and calculate accuracy. The program is implemented by using Python in Anaconda3.
6. Performance evaluation
In the simulated optical WDM network, about 5000 samples are randomly generated and of which 80% were used for training and the rest for testing. The k-fold cross-validation method divides the data set into k parts. One part is selected as the test data and the remaining k-1 part are used as the training data. In fact, the process of cross-validation is to repeat the experiment for k times. Different part is selected from the k parts as the test data each time to ensure that k parts of all the data have been tested. However, when the data volume is large enough, the accuracy is high without using this method. Since the data volume of 5000 samples is large enough that the k-fold cross-validation method is not applied. After repeated adjustment and training, the number of hidden layers of the DNN model in OSNR prediction is set to 4 and the total number of neurons in each hidden layer is set to 128. For the availability prediction method, the number of hidden layers is set to 1 and the total number of neurons in this hidden layer is set to 15. We evaluate the effect of sample size, threshold, and batch size on the accuracy for the DNN based OSNR prediction method and the DNN based availability prediction method. The maximum number of training times is set to 50000.
6.1 DNN based OSNR prediction method
For the OSNR prediction, we define two accuracies. The first prediction accuracy is defined as the ratio between the number of successfully predicted light-trees and the total number of light-trees. The OSNR of a light-tree is predicted successfully if and only if the OSNR of all its destination nodes are predicted successfully. For a destination node of a light-tree, if the difference between the predicted OSNR value and the real OSNR value is smaller than a given threshold value, the OSNR of the destination node is considered to be successful predicted. The second prediction accuracy is defined as the ratio between the number of successfully predicted destination nodes and the total number of destination nodes.
For each user, the prediction result is calculated by two values which can be modeled by < real OSNR value, predicted OSNR value > . Figure 10 presents three light-trees, and the real OSNR value and the predicted OSNR value for each user of these three light-trees. When the threshold is 1.0, then the OSNR predictions of users 2, 7, 8, 9 are success. Therefore, only one light-tree is predicted successfully. The prediction accuracy of light-trees is 1/3 = 33.3%. Moreover, the prediction accuracy of destination nodes is 4/9 = 44.4%. Figure 11(a) shows the relationship between the OSNR training accuracy of a light-tree and the threshold when the sample number is 1000. The results show that the training accuracy can reach 99.4% when the threshold is greater than 0.6 after 50000 iterations. Figure 11(b) shows the relationship between the OSNR training accuracy of a light-tree and the batch size when the sample number is 1000. The results show that the training accuracy can reach 99.6% when the batch size is greater than 100 after 50000 iterations. Figure 12(a) shows the relationship between the OSNR prediction accuracy of a light-tree and the threshold when the sample number is 1000. The results show that the prediction accuracy can reach 95% when the threshold is 1.4 after 50000 iterations. Figure 12(b) shows the relationship between the OSNR prediction accuracy of a light-tree and the batch size when the sample number is 1000. The results are extremely volatile. Figure 13(a) shows the relationship between the OSNR training accuracy of all destination nodes and the threshold when the sample number is 1000. The results show that all training accuracies can reach 99.7% after 50000 iterations. Figure 13(b) shows the relationship between the OSNR training accuracy of all destination nodes and the batch size when the sample number is 1000. The results show that the training accuracy can reach 99.8% when the batch size is greater than 100 after 50000 iterations. Figure 14(a) shows the relationship between the OSNR prediction accuracy of all destination nodes and the threshold when the sample number is 1000. The results show that the prediction accuracy can reach 98% when the threshold is 1.4 after 50000 iterations. The results obtained from Figs. 12(a) and 14(b) show that the DNN can precisely predict the OSNR of a destination node of a light-tree than predict the OSNR of a whole light-tree. Figure 14(b) shows the relationship between the OSNR prediction accuracy of all destination nodes and the batch size when the sample number is 1000. The results are relatively stable and can reach 95% when the batch size is 500 after 50000 iterations.
Fig. 11. Training accuracy of light-trees when sample number is 1000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 12. Prediction accuracy of light-trees when sample number is 1000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 13. Training accuracy of all destination nodes when sample number is 1000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 14. Prediction accuracy of all destination nodes when sample number is 1000 (a) batch size = 500 (b) threshold = 1.0.
Figure 15(a) shows the relationship between the OSNR training accuracy of a light-tree and the threshold when the sample number is 3000. The results show that the training accuracy can reach 99.9% when the threshold is greater than 0.6 after 50000 iterations. Figure 15(b) shows the relationship between the OSNR training accuracy of a light-tree and the batch size when the sample number is 3000. The results show that all training accuracies can reach 98.2% after 50000 iterations. Figure 16(a) shows the relationship between the OSNR prediction accuracy of a light-tree and the threshold when the sample number is 3000. The results show that the prediction accuracy can reach 95% when the threshold is 1.4 and 1.2 after 50000 iterations. Figure 16(b) shows the relationship between the OSNR prediction accuracy of a light-tree and the batch size when the sample number is 3000. The results are relatively stable and can reach 90% when the batch size is 500, 400, and 300 after 50000 iterations. Figure 17(a) shows the relationship between the OSNR training accuracy of all destination nodes and the threshold when the sample number is 3000. The results show that the training accuracy can reach 99.8% when the threshold is greater than 0.6 after 50000 iterations. Figure 17(b) shows the relationship between the OSNR training accuracy of all destination nodes and the batch size when the sample number is 3000. The results show that all training accuracies can reach 99.5% after 50000 iterations. Figure 18(a) shows the relationship between the OSNR prediction accuracy of all destination nodes and the threshold when the sample number is 3000. The results show that the prediction accuracy can reach 99.5% when the threshold is greater than 1.0 after 50000 iterations. Figure 18(b) shows the relationship between the OSNR prediction accuracy of all destination nodes and the batch size when the sample number is 3000. The results are relatively stable can reach 98% when the batch size is greater than 100 after 50000 iterations.
Fig. 15. Training accuracy of light-trees when sample number is 3000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 16. Prediction accuracy of light-trees when sample number is 3000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 17. Training accuracy of all destination nodes when sample number is 3000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 18. Prediction accuracy of all destination nodes when sample number is 3000 (a) batch size = 500 (b) threshold = 1.0.
Figure 19(a) shows the relationship between the OSNR training accuracy of a light-tree and the threshold when the sample number is 5000. The results show that the training accuracy can reach 97.9% when the threshold is greater than 0.6 after 50000 iterations. Figure 19(b) shows the relationship between the OSNR training accuracy of a light-tree and the batch size when the sample number is 5000. The results show that all training accuracies can reach 92% after 50000 iterations. Figure 20(a) shows the relationship between the OSNR prediction accuracy of a light-tree and the threshold when the sample number is 5000. The results show that the prediction accuracy can reach 95% when the threshold is 1.4, 1.2, and 1.0 after 50000 iterations. Figure 20(b) shows the relationship between the OSNR prediction accuracy of a light-tree and the batch size when the sample number is 5000. The results are relatively stable and can reach 90% when the batch size is greater than 100 after 50000 iterations. Figure 21(a) shows the relationship between the OSNR training accuracy of all destination nodes and the threshold when the sample number is 5000. The results show that the training accuracy can reach 96.5% when the threshold is greater than 0.6 after 50000 iterations. Figure 21(b) shows the relationship between the OSNR training accuracy of all destination nodes and the batch size when the sample number is 5000. The results show that all training accuracies can reach 98.7% after 50000 iterations. Figure 22(a) shows the relationship between the OSNR prediction accuracy of all destination nodes and the threshold when the sample number is 5000. The results show that the prediction accuracy can reach 98% when the threshold is greater than 1.0 after 50000 iterations. Figure 22(b) shows the relationship between the OSNR prediction accuracy of all destination nodes and the batch size when the sample number is 5000. The results are relatively stable can reach 98% when the batch size is greater than 100 after 50000 iterations. The training results show that the trained DNN is designed properly. All these results show that the OSNR prediction accuracies of all destination nodes and a light-tree increases when the number of sample increase. Moreover, the OSNR prediction accuracy of a light-tree can reach 95%.
Fig. 19. Training accuracy of light-trees when sample number is 5000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 20. Prediction accuracy of light-trees when sample number is 5000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 21. Training accuracy of all destination nodes when sample number is 5000 (a) batch size = 500 (b) threshold = 1.0.
Fig. 22. Prediction accuracy of all destination nodes when sample number is 5000 (a) batch size = 500 (b) threshold = 1.0.
6.2 DNN based availability prediction method
Figures 23, Fig. 24, and Fig. 25 show the relationship between the availability prediction accuracy of a light-tree and the batch size when the sample number is 1000, 3000, and 5000. When the sample number is 5000, the results are relatively stable can reach 98% when the batch size is greater than 100 after 50000 iterations.
In short, the DNN based OSNR prediction method and the DNN based availability prediction method both can reach high accuracy. Moreover, the number of hidden layers and the total number of neurons of the DNN based availability prediction method is relatively small. This method is simple but can reach high accuracy about 98%. Those two prediction methods both provide a fast decision approach for the light-tree construction in a living optical network. From all above numerical results, we can find that the trained DNN can accurately predict the OSNR and availability for multicast light-trees in optical WDM networks. In the practical application, when a new multicast service arrives, only the features of the calculated light-tree for this multicast service need to be input to the trained DNN to obtain the corresponding OSNR and availability. Moreover, the trained DNN does not need to be re-trained as long as the underlying optical WDM network does not change. This advantage simplifies the management and control of optical networks.
7. Conclusions
In this paper, a DNN based OSNR prediction method and an availability prediction method are proposed to improve the success rate of multicast service accommodation. Machine learning performs unexpectedly and exceptionally well when the underlying physics and mathematics of the problem are too difficult to analyze or impossible to describe explicitly. The DNN provides an accurate and simple method to determine the OSNR at each destination node of a multicast light-tree. Features are designed to indicate the effect of physical impairments for multicast light-trees. The DNN based OSNR and availability prediction methods are proposed. The results show that the proposed method is fast and relatively accurate. It helps to improve the success rate of multicast service accommodation.
Funding
National Natural Science Foundation of China (61701039, 61821001); Key Laboratory of Computer System and Architecture (CARCH201906).
Disclosures
The authors declare no conflicts of interest.
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