Method for predicting end-to-end time delay probability distribution of wireless network

Abstract

The invention relates to the technical field of edge computing, in particular to a method for predicting end-to-end time delay probability distribution of a wireless network, which constructs a probability density function by using an improved Gaussian mixture model and generalized Pareto distribution on the basis of data driving in a mixed density network mode. According to the variation trend of the trailing probability of the delay probability distribution of the data packets in the data set obtained through measurement, a segmentation threshold u of the main body part and the trailing part is obtained through calculation; other parameters of the probability density function are obtained through mixed density network training; and finally, for data packets with different sizes, predicting the probability that the time delay is less than (or greater than) a given value. Multiple experimental results verify that compared with the prior art, the accuracy of the distribution of the end-to-end time delay trailing probability (greater than the probability of given time delay) obtained by using the technology of the invention is significantly improved.

Description

Technical Field

[0001] The present invention relates to the field of edge computing technology, and in particular to a method for predicting the probability distribution of end-to-end delay in a wireless network. Background Art

[0002] The rapid development of time-sensitive services places increasingly high demands on the real-time performance of wireless networks. In application scenarios such as smart production, intelligent transportation, and telemedicine, the end-to-end transmission delay of control signals is required to be in the millisecond level, and the delay jitter is in the microsecond level. In order to make the end-to-end transmission delay of wireless networks fall within a small range, it is necessary to accurately predict the probability distribution of the delay, especially the tail part of the probability distribution.

[0003] There are two types of prediction methods for delay probability distribution: model-driven and data-driven. Model-driven methods are mainly based on queuing theory. For the convenience of analysis, idealized queuing models are established, which cannot accurately reflect the inherent transmission mechanism and external propagation environment characteristics of wireless networks. However, the closer the queuing model is to the actual network characteristics, the higher its complexity. For complex queuing models, there is still a lack of effective methods to obtain delay probability distribution.

[0004] The data-driven method mainly uses a mixed density network. The core is to construct a probability density function and train the parameter vector θ of the delay probability density function based on the measured data set of end-to-end transmission delay of data packets (mainly including information such as data packet size x and end-to-end transmission delay y). Data-driven is an effective way to establish a delay probability distribution prediction method, but when the existing data-driven method predicts the probability distribution of end-to-end delay in wireless networks (especially the tail part of the delay distribution), the prediction results have a larger fluctuation range compared with the actual measurement results, and cannot accurately reflect the changing characteristics of the actual delay. Summary of the invention

[0005] The purpose of the present invention is to provide a prediction method for the probability distribution of end-to-end delay in a wireless network, which is based on data-driven and adopts a mixed density network to adjust the tail part of the probability density function and improve the accuracy of the probability distribution of the end-to-end delay tail.

[0006] To achieve the above object, the present invention provides a method for predicting the probability distribution of end-to-end delay in a wireless network, comprising the following steps:

[0007] Step 1: Collect data and normalize the end-to-end latency of packets.

[0008] Step 2: Construct a probability density function based on the improved Gaussian mixture model and generalized Pareto distribution;

[0009] Step 3: Calculate the segmentation threshold of the main part and the tail part of the probability density function;

[0010] Step 4: Establish a mixed density network;

[0011] Step 5: Train to obtain the mixed density network model parameters;

[0012] Step 6: For packets of different sizes, predict the probability that the delay is less than / greater than a given value.

[0013] Optionally, the execution process of step 1 includes the following steps:

[0014] Step 1.1: Set the start and end time of data collection, and continuously record the size of the data packet in the wireless network and the delay between the terminal and the access point during this time period;

[0015] Step 1.2: Normalize the packet size to a value between [0,1];

[0016] Step 1.3: Calculate the average delay of the data packets, and then subtract the average delay from the delay of each data packet to obtain the standardized delay value.

[0017] Optionally, the tail portion of the probability density function is represented by a weighted sum of a Gaussian mixture model and a generalized Pareto probability density function, and the expression is as follows:

[0018]

[0019] Among them, u represents the segmentation threshold of the main part and the tail part of the probability density function; f(y) represents the weighted sum of Gaussian probability density functions (called Gaussian mixture model); F(u) represents the cumulative probability distribution of f(y) in [0,u]; g(y) is the probability density function of the generalized Pareto distribution; 0<α<1.

[0020] Optionally, the execution process of step 3 includes the following steps:

[0021] Step 3.1: Set equally spaced time points 0, x1, x2, …, x n , the delay in the data set obtained in step 1 is less than x i (i=1,2,…,n) packets, the calculated delay is less than x1,x2,…,x n The probability sequence of

[0022] Step 3.2: Calculate the difference of the obtained probability sequence, and the time point corresponding to the maximum value in the difference sequence is used as the segmentation threshold u for the main part and the tail part of the probability density function.

[0023] Optionally, the mixed density network consists of an input layer, a hidden layer, and an output layer. The neurons between the layers are connected in a fully connected manner. The input layer contains 1 neuron and has no activation function. The number of neurons in the output layer is consistent with the number of parameters that need to be trained for the probability density function, and its activation function is set according to the value range of the output parameters, and the output of each neuron is the parameter that needs to be trained for the probability density function.

[0024] Optionally, the execution process of step 5 includes the following steps:

[0025] Step 5.1: Input the normalized value of the packet size in each data record through the neurons in the input layer;

[0026] Step 5.2: The normalized delay of the data packets in each data record is also used as input for predicting the probability density during training, but it is not input through the neurons in the input layer;

[0027] Step 5.3: Change the learning rate and train to obtain the connection strength between neurons in the mixed density network and the bias of each neuron, that is, the mixed density network model parameters.

[0028] Optionally, the execution process of step 6 includes the following steps:

[0029] Step 6.1: Input the normalized data packet size value into the mixed density network obtained through training, and then output the parameters of the corresponding delay probability density function, that is, obtain the probability density function;

[0030] Step 6.2: Determine the corresponding delay cumulative distribution function and tail distribution function according to the delay probability density function of packets of different sizes;

[0031] Step 6.3: According to the cumulative distribution function of delay and the tail distribution function corresponding to packets of different sizes, the probability of being less than a given delay and the probability of being greater than a given delay are calculated respectively.

[0032] The present invention provides a prediction method for the probability distribution of end-to-end delay in a wireless network. The method is based on data-driven and adopts a mixed density network. The probability density function is constructed using an improved Gaussian mixture model and a generalized Pareto distribution. Specifically, the segmentation threshold u between the main part and the tailing part is calculated based on the change trend of the tailing probability of the delay probability distribution of the data packet in the measured data set; and the other parameters of the probability density function are obtained by training the mixed density network; finally, for data packets of different sizes, the probability of the delay being less than (or greater than) a given value is predicted. It has been verified by multiple experimental results that the accuracy of the distribution of the end-to-end delay tailing probability (the probability of being greater than a given delay) obtained using the technology of the present invention is significantly improved compared with the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0034] Figure 1 It is a schematic diagram of the steps of a method for predicting the probability distribution of end-to-end delay in a wireless network according to the present invention.

[0035] Figure 2 It is a schematic diagram of the end-to-end downlink delay tailing probability distribution of a 172-byte data packet in a WIFI network in a specific embodiment of the present invention.

[0036] Figure 3 It is a schematic diagram of the probability distribution of end-to-end downlink delay tailing of a 3440-byte data packet in a WIFI network in a specific embodiment of the present invention.

[0037] Figure 4 It is a schematic diagram of the end-to-end downlink delay tailing probability distribution of a 6880-byte data packet in a WIFI network in a specific embodiment of the present invention.

[0038] Figure 5 It is a schematic diagram of the end-to-end downlink delay tailing probability distribution of a 10320-byte data packet in a WIFI network in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0039] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0040] See also Figure 1 The present invention provides a method for predicting the probability distribution of end-to-end delay in a wireless network, comprising the following steps:

[0041] S1: collects data and normalizes the end-to-end latency of packets;

[0042] S2: Constructing probability density function based on improved Gaussian mixture model and generalized Pareto distribution;

[0043] S3: Calculate the segmentation threshold of the main part and the tail part of the probability density function;

[0044] S4: Establishing a mixed density network;

[0045] S5: training to obtain the mixed density network model parameters;

[0046] S6: For packets of different sizes, predict the probability that the delay is less than / greater than a given value.

[0047] The following is further described in conjunction with specific embodiments and execution steps:

[0048] The process of step S1 is the process of preparing data, and the specific steps are as follows:

[0049] a) Set the start and end time of data collection, and continuously record the size of the data packet in the wireless network and its end-to-end delay (between the terminal and the access point) during this time period.

[0050] b) Normalize the data packet size to a value between [0,1].

[0051] c) For packets of different sizes, their end-to-end delays are standardized. First, the average delay of the packets is calculated, and then the delay of each packet minus the average delay is used as the standardized delay value.

[0052] The probability density function expression in step S2 is as follows:

[0053]

[0054] Among them, u represents the segmentation threshold of the main part and the tail part of the probability density function; f(y) represents the weighted sum of Gaussian probability density functions (called Gaussian mixture model); F(u) represents the cumulative probability distribution of f(y) in [0,u]; g(y) is the probability density function of the generalized Pareto distribution; 0<α<1.

[0055] The corresponding parameters in the probability density function and how to obtain them are as follows:

[0056] a) Setting the number of Gaussian probability density functions contained in the main part of the probability density function f(y) (expressed as a Gaussian mixture model) (e.g., 10 or 15 Gaussian probability density functions).

[0057] b) The segmentation threshold u of the main part and the tail part of the probability density function is calculated and obtained in step S3.

[0058] c) The weights of each Gaussian probability density function in the Gaussian mixture model (GMM) f(y) in the main part of the probability density function, as well as their means and standard deviations, the parameters of the probability density function g(y) of the generalized Pareto distribution (GPD) in the tail part, i.e., the tail index (TailIndex) and the scale parameter (Scale Parameter), and the weight value α of GMM and GPD in the tail part are obtained by the mixture density network training in step S4.

[0059] Step S3: calculating the segmentation threshold of the main part and the tail part of the probability density function;

[0060] a) Set equally spaced time points 0, x1, x2, …, x n , for example, convert 0 to x n =100ms divided into 200 intervals at equal intervals; the delay in the data set obtained in step 1 is less than x i (i=1,2,…,n) packets; then divide this number by the total amount of data to get the delay less than x1,x2,…,x n The probability sequence of .

[0061] b) Calculate the difference of the probability sequence obtained above, and the time point corresponding to the maximum value in the difference sequence is used as the segmentation threshold u for the main part and the tail part of the probability density function.

[0062] Step S4: Building a mixed density network

[0063] The mixed density network consists of an input layer, a hidden layer, and an output layer. The neurons between each layer are connected in a fully connected manner. The establishment steps are as follows.

[0064] a) Configure the input layer to contain 1 neuron and no activation function.

[0065] b) Configure the hidden layers, determine the number of layers, the number of neurons in each layer, and the activation function of each neuron. For example, for four hidden layers, the number of neurons in each layer is 10, 50, 50, and 40 respectively, and the activation function of each neuron is the hyperbolic tangent function, i.e. "tanh".

[0066] c) Configure the output layer. The number of neurons in this layer is consistent with the number of parameters that need to be trained for the probability density function. The output of each neuron is the parameter that needs to be trained for the probability density function (see step S2(c)). The activation function on the neuron is set according to the value range of the output parameter. For example, the neurons corresponding to the weights of each Gaussian probability density function in f(y) use the activation function "softmax", the neurons corresponding to the mean of the Gaussian function do not have an activation function, and the activation function of the neurons corresponding to the standard deviation is set to "softplus"; the activation functions of the neurons corresponding to the tail exponent and scale parameter of g(x) are both set to "softplus"; the activation function of the neurons corresponding to the weight value α of GMM and GPD in the tail part is also set to "softplus".

[0067] d) Configure the number of training epochs, batch size, and multiple learning rates. For example, the learning rate is set to 10e-3, 10e-4, and 10e-5. For each case, epoch = 300 and batch size = 100000.

[0068] e) Set the loss function to the mean negative log predictive density.

[0069] Step S5: Train to obtain mixed density network model parameters.

[0070] a) Input data: The normalized value of the packet size in each data record is input through the neurons in the input layer. In addition, the normalized delay of the packet in each data record is also used as input to predict the probability density during training and then calculate the loss function, but it is not input through the neurons in the input layer.

[0071] b) Changing the learning rate, training to obtain the connection strength between neurons in the mixed density network and the bias of each neuron, that is, the mixed density network model parameters.

[0072] Step S6: For data packets of different sizes, predict the probability that the delay is less than (or greater than) a given value.

[0073] a) Input the normalized data packet size value into the mixed density network obtained through training, and then output the parameters of the corresponding delay probability density function, that is, obtain the probability density function.

[0074] b) According to the delay probability density function of data packets of different sizes, determine the corresponding delay cumulative distribution function (Cumulative Distribution Function) and tailing distribution function (Tailed Distribution Function).

[0075] c) According to the cumulative distribution function of delay and the tail distribution function corresponding to packets of different sizes, the probability of being less than a given delay and the probability of being greater than a given delay are calculated respectively.

[0076] Furthermore, the present invention also proposes a specific embodiment for verification testing, and selects corresponding data sets combined with different methods for testing. The data set records the uplink, downlink and round-trip delays of four data packets of different sizes (172B, 3440B, 6880B and 10320B respectively) in the WIFI network, wherein the sending interval of each data packet is 1ms, and there are approximately 4 million records respectively.

[0077] The corresponding method names and comparison results are as follows Figures 2 to 5 As shown, gmevmw represents the technology of the present invention; gmevm represents the existing method. The main difference between this method and the technology of the present invention is that the tail part of the delay probability density function of the existing method does not consider the influence of GMM, that is, the tail part is only represented by [1-F(u)]g(y). In addition, the segmentation threshold of the main part and the tail part of the delay probability density function is obtained through mixed density network training; gmm indicates that the main part and the tail part of the probability density function are both represented by a mixed Gaussian model; the black solid line represents the actual measurement result.

[0078] As shown in the figure, the delay tail probability distribution obtained by the technology of the present invention is closer to the actual measurement result. Although there are fluctuations in each experimental result, the fluctuation range is small.

[0079] The results of multiple experiments show that compared with the prior art, the accuracy of the distribution of the end-to-end downlink delay tail probability (the probability of being greater than a given delay) obtained using the technology of the present invention is significantly improved.

[0080] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for predicting the probability distribution of end-to-end delay in a wireless network, characterized in that: The following steps are involved: Step 1: Collect data and normalize the end-to-end latency of packets. Step 2: Construct a probability density function based on the improved Gaussian mixture model and generalized Pareto distribution; Step 3: Calculate the segmentation threshold of the main part and the tail part of the probability density function; Step 4: Establish a mixed density network; Step 5: Train to obtain the mixed density network model parameters; Step 6: For packets of different sizes, predict the probability that the delay is less than / greater than a given value.

2. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 1, characterized in that: The execution process of step 1 includes the following steps: Step 1.1: Set the start and end time of data collection, and continuously record the size of the data packet in the wireless network and the delay between the terminal and the access point during this time period; Step 1.2: Normalize the packet size to a value between [0,1]; Step 1.3: Calculate the average delay of the data packets, and then subtract the average delay from the delay of each data packet to obtain the standardized delay value.

3. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 2, characterized in that: The tail part of the probability density function is represented by the weighted sum of the Gaussian mixture model and the generalized Pareto probability density function, and the expression is as follows: Among them, u represents the segmentation threshold of the main part and the tail part of the probability density function; f(y) represents the weighted sum of Gaussian probability density functions (called Gaussian mixture model); F(u) represents the cumulative probability distribution of f(y) in [0,u]; g(y) is the probability density function of the generalized Pareto distribution; 0<α<1.

4. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 3, characterized in that: The execution process of step 3 includes the following steps: Step 3.1: Set equally spaced time points 0, x1, x2, …, x n , the delay in the data set obtained in step 1 is less than x i (i=1,2,…,n) packets, the delays calculated are less than x1,x2,…,x n The probability sequence of Step 3.2: Calculate the difference of the obtained probability sequence, and the time point corresponding to the maximum value in the difference sequence is used as the segmentation threshold u for the main part and the tail part of the probability density function.

5. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 4, characterized in that: The mixed density network consists of an input layer, a hidden layer, and an output layer. The neurons between the layers are connected in a fully connected manner. The input layer contains 1 neuron and no activation function. The number of neurons in the output layer is consistent with the number of parameters that need to be trained for the probability density function. Its activation function is set according to the value range of the output parameters, and the outputs of each neuron are the parameters that need to be trained for the probability density function.

6. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 5, characterized in that: The execution process of step 5 includes the following steps: Step 5.1: Input the normalized value of the packet size in each data record through the neurons in the input layer; Step 5.2: The normalized delay of the data packets in each data record is also used as input for predicting the probability density during training, but it is not input through the neurons in the input layer; Step 5.3: Change the learning rate and train to obtain the connection strength between neurons in the mixed density network and the bias of each neuron, that is, the mixed density network model parameters.

7. The method for predicting the probability distribution of end-to-end delay in a wireless network as claimed in claim 6, characterized in that: The execution process of step 6 includes the following steps: Step 6.1: Input the normalized data packet size value into the mixed density network obtained through training, and then output the parameters of the corresponding delay probability density function, that is, obtain the probability density function; Step 6.2: Determine the corresponding delay cumulative distribution function and tail distribution function according to the delay probability density function of packets of different sizes; Step 6.3: According to the cumulative distribution function of delay and the tail distribution function corresponding to packets of different sizes, the probability of being less than a given delay and the probability of being greater than a given delay are calculated respectively.

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