A method and apparatus for determining performance of non-deterministic traffic

Abstract

The embodiment of the application discloses a non-deterministic flow performance determination method and device, which is used for reducing the modeling difficulty and prediction complexity of the transmission performance of the non-deterministic flow. The method first acquires network state information of a deterministic network; the network state information comprises node attributes, link attributes and flow attributes of the deterministic network; then, feature extraction is performed on the network state information, and the extracted features are transformed to a complex frequency domain to obtain complex frequency domain features; the complex frequency domain features comprise amplitude information and phase information; and the complex frequency domain features are processed to obtain performance parameters of the non-deterministic flow. The network state information is transformed to the complex frequency domain, the complex frequency domain features contain the amplitude information reflecting the network fluctuation intensity and the phase information reflecting the propagation characteristics, and the transmission law of the non-deterministic flow under the complex network topology is captured from the frequency domain perspective.

Description

Technical Field

[0001] This application relates to the field of network technology, and in particular to a method and apparatus for determining the performance of non-deterministic networks. Background Technology

[0002] With the rise of industrial internet, telemedicine, and autonomous driving, the requirements for network transmission stability, reliability, and low latency are increasing. Deterministic networking is a network architecture that uses time-sensitive networking and deterministic IP protocols for network transmission. Deterministic networking can achieve low latency, low jitter, and high reliability in network transmission, and its applications are becoming increasingly widespread.

[0003] Deterministic networks include two types of traffic: deterministic traffic and non-deterministic traffic. To ensure the priority transmission of deterministic traffic, existing technologies often employ Time Aware Shaper (TAS) gating lists to differentiate the transmission time slots for the two types of traffic, and combine this with frame preemption protocols to ensure that deterministic traffic dynamically interrupts non-deterministic traffic during transmission.

[0004] While this approach can guarantee the transmission performance of deterministic traffic, high-priority deterministic traffic can dynamically interrupt the transmission of nondeterministic traffic, causing sudden fluctuations and long-tail effects in the latency of nondeterministic traffic. This significantly affects the modeling of its transmission performance and consequently leads to the inaccuracy of performance evaluation of nondeterministic traffic. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a method and apparatus for determining the performance of nondeterministic networks. This method solves the problem that the delay fluctuations of nondeterministic traffic are complex due to periodic preemption and that traditional methods cannot effectively model the periodic characteristics in the frequency domain. The goal is to accurately identify the patterns of delay fluctuations and improve the accuracy of performance evaluation for nondeterministic traffic.

[0006] The embodiments of this application disclose the following technical solutions: In a first aspect, embodiments of this application provide a method for determining the performance of a nondeterministic network, the method comprising: Obtain network state information of the deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network; Feature extraction is performed on the network state information, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information. The performance parameters of the deterministic network are obtained by processing the complex frequency domain features.

[0007] Optionally, the step of extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features includes: Based on the network topology connections, graph features are extracted from the network state information to generate corresponding message sequences; the message sequences are then transformed into the complex frequency domain to obtain complex frequency domain features containing amplitude and phase information.

[0008] Optionally, the method further includes; The network state information is normalized to map it to a preset numerical range; the mapped network state information is then subjected to linear and nonlinear transformations to obtain initial latent variables. The step of extracting graph features from the network state information based on network topology connections to generate corresponding message sequences includes: Based on the network topology connections, graph features are extracted from the initial latent variables to generate corresponding message sequences.

[0009] Optionally, transforming the message sequence to the complex frequency domain to obtain complex frequency domain features containing amplitude and phase information includes: The message sequence is transformed from the time domain to the complex frequency domain by using Discrete Fourier Transform; the amplitude and phase features of the transformed message sequence are extracted as the complex frequency domain features.

[0010] Optionally, the method further includes: iteratively updating the network state information using the complex frequency domain features to obtain updated information; The step of processing the complex frequency domain features to obtain the performance parameters of the deterministic network includes: processing the updated information to obtain the performance parameters of the deterministic network.

[0011] Optionally, the iterative update of the network state information using the complex frequency domain features includes: The network state information is iteratively updated based on the complex frequency domain characteristics using a gated recurrent unit (GRU) structure.

[0012] Optionally, before extracting graph features from the network state information based on network topology connections, the method further includes: processing the network state information through an attention mechanism; The step of extracting graph features from the network state information based on network topology connections to generate a corresponding message sequence includes: extracting graph features from the network state information processed by the attention mechanism based on network topology connections to generate a corresponding message sequence.

[0013] Optionally, the step of extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features; and processing the complex frequency domain features to obtain the performance parameters of the deterministic network, includes: The network state information is converted into initial latent variables used by the graph message interaction network through the input network of the graph neural network model; The graph features of the initial latent variables are extracted through the graph message interaction network of the graph neural network model, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features. The complex frequency domain features are processed by the output network of the graph neural network model to obtain the performance parameters of the deterministic network.

[0014] Optionally, the graph message interaction network includes a message extraction layer and a complex enhanced convergence layer; The message extraction layer extracts graph features from the initial latent variables based on network topology connections to generate corresponding message sequences. The message sequence is transformed to the complex frequency domain by the complex enhancement convergence layer to obtain complex frequency domain features containing amplitude and phase information.

[0015] Optionally, the complex enhancement convergence layer is used to: transform the message sequence from the time domain to the complex frequency domain through discrete Fourier transform, and extract the amplitude and phase features of the message sequence as the complex frequency domain features.

[0016] Optionally, the graph message interaction network further includes a latent variable update layer, and the method further includes: The initial latent variables are iteratively updated using the complex frequency domain features to obtain the updated latent variables. The process of processing the complex frequency domain features through the output network to obtain the performance parameters of the deterministic network includes: The updated latent variables are processed by the output network to obtain the performance parameters of the deterministic network.

[0017] Optionally, the graph message interaction network further includes an attention mechanism layer; The initial latent variables are processed using the attention mechanism described above; The step of extracting graph features from the initial latent variables based on network topology connections through the message extraction layer to generate corresponding message sequences includes: The message extraction layer extracts graph features from the initial latent variables processed by the attention mechanism based on the network topology connection relationship, generating the corresponding message sequence.

[0018] Optionally, the performance parameters include latency and / or packet loss rate for nondeterministic traffic.

[0019] Secondly, embodiments of this application provide a performance determination apparatus for nondeterministic networks, the apparatus comprising: The acquisition unit is used to acquire network state information of the deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network. The processing unit is used to extract features from the network state information and transform the extracted features to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; and to process the complex frequency domain features to obtain the performance parameters of the deterministic network.

[0020] Thirdly, embodiments of this application also provide a computer-readable storage medium having a computer program stored thereon, which, when run on a computer, causes the computer to perform any of the possible methods described in the first aspect.

[0021] Fourthly, embodiments of this application also provide a computer program product that, when run on a computer, executes the method as described in any of the first aspects.

[0022] Fifthly, embodiments of this application provide a computing device, which includes a memory and a processor; the memory and the processor are coupled together. The memory is used to store program instructions; the processor is used to invoke the program instructions to cause the computing device to perform the method as described in any of the first aspects.

[0023] Beneficial effects: This application provides a method and apparatus for determining the performance of nondeterministic networks, which reduces the modeling difficulty and prediction complexity of the transmission performance of nondeterministic traffic. The method first obtains network state information of the deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network; then, features are extracted from the network state information, and the extracted features are transformed to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; the performance parameters of the deterministic network are obtained by processing the complex frequency domain features. This application, by transforming the network state information to the complex frequency domain, utilizes the fact that the complex frequency domain features contain amplitude information reflecting the intensity of network fluctuations and phase information reflecting propagation characteristics, thus enabling the capture of the transmission patterns of nondeterministic traffic under complex network topologies from a frequency domain perspective.

[0024] This processing method overcomes the limitation of traditional graph neural networks, which only model in the time domain and thus loses periodic features, enabling amplitude information to accurately reflect the intensity of fluctuations and phase information to accurately characterize the temporal relationship of fluctuations. Furthermore, through systematic processing of complex frequency domain features, it achieves efficient capture and quantitative analysis of complex time delay fluctuation behavior in deterministic networks, ultimately accurately deriving network performance parameters. Therefore, it can solve the problem in existing technologies where periodic preemption leads to complex time delay fluctuations and traditional methods cannot effectively model frequency domain periodic features, achieving the effects of accurately identifying time delay fluctuation patterns, improving the accuracy of performance evaluation, and enhancing the quality of service assurance capabilities of deterministic networks. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A system architecture diagram of a deterministic network provided in the embodiments of this application; Figure 2 This is a schematic diagram of an application scenario provided by an embodiment of this application; Figure 3 A flowchart illustrating a method for determining the performance of a nondeterministic network, as provided in this application embodiment; Figure 4 A flowchart illustrating a method for determining the performance of a nondeterministic network, as provided in this application embodiment; Figure 5 A schematic diagram of the processing of an output network provided in an embodiment of this application; Figure 6 A schematic diagram illustrating another graph message interaction network provided in an embodiment of this application; Figure 7 A feature extraction method diagram for an attention mechanism provided in an embodiment of this application; Figure 8 A diagram illustrating an attention-based input feature extraction structure provided in this application embodiment; Figure 9 A complex enhanced graph message interaction structure diagram provided in this application embodiment; Figure 10 A network structure diagram for outputting packet loss rate is provided in an embodiment of this application; Figure 11 A time-delay output network structure diagram provided in an embodiment of this application; Figure 12This is a schematic diagram of a performance determination device for a nondeterministic network provided in an embodiment of this application. Detailed Implementation

[0027] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0028] Deterministic networks comprise two categories: deterministic traffic and non-deterministic traffic. To ensure priority transmission of deterministic traffic, existing technologies often employ a Transmission Allocation System (TAS) gating list to differentiate the transmission time slots for the two types of traffic, combined with a frame preemption protocol, to ensure that deterministic traffic dynamically interrupts non-deterministic traffic during transmission. The TAS gating list is a pre-configured timetable used to precisely control the transmission status of each gating queue on each network node within a specific time window. The transmission status includes two options: transmission enabled and transmission disabled.

[0029] For example, see Figure 1 This figure illustrates a system architecture of a deterministic network provided in an embodiment of this application. The deterministic network provided in this embodiment includes network nodes, transmission links, and the overall network. The overall network includes network topology, traffic demand matrix, deterministic performance constraint matrix, traffic routing paths, etc. Furthermore, the deterministic network also includes elements such as gated queues, centralized controllers, and deterministic traffic scheduling strategies.

[0030] Gated queues are buffer queues set up within network nodes in a deterministic network to cache data awaiting transmission. These gated queues are bound to a TAS (Time-Sensitive Access) scheduling mechanism, capable of opening and closing transmission permissions according to preset periodic scheduling instructions. Each gated queue has a one-to-one correspondence with traffic: different types and priorities of traffic are mapped to different gated queues. Deterministic time-sensitive traffic is mapped to dedicated gated queues, while non-deterministic traffic is mapped to other ordinary gated queues. The core of gated queue transmission is the TAS gated list. Based on a periodic scheduling time-slice sequence, the TAS gated list dynamically controls the transmission status of each gated queue through binary encoding.

[0031] For example, Figure 1 Eight gated queues are illustrated, numbered 0 through 7. The TAS gating list is explained using the example where the corresponding queue starts transmission when the code bit is 1, and stops transmission when the code bit is 0, with data in the queue being forcibly cached until the next activation cycle. For example... Figure 1 In the T05 time slice, the gating code is 01001000, where bits 1 and 4 are 1 and the remaining bits are 0. This means that only queues 1 and 4 have transmission permissions enabled, and data from the remaining queues is buffered to the next cycle. Therefore, the TAS-gated queues, through the TAS gating list, can implement a periodic scheduling mechanism, differentially allocating transmission time slots for deterministic and non-deterministic traffic, thereby achieving ordered transmission of both types of traffic.

[0032] The core of a deterministic network is its network topology. This topology consists of multiple network nodes and transmission links, with each network node corresponding to a switch or router. The nodes collaborate based on TSN-related protocols to construct a unified time synchronization domain, providing a time reference for the synchronous execution of network-wide gating scheduling and ensuring the network's deterministic low-latency transmission characteristics. TSN-related protocols include, but are not limited to: IEEE 802.1AS time synchronization protocol, IEEE 802.1Qbv gating scheduling protocol, IEEE 802.1Qbu frame preemption protocol, and IEEE 802.1Qci flow filtering protocol. The transmission link is the physical or logical communication channel connecting the network nodes, used to carry data interaction and protocol message transmission between nodes, providing data path support for the network topology. The transmission link possesses corresponding link attributes such as bandwidth, length, and load status, and can complete the transmission of deterministic and non-deterministic traffic according to node scheduling instructions.

[0033] For example, Figure 1 The diagram illustrates the time synchronization domain network topology, which includes four network nodes: an 802.1AS node operating based on the IEEE 802.1AS time synchronization protocol, an 802.1Qbv node operating based on the IEEE 802.1Qbv gating scheduling protocol, an 802.1Qbu node operating based on the IEEE 802.1Qbu frame preemption protocol, and an 802.1Qci node operating based on the IEEE 802.1Qci stream filtering protocol. These network nodes are interconnected via transmission links, forming a complete deterministic network communication architecture.

[0034] In a deterministic network, the centralized controller communicates with each network node within the time synchronization domain network topology and undertakes global network management functions. These functions include, but are not limited to: sensing and / or collecting current network status information; executing explicit routing management and issuing traffic scheduling control commands to achieve global network management; and summarizing various network parameters, including traffic matrices, routing matrices, and controller scheduling parameters, to provide data input for performance evaluation.

[0035] It is understandable that when the transmission time slots of deterministic and non-deterministic traffic are allocated differently through the TAS gating list, the transmission of non-deterministic traffic will be affected by the IEEE 802.1Qbu frame preemption protocol. High-priority deterministic traffic will dynamically interrupt the transmission of non-deterministic traffic, resulting in sudden fluctuations and long-tail effects in the latency of non-deterministic traffic, which significantly increases the complexity of modeling and predicting its transmission performance.

[0036] In view of this, embodiments of this application provide a method for determining the performance of nondeterministic networks. This method accurately reflects the intensity of fluctuations through amplitude information and accurately characterizes the temporal relationship of fluctuations through phase information. Furthermore, through systematic processing of complex frequency domain characteristics, it achieves efficient capture and quantitative analysis of complex time-delay fluctuation behavior in deterministic networks, and ultimately accurately derives network performance parameters. For ease of description, the networks mentioned below refer to deterministic networks.

[0037] The following description, in conjunction with the accompanying drawings, provides a detailed and complete explanation of the performance determination method for nondeterministic networks provided in the embodiments of this application.

[0038] First, we will introduce the application scenarios of the embodiments of this application.

[0039] For example, see Figure 2 This figure is a schematic diagram of an application scenario provided by an embodiment of this application.

[0040] In this application scenario, the network topology is a time-synchronization domain network topology. The centralized controller (hereinafter referred to as the controller) is connected to the network topology in the deterministic network and is used to perform the following operations: acquire network state information, extract features from the network state information, and transform the extracted features to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; process the complex frequency domain features to obtain the performance parameters of the nondeterministic traffic.

[0041] For example, such as Figure 2 As shown, the controller can process network state information using a deterministic network performance prediction model (specifically, a graph neural network model) to obtain performance evaluation results for nondeterministic traffic. Specifically, the controller inputs network state information such as the traffic matrix, routing matrix, network topology, and scheduling parameters into the deterministic network performance prediction model. The model processes this information and predicts the network performance parameters for nondeterministic traffic. Based on these parameters, the controller generates control commands and adjusts each network node in the network topology accordingly.

[0042] It should be understood that Figure 2The application scenarios shown are merely one possible implementation and do not constitute a limitation on the scope of protection of this application. The performance determination method provided in the embodiments of this application is also applicable to other network devices or computing platforms with data processing capabilities.

[0043] See Figure 3 The figure is a flowchart of a method for determining the performance of a nondeterministic network according to an embodiment of this application. For ease of explanation, the method is described using... Figure 2 Taking the application scenario shown as an example, the method includes the following steps: S310, Obtain network state information for a deterministic network.

[0044] In this embodiment of the application, network status information is used to reflect the current operating status of a deterministic network, including the node attributes, link attributes, and traffic attributes of the deterministic network.

[0045] Node attributes are a set of parameters that characterize a network node's configuration, operational status, and port relationships. Node attributes include, but are not limited to, the following information: node identifier, node location, node type, node clock, node traffic shaping rules, node time synchronization rules, neighboring nodes for each port, neighboring links for each port, queuing status for each port, priority settings for each port, and forwarding performance utilization.

[0046] Link attributes are a set of parameters that characterize the physical characteristics, transmission capacity, and load status of a communication link. Link attributes include, but are not limited to, the following information: link identifier, the nodes connected to the link, the link bandwidth, the link load status, and the link length.

[0047] Traffic attributes are a set of parameters that characterize network topology, traffic demand, performance constraints, and routing paths, including but not limited to the following information: specific network topology, traffic demand matrix between nodes, performance constraint matrix of deterministic traffic, and routing path of each traffic flow.

[0048] This information together constitutes a complete description of the network's real-time operating status, providing a unique and irreplaceable input basis for subsequent performance evaluation. The acquisition process directly ensures that the data source on which the evaluation relies is completely consistent with the actual network configuration, thus laying the foundation for establishing an accurate performance prediction model.

[0049] S320, feature extraction is performed on the network state information, and the extracted features are transformed to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information.

[0050] Feature extraction of network state information refers to extracting structured data that characterizes the operational status of nodes, links, and traffic attributes from the network topology, forming features that can be used for subsequent analysis; these features are time-domain features. In one example, time-domain features can exist in the form of message queues. Specifically, the controller can extract time-domain features of node attributes, link attributes, and traffic attributes based on the network topology connections, and generate corresponding message queues. The message queue for node attributes is a node queue, the message queue for link attributes is a link queue, and the message queue for traffic attributes is a traffic message queue.

[0051] The controller can then transform the time-domain features to the complex frequency domain, obtaining complex frequency domain features. The complex frequency domain refers to the domain in which the frequency characteristics of a signal are represented using complex numbers. In the complex frequency domain, the signal is decomposed into a superposition of sine waves of different frequencies. For example, the controller can use a Discrete Fourier Transform (DFT) to transform the time-domain features from the time domain to the complex frequency domain, obtaining complex frequency domain features. Specifically, the controller uses a DFT to transform the message queue to the corresponding complex frequency domain.

[0052] Complex frequency domain features include amplitude and phase information. Amplitude information represents the energy intensity of a specific frequency component. In network analysis, a larger amplitude indicates more severe periodic fluctuations at that frequency (such as periodic traffic bursts). Phase information represents the offset of a specific frequency component relative to the original signal. In network analysis, phase information reflects the cumulative delay characteristics of data packets propagating in the network or the phase difference of congestion between different nodes. Compared to simple time-domain analysis, complex frequency domain features can more sensitively capture subtle periodic interferences and long-range dependencies that are difficult to detect in the time domain, significantly improving the accuracy of subsequent performance predictions.

[0053] In one example, the controller can also extract features from network state information using a graph attention mechanism based on network topology connections. Unlike traditional graph convolution, the attention mechanism allows network nodes to dynamically focus on neighboring nodes (such as upstream congested nodes) that have the greatest impact on their performance, thereby generating message sequences that reflect topological dependencies.

[0054] In another example, to improve processing efficiency, the controller first preprocesses the network state information before performing graph feature extraction: by standardizing data of different dimensions to a preset numerical range (e.g., [0, 1]), and then introducing expressive power through linear and nonlinear transformations to generate initial latent variables. These initial latent variables are intermediate values ​​of network state information. The controller then performs graph feature extraction on these initial latent variables to obtain the message queue.

[0055] By first normalizing the network state information of the deterministic network and mapping it uniformly to a preset numerical range, the input bias caused by differences in the dimensions and numerical distributions of node attributes, link attributes, and traffic attributes is effectively eliminated, ensuring the stability of subsequent processing. Then, linear and nonlinear transformations are applied to the normalized information to construct initial latent variables with stronger expressive power and robustness, enhancing the nonlinear modeling ability for complex network states. On this basis, graph feature extraction is performed on the initial latent variables rather than the original state information based on the network topology connection relationship, generating semantically consistent and structurally stable message sequences. This avoids the problem of inaccurate message transmission in graph neural networks caused by fluctuations in the original data, thereby significantly improving the accuracy and reliability of amplitude and phase information after complex frequency domain transformation. Finally, it achieves accurate capture of the time delay fluctuation characteristics caused by the periodic preemption of nondeterministic traffic in deterministic networks and high-precision inference of performance parameters, effectively overcoming the shortcomings of traditional methods such as frequency domain feature distortion and insufficient periodic pattern recognition ability due to unstable input.

[0056] In another example, after the controller obtains the message queue, it can use discrete Fourier transform to convert the message sequence from the time domain to the complex frequency domain; and extract the amplitude and phase features of the converted message sequence as the complex frequency domain features.

[0057] By using Discrete Fourier Transform, the message sequence generated by graph feature extraction is accurately mapped from the time domain to the complex frequency domain. This transforms the time delay tail distribution characteristics caused by periodic preemption behavior, which was originally hidden in time domain fluctuations, into quantifiable amplitude and phase components. The amplitude feature reflects the intensity of time delay fluctuations caused by periodic scheduling, while the phase feature captures the temporal offset patterns of gating period opening and closing. This overcomes the problem of periodic feature loss caused by traditional graph neural networks modeling only in the time or topological domains. It enables complex frequency domain features to directly characterize the frequency domain resonance and phase coupling effects caused by periodic gating scheduling in deterministic networks, significantly improving the modeling accuracy and prediction stability of network performance fluctuations under nondeterministic traffic interference. Ultimately, it achieves accurate identification of the root causes of time delay jitter in deterministic networks and high-reliability evaluation of performance parameters.

[0058] In another example, the network state information can be iteratively updated using the complex frequency domain features to obtain updated information. Specifically, a gated recurrent unit (GRU) structure can be used to iteratively update the network state information based on the complex frequency domain features. By using the GRU structure to perform time-series modeling on these complex frequency domain features, the amplitude and phase information, under the synergistic effect of the GRU's update gate, reset gate, and memory state mechanism, achieves stable transmission and long-term dependency accumulation of the dynamic evolution process of network state information across multiple time steps. This effectively overcomes the problems of difficulty in modeling time delay fluctuations caused by periodic preemption and the instability of frequency domain features over time in traditional methods. It also enables the calculation process of network performance parameters to have adaptive response capabilities to periodic interference, significantly improving the accuracy, consistency, and robustness of the prediction results.

[0059] In another example, the controller can also process the network state information through an attention mechanism. Based on the network topology connections, graph features are extracted from the network state information processed by the attention mechanism to generate corresponding message sequences. By dynamically adjusting the weights of node attributes, link attributes, and traffic attributes of the deterministic network through the attention mechanism, the model can identify and strengthen key network features closely related to periodic preemption behavior, thereby effectively improving the expression intensity of delay fluctuation signals caused by nondeterministic traffic in the graph structure. Subsequently, before performing graph feature extraction based on the network topology connections, message passing and aggregation are performed only on the network state information enhanced by the attention mechanism, ensuring that the generated message sequences are more focused on the sudden and time-varying fluctuation patterns caused by periodic preemption. This allows the amplitude and phase information obtained by subsequent transformation to the complex frequency domain to more accurately characterize the frequency domain periodic features of nondeterministic traffic, significantly improving the problem of insufficient feature capture caused by traditional graph neural networks failing to distinguish the importance of attributes. Ultimately, this achieves high-precision modeling and performance evaluation of the complexity of delay fluctuations in deterministic networks.

[0060] S330, The complex frequency domain features are processed to obtain the performance parameters of the deterministic network.

[0061] The network performance parameters include latency and packet loss rate for nondeterministic traffic. In this embodiment, complex frequency domain features can be processed, and the amplitude and phase information extracted from the complex frequency domain can be directly mapped to the performance parameters of the deterministic network.

[0062] The complex frequency domain features originate from the complex representation obtained after performing a discrete Fourier transform on the message sequence. These features contain the temporal structure information implicit in the periodic scheduling of the network. By preserving the original expressions of amplitude and phase components, they can directly reflect the latency fluctuation patterns caused by the periodic preemption of non-deterministic traffic by deterministic traffic. This processing does not rely on the direct aggregation of time-domain features, but rather utilizes the distribution characteristics of spectral components in the complex domain to more compactly represent the periodic patterns of network behavior. Thus, without increasing computational redundancy, it establishes a direct correlation between the final output latency and packet loss rate parameters and the scheduling essence of the deterministic network.

[0063] The performance determination method provided in this application overcomes the shortcomings of traditional graph neural networks, which only model in the time domain and thus lose periodic features. It enables amplitude information to accurately reflect the intensity of fluctuations and phase information to accurately characterize the temporal relationships of fluctuations. Furthermore, through systematic processing of complex frequency domain features, it achieves efficient capture and quantitative analysis of complex time delay fluctuation behavior in deterministic networks, ultimately accurately deriving network performance parameters. Therefore, it solves the problem in existing technologies where periodic preemption leads to complex time delay fluctuations and traditional methods cannot effectively model frequency domain periodic features, achieving the effects of accurately identifying time delay fluctuation patterns, improving the accuracy of performance evaluation, and enhancing the quality of service assurance capabilities of deterministic networks.

[0064] Furthermore, this application embodiment also provides a graph neural network model for extracting features from network state information in a deterministic network, transforming the extracted features to the complex frequency domain to obtain complex frequency domain features; and processing the complex frequency domain features to obtain performance parameters of nondeterministic traffic.

[0065] In this embodiment, the graph neural network model includes an input network, a graph message exchange network, and an output network. The input network primarily transforms node attributes, link attributes, and traffic attributes in the network topology into initial latent variables with a unified dimension that the graph neural network can use. The graph message exchange network primarily transmits the aggregated latent variables to the output network on the network topology graph. The aggregated latent variables refer to the latent variables obtained by aggregating node latent variables, link latent variables, and traffic latent variables. The output network primarily transforms the aggregated latent variables into predicted values ​​of network performance parameters.

[0066] Appendix Figure 4 This is a schematic diagram illustrating the processing of a graph neural network model provided in an embodiment of this application.

[0067] in, Figure 4(a) in the diagram illustrates the processing of the input network. The input network first obtains network state information from the network topology. For example, suppose the network topology includes N nodes, L links, and F traffic flows, where N, L, and F are positive integers. Then, the node attributes in the network state information can be obtained using the node attribute vector (…). Link attributes can be represented using link attribute vectors (). ) represents flow information. Flow information can be represented using flow attribute vectors ( )express.

[0068] To eliminate the impact of attribute dimension differences on training stability, the input network first standardizes the node attributes using a standardization layer, scaling each value in the attribute vector to the target range (e.g., between 0 and 1). This method improves the training performance of the prediction model. For example, equations 1-3 can be used to standardize the node attribute vectors:

[0069] in, Let represent the mean of the s-th attribute in the attribute vector of all nodes. Let represent the variance of the s-th attribute in the attribute vector of all nodes. This represents the result of the standardization of the s-th attribute of the i-th node.

[0070] In this embodiment, the link attribute vector can also be standardized using the same standardization method as for the node attribute vector. Specifically, the mean and variance of the attribute vector are first obtained, and then normalization is performed on each element of the attribute vector based on the mean and variance, mapping each attribute component to a value range of 0 to 1.

[0071] Furthermore, the input network can also use two hidden layers to transform the standardized attribute vector into latent variables of a specified size for processing in the graph message interaction network. The hidden layers consist of fully connected layers and activation layers. The fully connected layers perform linear transformations on the attribute vectors, while the activation layers use the ReLU activation function for nonlinear transformations to obtain the dependent variable.

[0072] For example, Equation 4 can be used to obtain the node's latent variables:

[0073] in Represents a node The corresponding hidden variables of the nodes, and These represent the weight matrix and offset vector of the first fully connected layer, respectively. and These represent the weight matrix and offset vector of the second fully connected layer of the node, respectively. The vector indicating the normalized node attribute vector of the i-th node.

[0074] It should be noted that the embodiments of this application can use the same method to obtain the link implicit variables corresponding to the link attributes and the traffic implicit variables corresponding to the traffic information. The only difference is that the standardized node attribute vector in Formula 4 is replaced with either the link attribute vector or the traffic attribute vector.

[0075] The input network outputs three sets of initial hidden variables, specifically the node hidden variables. Link hidden variables and traffic latent variables .

[0076] Figure 4 Figure (b) illustrates the processing of the graph message interaction network. The graph message interaction network is responsible for iteratively transmitting and aggregating latent variable information on the topology graph. Specifically, in the graph message interaction phase, the message extraction layer first generates node queues, link queues, and traffic message queues based on message functions constructed from network topology connections and latent variable relationships, completing the transmission and aggregation of neighborhood information. The message functions are shown in Equations 5 and 6:

[0077] in It is a node In the The hidden variable state of the next message passing. Through nodes Go to node Traffic latent variables, . It is the vertex The neighborhood group, It is a message function.

[0078] In the network topology diagram, node queues, link queues, and traffic message queues are aggregated. Finally, a latent variable update layer updates the aggregated message queues with the latent variables for the next message transmission. The specific update function is shown in Equation 7. For update functions.

[0079] In this embodiment, the update layer employs a gated recurrent unit (GRU) structure from an improved recurrent neural network to improve the latent variables, thereby better maintaining the update information of the hidden state. The GRU processes node attributes, link attributes, and traffic information in exactly the same way; a general approach is used here. , This represents the hidden variables input to the update function and the corresponding messages. The GRU structure mainly consists of four parts: update gate, reset gate, current memory state, and final output.

[0080] The update gate formula is shown in Formula 8:

[0081] in, It is the sigmoid activation function, which restricts values ​​to between 0 and 1. It is the weight matrix of the updated gate. ( ) is the hidden state of the previous iteration step, while ( +1) is the corresponding message obtained in the current message passing. The update gate determines how much past state information is passed to the current state.

[0082] The reset door formula is shown in Formula 9:

[0083] in, This is the weight matrix of the reset gate. It is similar to the update gate in GRU, but is used to control the degree of influence of the previous state on the current state.

[0084] The formula for the current memory state is shown in Formula 10:

[0085] Where tanh is the hyperbolic tangent activation function. W is the weight matrix of the current memory state. It represents a candidate value for the current memory state, used to calculate the final hidden state.

[0086] The final output formula is shown in Formula 11:

[0087] in, It is the Hadamard product of vectors. The formula, which combines the update gate and the current memory state to calculate the final hidden state, represents the hidden state of the current iteration step and is the output of the update layer. This GRU structure effectively models long-term dependencies and state memory in the message passing process, enabling the model to perceive the cumulative impact of gating cycles on nondeterministic traffic. In this embodiment, after t iterations, the final set of hidden variables can be output as the input to the output network. The final set of hidden variables includes the final node hidden variables, link hidden variables, and traffic hidden variables.

[0088] The output network mainly includes linear transformations and activation function processing of the output layer, which are used to transform the final set of latent variables after aggregation of the network graph message interaction network into predicted values ​​of network performance parameters.

[0089] For example, see Figure 5 This figure is a schematic diagram of the processing of an output network provided in an embodiment of this application. Figure 5 As shown, the output network transforms the final set of latent variables from the aggregated graph message interaction network into latency and packet loss rate through linear transformation of fully connected layers and processing with a ReLU-based nonlinear activation function. A ReLU activation function is applied before the final output layer to shift negative values ​​to zero while retaining other values ​​in their original state, thus avoiding the problem of negative values ​​in the output network performance parameters.

[0090] The calculation formulas for the linear transformation and activation function processing of the fully connected layer are shown in Equation 12:

[0091] in This represents the predicted values ​​of the network performance parameters that need to be output. If it contains d elements, then , , and These represent the corresponding output weight matrix and offset vector, respectively.

[0092] Furthermore, the graph message interaction network can also include a complex-enhanced convergence layer, which transforms the input message into the complex frequency domain using the discrete Fourier transform. This leverages the characteristics of the complex frequency domain to express more periodic information about the network, thereby improving the ability to predict network performance parameters. In the complex frequency domain, the dimensionality of the input features can be compressed by partially selecting Fourier components, while preserving the original information with a high probability. This reduces computational load and increases the speed of network performance parameter prediction.

[0093] For example, see Figure 6 The diagram shown is a processing schematic of another graph message interaction network provided in an embodiment of this application. Figure 6As shown, a complex-enhanced convergence layer is added between the message extraction layer and the update layer. During the first iteration of the graph message interaction network, the message is transformed into the complex frequency domain through the complex-enhanced convergence layer, and then the latent variables are updated using GRU.

[0094] In yet another example, a graph message interaction network can also include an attention layer. By assigning different attention weights to different latent variables in the attention layer, the graph message interaction network can focus more on latent variables of interest, such as node latent variables or link latent variables.

[0095] For example, see [link to previous article] Figure 6 As shown, the attention layer is located above the message extraction layer. That is, the latent variables are first extracted through the attention layer in the first round, and then the extracted information is input into the message extraction layer.

[0096] Furthermore, see Figure 7 As shown in the figure, this is a feature extraction method for an attention mechanism provided in an embodiment of this application. Specifically, the attributes of N nodes, L links, and F traffic flows extracted from the network are first expressed as vectors through a fully connected layer and a ReLU activation layer. The attention weights of each attribute are evaluated by training the weight matrix W and the offset vector b. a Finally, the latent variables of each attribute are updated using attention weights, and the initial latent variables are obtained again through a fully connected layer and a ReLU activation layer.

[0097] Latent variables for node attention enhancement Feature extraction, the calculation formulas are shown in formulas 13-16:

[0098] In the formula Represents a node Attribute vectors, and These represent the weight matrix and offset vector of the fully connected layer in the node, respectively.

[0099]

[0100] In the formula Represents a node The attention weight vector is defined by the Softmax function, which exponentially normalizes it, and the tanh function, which activates it. The range of the attention weight vector is [-1, 1]. and These represent the weight matrix and offset vector of the node attention layer, respectively.

[0101]

[0102] In the formula, ⊙ represents the Hadamard product operation of matrices. Represents a node The updated hidden variable state, W2 and b2 represent the weight matrix and offset vector of the second hidden fully connected layer of the node, respectively.

[0103] In yet another example, this application proposes a Graph Attention Complex Neural Network (CAE-GNN) model. The overall structure of the CAE-GNN model is as follows: Figures 8 to 11 As shown, it mainly consists of four parts: attention-based input feature extraction, complex augmented graph message interaction, latency output network, and packet loss rate output network.

[0104] Attention-based input feature extraction structures, such as Figure 8 As shown, the CAE-GNN model first standardizes the node attributes, link attributes, and flow attributes in the network to reduce the impact of differences in attribute value ranges on the prediction of network performance parameters. Then, it encodes the attributes using a fully connected layer and a ReLU activation function, encoding attributes of different lengths into intermediate variables of a specified shape for subsequent matrix operations in the attention mechanism. Next, it calculates the attention weights of nodes and flow in the network using the attention mechanism, and updates the intermediate variable states of nodes and flows using the Hadamard product operation. The attention weights are then used to weight the attributes, increasing the focus on key attributes. Finally, another fully connected layer and a ReLU activation function encode the attributes again, obtaining the initial latent variable states of nodes, links, and flows as the zero-state input for the next layer.

[0105] Complex augmented graph message interaction structure as follows Figure 9 As shown, the CAE-GNN model will use the initial latent variables of the initial nodes, links, and traffic as a basis, and through graph message interaction mechanism and complex attention enhancement, iteratively update the latent variable states of the initial nodes, links, and traffic in the network.

[0106] First, the CAE-GNN model performs an attention weighting on the latent variable states of the initial node, links, and traffic during the first round of graph message interaction. The calculation method is the same as that for attention-based input feature extraction, in order to increase the attention paid to key initial nodes, links, and traffic. However, for speed and convergence considerations, the attention weighting is only calculated in the first round of graph message interaction.

[0107] Next, the CAE-GNN model generates message sequences of initial nodes, links, and traffic through message functions based on graph relationships and the influence relationships between latent variables defined in Equations 1-3. The message sequences are then transformed into the complex frequency domain, and the characteristics of the complex frequency domain are used to express more network periodic information, thereby improving the ability to predict network performance parameters.

[0108] In the complex frequency domain, this embodiment of the application can compress the dimensionality of input features by randomly selecting the expected Fourier components, while preserving the original information with a high probability, thereby reducing the amount of computation and improving the speed of network performance parameter prediction. The compressed and simplified Fourier components extract amplitude and phase from the complex frequency domain as the output of complex-enhanced convergence.

[0109] Then, the message sequence used for updating and the latent variables from the previous iteration are input into the corresponding GRU. Through the GRU's reset gate, update gate, and calculation of the current memory state, the hidden state of the current iteration, i.e., the output of the update layer, is obtained. This output will serve as the input for the next iteration. After iterating t times, the CAE-GNN model will obtain the final latent variable states of nodes, edges, and flows, which will then serve as the inputs to the latency output network and the packet loss rate output network. Here, t is a positive integer.

[0110] Packet loss rate output network structure as follows Figure 10 As shown, the first half is the same as the delay output network. The CAE-GNN model uses the final latent variable state of the obtained nodes as the input to the packet loss rate output network. It transforms the latent variable state through two fully connected layers and the ReLU activation function, and finally outputs the predicted value of the packet loss rate. Of course, in actual training and prediction, due to the numerical characteristics of the input data, the packet loss rate will be converted into the arrival rate for calculation, i.e., 1 - packet loss rate, so as to facilitate the training and fast prediction of the neural network within the limited floating-point precision. However, the overall network structure and calculation are still the same as described above.

[0111] Delayed output network structure as follows Figure 11 As shown, the CAE-GNN model uses the final latent variable state of the obtained flow as input to the delay output network. It transforms the latent variable state through two fully connected layers and a ReLU activation function, finally outputting the predicted values ​​of the network performance parameters. The CAE-GNN model only uses the neural network output value as a part of the delay, instead of directly outputting the entire delay value. Then, it calculates the propagation delay and transmission delay using the link attributes and flow attributes of the original input, and adds these three parts of the delay to obtain the final delay output. By separating the directly and quickly computed parts from the target result, the difficulty of neural network prediction can be reduced, and the accuracy of network performance parameter prediction can be improved.

[0112] Latent variables that enhance attention in streams The feature extraction process is similar to the latent variable feature extraction process with attention enhancement for nodes. However, due to the limited number of input attributes for edges, the attention mechanism does not have a significant positive effect and may even increase the time required for training and prediction. Therefore, for the latent variable h of the edges... Feature extraction uses only two fully connected layers and a ReLU activation layer for latent variable encoding, and its calculation formula is shown in Equations 17-18:

[0113] In the formula, x represents the edge. The attribute vectors, W3 and b3 represent the weight matrix and offset vector of the edge-hidden fully connected layer, respectively.

[0114]

[0115] In the formula Representing an edge The updated hidden variable state, where W4 and b4 represent the weight matrix and offset vector of the second hidden fully connected layer, respectively.

[0116] In addition, the attention mechanism was also used before the message passing function in the first round of graph message interaction to enhance the expressiveness of the message passing function and improve the accuracy of network performance parameter prediction.

[0117] This invention is the first to combine the periodic behavior of communication protocols with complex frequency domain deep learning modeling, and introduces attention weighting and physical decomposition output mechanisms. Without increasing model complexity, it achieves a quadruple breakthrough in accuracy, efficiency, interpretability, and deployability. Compared with existing technologies, it evaluates network state information through graph attention neural networks, which helps to improve prediction speed and reduce long-tail latency prediction errors while ensuring high accuracy. It also has good cross-network generalization ability, providing the first high-performance, low-overhead, and deployable evaluation engine for deterministic networks.

[0118] Furthermore, embodiments of this application also provide a performance determination apparatus for nondeterministic networks, used to execute the performance determination method described above.

[0119] Appendix Figure 12 This application provides a schematic diagram of a performance determination device for nondeterministic networks, comprising: The acquisition unit 1201 is used to acquire network state information of a deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network. The processing unit 1202 is used to extract features from network state information and transform the extracted features to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; the complex frequency domain features are processed to obtain performance parameters of nondeterministic traffic.

[0120] Optionally, the step of extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features includes: Based on the network topology connections, graph features are extracted from the network state information to generate corresponding message sequences; The message sequence is transformed to the complex frequency domain to obtain the complex frequency domain features.

[0121] Processing unit 1202 is also used for: The network state information is normalized to map it to a preset numerical range; the mapped network state information is then subjected to linear and nonlinear transformations to obtain initial latent variables. The step of extracting graph features from the network state information based on the network topology connection relationship to generate a corresponding message sequence includes: extracting graph features from the initial latent variables based on the network topology connection relationship to generate a corresponding message sequence.

[0122] Optionally, transforming the message sequence to the complex frequency domain to obtain the complex frequency domain features includes: The message sequence is transformed from the time domain to the complex frequency domain by using Discrete Fourier Transform; the amplitude and phase features of the transformed message sequence are extracted as the complex frequency domain features.

[0123] Optionally, the processing unit 1202 is further configured to: iteratively update the network state information using the complex frequency domain features to obtain updated information; The step of processing the complex frequency domain features to obtain the performance parameters of the nondeterministic traffic includes: processing the updated information to obtain the performance parameters of the nondeterministic traffic.

[0124] Optionally, the iterative update of the network state information using the complex frequency domain features includes: The network state information is iteratively updated based on the complex frequency domain characteristics using a gated recurrent unit (GRU) structure.

[0125] Optionally, before performing graph feature extraction on the network state information based on network topology connections, the processing unit 1202 is further configured to: The network state information is processed using an attention mechanism; The step of extracting graph features from the network state information based on the network topology connection relationship to generate a corresponding message sequence includes: extracting graph features from the network state information after the attention mechanism processing based on the network topology connection relationship to generate a corresponding message sequence.

[0126] Optionally, the step of extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features; and processing the complex frequency domain features to obtain the performance parameters of the nondeterministic traffic, includes: The network state information is converted into initial latent variables used by the graph message interaction network through the input network of the graph neural network model; The graph features of the initial latent variables are extracted through the graph message interaction network of the graph neural network model, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features. The complex frequency domain features are processed by the output network of the graph neural network model to obtain the performance parameters of the deterministic network.

[0127] Optionally, the performance parameters include latency and / or packet loss rate for nondeterministic traffic.

[0128] This application provides a performance determination apparatus for nondeterministic networks. The apparatus can perform the following steps: acquiring network state information of a deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network; then, extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; and processing the complex frequency domain features to obtain the performance parameters of the deterministic network. The apparatus provided in this application can capture the transmission patterns of nondeterministic traffic in complex network topologies from a frequency domain perspective by transforming the network state information to the complex frequency domain and utilizing the fact that the complex frequency domain features contain amplitude information reflecting the intensity of network fluctuations and phase information reflecting propagation characteristics.

[0129] It should be noted that the various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for the device and equipment embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method embodiments. The device and equipment embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components indicated as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the solution in this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0130] The above description is merely one specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for determining the performance of nondeterministic flow, characterized in that, Applied to deterministic networks, the method includes: Obtain network state information of the deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network; Feature extraction is performed on the network state information, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information. The performance parameters of the nondeterministic flow are obtained by processing the complex frequency domain features.

2. The method according to claim 1, characterized in that, The step of extracting features from the network state information and transforming the extracted features to the complex frequency domain to obtain complex frequency domain features includes: Based on the network topology connections, graph features are extracted from the network state information to generate corresponding message sequences; The message sequence is transformed to the complex frequency domain to obtain the complex frequency domain features.

3. The method according to claim 2, characterized in that, The method further includes; The network state information is normalized to map it to a preset numerical range; the mapped network state information is then subjected to linear and nonlinear transformations to obtain initial latent variables. The step of extracting graph features from the network state information based on the network topology connection relationship to generate a corresponding message sequence includes: extracting graph features from the initial latent variables based on the network topology connection relationship to generate a corresponding message sequence.

4. The method according to claim 2, characterized in that, The step of transforming the message sequence to the complex frequency domain to obtain the complex frequency domain features includes: The message sequence is transformed from the time domain to the complex frequency domain by using Discrete Fourier Transform; the amplitude and phase features of the transformed message sequence are extracted as the complex frequency domain features.

5. The method according to claim 2, characterized in that, The method further includes: iteratively updating the network state information using the complex frequency domain features to obtain updated information; The step of processing the complex frequency domain features to obtain the performance parameters of the nondeterministic traffic includes: processing the updated information to obtain the performance parameters of the nondeterministic traffic.

6. The method according to claim 5, characterized in that, The iterative update of the network state information using the complex frequency domain features includes: The network state information is iteratively updated based on the complex frequency domain characteristics using a gated recurrent unit (GRU) structure.

7. The method according to claim 2, characterized in that, Before extracting graph features from the network state information based on network topology connections, the method further includes: The network state information is processed using an attention mechanism; The step of extracting graph features from the network state information based on the network topology connection relationship to generate a corresponding message sequence includes: extracting graph features from the network state information after the attention mechanism processing based on the network topology connection relationship to generate a corresponding message sequence.

8. The method according to claim 1, characterized in that, The network state information is subjected to feature extraction, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features. The performance parameters of the nondeterministic flow are obtained by processing the complex frequency domain features, including: The network state information is converted into initial latent variables used by the graph message interaction network through the input network of the graph neural network model; The graph features of the initial latent variables are extracted through the graph message interaction network of the graph neural network model, and the extracted features are transformed into the complex frequency domain to obtain complex frequency domain features. The complex frequency domain features are processed by the output network of the graph neural network model to obtain the performance parameters of the deterministic network.

9. The method according to any one of claims 1-8, characterized in that, The performance parameters include latency and / or packet loss rate for nondeterministic traffic.

10. A device for determining the performance of a nondeterministic network, characterized in that, The device includes: The acquisition unit is used to acquire network state information of the deterministic network; the network state information includes node attributes, link attributes, and traffic attributes of the deterministic network. The processing unit is used to extract features from the network state information and transform the extracted features to the complex frequency domain to obtain complex frequency domain features; the complex frequency domain features include amplitude information and phase information; and to process the complex frequency domain features to obtain the performance parameters of the nondeterministic traffic.

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