A Bandwidth Estimation Method for Tactile Teleoperation Services

Abstract

The present invention is applicable to the field of communication technologies of wireless communication systems, and provides a bandwidth estimation method for haptic teleoperation services, including: modeling the arrival process of haptic services; analyzing the correlation between the arrival processes of the two parts; a martingale expression method for the haptic burst arrival process; predicting the service arrival process; and estimating the bandwidth of service traffic. The present invention models the arrival process of haptic services, analyzes the correlation between the haptic service arrival processes from the master to the slave and from the slave to the master, considers the time domain, frequency domain, and high-order characteristics of service arrivals, proposes a new method for constructing an arrival martingale process, predicts service arrivals, realizes accurate measurement of the burstiness of haptic services, proposes a new bandwidth estimation method, and realizes dynamic estimation of the bandwidth requirements of haptic services. The present invention can efficiently handle the burstiness of haptic services, laying a foundation for ensuring the quality of service of haptic communication, optimizing bandwidth resource allocation, and improving network performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication system communication, and particularly relates to a bandwidth estimation method for tactile teleoperation services. Background Art

[0002] The tactile Internet is one of the potential key technologies for 6G mobile Internet. The IEEE P1918.1 standard working group defines the tactile Internet as a network architecture that allows remote access, perception, and operation of real (or virtual) objects (or processes).

[0003] The delay of a data packet is jointly determined by its arrival and service processes. How to model the service arrival process of tactile teleoperation and estimate the bandwidth has become a prerequisite for ensuring the quality of service of tactile communication delay. However, there is currently a lack of research on the modeling and prediction of tactile teleoperation service arrivals, and there are also deficiencies in bandwidth estimation research. Different from classical mobile communication services, tactile teleoperation is a "human-in-the-loop" system. Its service arrival frequency and characteristics are closely related to the real-time operations of the operator, and due to the strict delay requirements, it is impossible to rely on strategies such as conventional caching mechanisms to compensate for the delay. Therefore, the tactile communication system needs to pay special attention to the dynamic estimation and adjustment of the bandwidth to ensure the real-time and efficient data transmission during high-frequency operations. Specifically, when the master operator performs high-frequency pushing, grasping, releasing and other actions, the system will generate a large amount of tactile information in a short time. In order to reduce the burden on the communication network, tactile compression coding technology (such as the perceptual dead zone coding method) is essential. However, although compression coding technology can control the average arrival rate of tactile data packets, it exacerbates the burstiness of the instantaneous arrival rate and the arrival time interval. This bursty characteristic poses challenges to traditional bandwidth estimation methods. Especially during peak hours or high-frequency operations, the burstiness and volatility of bandwidth requirements may cause huge pressure on the network.

[0004] In summary, tactile information interaction has a natural burst characteristic, and compression coding technologies such as perceptual dead zone coding further enhance the burst attribute of tactile services. Since the arrival of tactile service traffic is random, accurately estimating the bandwidth becomes a complex task. Therefore, how to accurately estimate the bandwidth of tactile services with burst characteristics is a difficult problem for realizing the efficient guarantee of tactile communication service quality. For this reason, the present invention proposes a bandwidth estimation method for tactile teleoperation services. Summary of the Invention

[0005] The purpose of the present invention is to provide a bandwidth estimation method for tactile teleoperation services, aiming to solve the problems proposed in the above background art.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A bandwidth estimation method for tactile teleoperation services, comprising the following steps:

[0008] Step 1: Modeling the arrival process of tactile services;

[0009] Analyze the autocorrelation and partial autocorrelation coefficients of the arrival rates of master-to-slave and slave-to-master data packets. According to the characteristics of the autocorrelation and partial autocorrelation coefficients, select a model for modeling: If it is independent and identically distributed, use maximum likelihood estimation to fit the candidate probability distribution; if it is first-order autocorrelated, adopt a Markov chain model; if it is order autocorrelated and , adopt order autoregressive process for modeling. The probability distribution of the random variables involved in the autoregressive process adopts the candidate distribution, and the parameters of the candidate distribution are fitted using maximum likelihood estimation;

[0010] Step 2: Correlation analysis of the two arrival processes;

[0011] Calculate the time difference correlation coefficient of the master-to-slave and slave-to-master service arrival processes to measure the degree of correlation between the two;

[0012] Step 3: Martingale expression method for the tactile burst arrival process;

[0013] Construct a martingale expression for the tactile service arrival process to reflect its burstiness and time correlation, specifically including:

[0014] Independent and identically distributed Pareto distribution: Construct an exponential supermartingale, considering the influence of the tail index on the arrival martingale;

[0015] order autoregressive process: Construct an exponential supermartingale, considering the influence of the order on the arrival martingale;

[0016] Step 4: Predict the service arrival process;

[0017] Use the properties of the martingale to predict the cumulative arrival data packet traffic in future time slots, specifically including:

[0018] Independent and identically distributed Pareto distribution: Predict through the martingale expression;

[0019] order autoregressive process: Predict through the martingale expression;

[0020] Step 5: Estimate the bandwidth of the service traffic;

[0021] Define the service rate as the bandwidth and construct a constant rate service model; for the autoregressive arrival model AR(p), calculate the delay violation probability; use the bisection method to estimate the bandwidth.

[0022] Furthermore, in step 1, the calculation formulas for the autocorrelation coefficient and the partial autocorrelation coefficient are as follows:

[0023] Assume that the time series data is , Indicates t Observed value of business traffic at the moment;

[0024] Autocorrelation coefficient To measure the t Data at the moment With hysteresis Data at the moment The correlation between them is calculated as:

[0025] Formula 1: ;

[0026] in, It is a time series The mean of is the lag period; n is the sample size of the time series, that is, the total number of observations; the partial autocorrelation coefficient To measure the t Data at the moment With hysteresis Data at the moment The direct relationship between The correlation between the two after the influence of the lag period is calculated as:

[0027] Formula 2: ;

[0028] in: Indicates that before it is known Under the condition of lagged data, t Time data With hysteresis Time data The conditional covariance between Indicates t Time data Before known The conditional variance under the condition of lag period.

[0029] Furthermore, in step 2, the calculation formula of the time difference correlation coefficient is:

[0030] Formula 3: ;

[0031] in: Indicates that the service arrival process from the master to the slave and from the slave to the master is The time difference correlation coefficient of , represents the observed value of the service traffic from the master control to the slave control and from the slave control to the master control at a certain moment; represents the observed value of the service traffic from the master control to the slave control at a certain moment; represents the sample mean of the observed value of the service traffic from the master control to the slave control; represents the sample mean of the observed value of the service traffic from the slave control to the master control; t represents a time slot; represents the sample size; represents the lag period.

[0032] Further, the specific process of step three is as follows:

[0033] Let represent the arrival process, depicting the packet traffic arriving per unit time; represents the cumulative arrival process, equal to the cumulative packet traffic arriving from the initial moment to the time slot ;

[0034] If follows an independent and identically distributed Pareto distribution, and its probability distribution function is:

[0035] Equation 4: ;

[0036] where: represents the probability of the event occurring; x represents the value of the random variable; represents the random variable 's lower bound; represents the tail index;

[0037] Let represent the arrival martingale process. The arrival martingale of the tactile service is constructed as an exponential supermartingale, considering the influence of the tail index on the arrival martingale. According to the properties of the Pareto distribution, the arrival martingale expression corresponding to the Pareto distribution is constructed as:

[0038] Equation 5: ;

[0039] where: represents the martingale parameter, represents the martingale parameter ratio factor; According to the properties of the martingale , solve the martingale expression parameters and , where represents the expectation operator; represents the arrival martingale process at the moment; Denote the arrival process from time slot 0 to time slot ; prove that and when is a martingale process;

[0040] If belongs to the autoregressive process of order

[0041] Equation 6: ;

[0042] where: denotes the autoregressive coefficient at the previous time instants; i denotes the index of the lag term; denotes the value of the autoregressive process at the previous time instants; denotes the constant expected value, which determines the overall offset of the sequence; denotes the standard deviation; is subject to an independent and identically distributed Gaussian distribution with a mean of 0 and a variance of 1;

[0043] Construct the arrival martingale of the autoregressive process of order using the exponential supermartingale, considering the influence of the order , that is, the time-domain characteristics of the arrival process, and construct the arrival martingale expression as:

[0044] Equation 7: ;

[0045] where: j denotes the time point; denotes the value of the autoregressive process at the previous time instants; denotes the martingale expression parameter, which is the service rate;

[0046] Using the properties of the martingale , solve the martingale expression parameter .

[0047] Furthermore, the specific process of Step 4 is as follows:

[0048] According to the prediction theory, the random variable is measurable. If is measurable, there is:

[0049] Equation 8: ;

[0050] It can be known from the definition of conditional mathematical expectation that is measurable. If is measurable, according to the properties of martingale, it is deduced that and finally solved to obtain , is equal to the cumulative arrival data packet traffic from the initial time to time slot ;

[0051] If follows an independent and identically distributed Pareto distribution, according to the properties of martingale, the random variable is measurable. From Equation 5, it can be seen that the arrival martingale is measurable, that is is measurable;

[0052] Therefore, is transformed into , that is:

[0053] Equation 9: ;

[0054] Finally solved to obtain:

[0055] Equation 10: ;

[0056] If belongs to the order autoregressive (AR) process, then it is measurable, that is is measurable; from Equation 7, it can be seen that the arrival martingale is measurable, that is is measurable;

[0057] Therefore, is transformed into , that is:

[0058] Equation 11: ;

[0059] Finally solved to obtain:

[0060] Equation 12: ;

[0061] where: represents the value of the autoregressive process at the previous moments.

[0062] Furthermore, the specific process of Step 5 is as follows:

[0063] Define the service rate as the bandwidth required by the traffic and represent the service as a constant-rate service model; if belongs to the p-th order autoregressive process, which is in the form of Equation 6; for the service rate satisfies the autoregressive arrival model AR(p), let:

[0064] Equation 13: ;

[0065] Equation 14: ;

[0066] where: represents the martingale parameter, which is a special value defined within the range of ; represents the variance; represents the delay violation probability coefficient; represents the autoregressive coefficient; represents the standard deviation of

[0067] Then the delay violation probability is:

[0068] Equation 15: ;

[0069] where: represents the probability; represents the delay at time slot ; represents the delay bound;

[0070] Consider a special case, i.e.:

[0071] Equation 16: ;

[0072] Then the variance is:

[0073] Equation 17: ;

[0074] where: represents the variance of represents the variance operator; represents the Gaussian process at time

[0075] Therefore:

[0076] Equation 18: ;

[0077] Equation 19: ;

[0078] Wherein: represents the symbol for taking the mean; represents the correlation characteristic function of the arrival process, which can reflect the correlation between random variables; represents the correlation characteristic function of the service process;

[0079] Then the derivation of the delay violation probability is as follows:

[0080] Equation 20: ;

[0081] Let the target delay violation probability , and use the bisection method to estimate the bandwidth C , and the specific process is as follows:

[0082] Initialize parameters: Define the constants in the formula, set the range of the delay bound k as , and generate multiple k values;

[0083] Define the bisection search interval: For each k value, set the initial search range of the bandwidth as ;

[0084] Bisection iteration, including:

[0085] Calculate the midpoint of the bandwidth :

[0086] Equation 21: ;

[0087] Calculate the intermediate value of the delay violation probability according to the formula :

[0088] Equation 22: ;

[0089] Judge the relationship between and the target delay violation probability :

[0090] If , the bandwidth is too large, and the search interval is reduced: ;

[0091] If , the bandwidth is too small, and the search interval is increased: ;

[0092] Stop interval: Stop the iteration when , where is the accuracy requirement, and the estimated value of the bandwidth is:

[0093] Equation 23: ;

[0094] Wherein: respectively represent the minimum bandwidth and the maximum bandwidth.

[0095] Compared with the prior art, the beneficial effects of the present invention are:

[0096] In view of the burst characteristics of tactile services in a teleoperation system, the present invention models the arrival process of tactile services. It not only analyzes the correlation of the arrival process of tactile services in two directions, from the master to the slave and from the slave to the master, but also considers the time domain, frequency domain, and high-order characteristics of service arrival. A new method for constructing an arrival martingale process is proposed, and the service arrival is predicted to achieve accurate measurement of the burstiness of tactile services. A new bandwidth estimation method is proposed to realize dynamic estimation of the bandwidth requirements of tactile services. The present invention can efficiently handle the burstiness of tactile services, laying a foundation for ensuring the quality of service of tactile communication, optimizing bandwidth resource allocation, and improving network performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 is a flowchart of the method of the present invention.

[0098] Figure 2 When set λ = 10 Mbps, σ = 4 Mbps, changing the k value, the changing trend of the estimated bandwidth C under different delay bounds.

[0099] Figure 3 When set = 1 e -3, σ = 4 Mbps, λ changing the k value, the changing trend of the estimated bandwidth C under different delay bounds.

[0100] Figure 4 When set = 1 e -3, λ = 10 Mbps, changing the k value, the changing trend of the estimated bandwidth C under different delay bounds.

[0101] Figure 5 When set σ = 4 Mbps, k= 20 ms changing the value, the estimated bandwidth λ under differentC Change trend

[0102] Figure 6 When set λ = to 10 Mbps k= 10 ms and change the value, the estimated bandwidth under different standard deviations C change trend Specific implementation mode

[0103] In order to have a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention will be described in detail below, but it should not be construed as a limitation on the implementable scope of the present invention

[0104] The following describes the specific implementation of the present invention in detail with reference to specific embodiments

[0105] An embodiment of the present invention provides a bandwidth estimation method for tactile teleoperation services, and its flowchart is as Figure 1 shown, and the method includes the following steps

[0106] Step 1: Modeling the arrival process of tactile services

[0107] Existing research on tactile service modeling assumes that the arrival of tactile services is independent and identically distributed. Different from this, the present invention first analyzes the autocorrelation and partial autocorrelation coefficients of the arrival rates of "master → slave" (from master to slave) and "slave → master" (from slave to master) data packets to determine whether the arrival processes of their respective data packets are independent and identically distributed. According to the characteristics of their autocorrelation and partial autocorrelation coefficients, a suitable model is selected for modeling: if it is independent and identically distributed, the maximum likelihood estimation is used to fit the parameters of the candidate probability distribution function. To ensure the rationality of the analysis results of the invention, the present invention will compare the fitting results of multiple candidate probability distributions such as Poisson distribution, gamma distribution, lognormal distribution and generalized Pareto distribution. If it is first-order autocorrelated, a Markov chain model is used for modeling. If it is order autocorrelated and , then an order autoregressive (AR) process is used for modeling, and the probability distribution of the random variables involved in the autoregressive process uses the candidate distribution, and the parameters of the candidate distribution are fitted by maximum likelihood estimation

[0108] Assume that the time series data is , where represents the business traffic observation value at the t th moment

[0109] The autocorrelation coefficient measures the correlation between thet Data at a moment and lag Data at a moment The correlation between them is calculated as follows:

[0110] Equation 1: ;

[0111] Where is the mean of the time series ; is the lag period; n is the sample size of the time series, that is, the total number of observations;

[0112] Partial autocorrelation coefficient is used to measure the t Data at a moment and lag Data at a moment The direct relationship between them, that is, the correlation between them after removing the influence of the first lag periods is calculated as follows:

[0113] Equation 2: ;

[0114] Where: represents the conditional covariance between the data at the th moment and the data at the lag t th moment under the condition that the data of the first lag periods are known; Data at a moment represents the conditional variance of the data at the th moment under the condition that the data of the first t lag periods are known; If the autocorrelation coefficients of all lag periods and the partial autocorrelation coefficients

[0115] are all close to 0, that is, there is no significant correlation, then it can be considered that the time series data is independently and identically distributed, indicating that there is no dependence relationship between the data at the current moment and the data of any lag period, which conforms to the characteristics of independent and identical distribution. and the partial autocorrelation coefficients are all close to 0, that is, there is no significant correlation, then it can be considered that the time series data is independently and identically distributed, indicating that there is no dependence relationship between the data at the current moment and the data of any lag period, which conforms to the characteristics of independent and identical distribution.

[0116] Step 2: Correlation analysis of the two-part arrival process;

[0117] For the correlation between the arrivals of the two parts of "master control → slave control" and "slave control → master control", their tactile information has an obvious guiding-following relationship. By calculating their time difference correlation coefficient, the degree of correlation between them is measured.

[0118] The time difference correlation coefficient is used to test the lag relationship between time series variables by using the coefficient, that is, to judge the time difference relationship between two variables by the magnitude of the absolute value of the correlation coefficient. Its calculation formula is:

[0119] Formula 3: ;

[0120] Where: represents the time difference correlation coefficient when the service arrival processes of "master control → slave control" and "slave control → master control" are at a time difference of ; , represents the observed values of the service traffic from the master control to the slave control and from the slave control to the master control at time represents the observed value of the service traffic from the master control to the slave control at time represents the sample average of the observed values of the service traffic from the master control to the slave control; represents the sample average of the observed values of the service traffic from the slave control to the master control; t represents the time slot; represents the sample size; represents the lag period.

[0121] Step 3: Martingale expression method for the tactile burst arrival process;

[0122] The definition of the arrival martingale is: If for any there exists an arrival martingale parameter such that the stochastic process is a supermartingale, then a cumulative arrival process obeys the arrival martingale; where: represents the martingale parameter; represents the time slot the number of data packets served; represents the number of data packets cumulatively served from time slot 0 to time slot ; similar to the arrival martingale, represents the correlation characteristic function of the arrival process, reflecting the correlation between random variables. If are independent and identically distributed, then ; represents the arrival martingale parameter used to maintain the supermartingale property of the arrival martingale; represents the parameter of the arrival martingale.

[0123] Let represent the arrival process, depicting the data packet traffic arriving per unit time; represent the cumulative arrival process, equals the cumulative data packet traffic arriving from the initial moment to time slot .

[0124] If obeys the independent and identically distributed Pareto distribution, which is a special case of the general Pareto distribution. Its probability distribution function is:

[0125] Equation 4: ;

[0126] Where: represents the probability of event occurring; x represents the value of the random variable; represents the random variable 's lower bound; represents the tail index.

[0127] The present invention uses the tail index to measure the burstiness of tactile services. The smaller it is, the more severe the heavy-tailed burst. Let represent the arrival martingale process. The present invention constructs the arrival martingale of tactile services as an exponential supermartingale. Heavy-tailed bursts are the main factor leading to deteriorated delay. On the one hand, the present invention uses the exponential supermartingale structure to assign higher impact weights to burst arrivals. On the other hand, since the tail index reflects both the heavy-tailed burstiness and the higher-order characteristics of the arrival process. The present invention will focus on considering the influence of the tail index on the arrival martingale. According to the properties of the Pareto distribution, the present invention constructs the arrival martingale expression corresponding to the Pareto distribution as:

[0128] Equation 5: ;

[0129] Where: represents the martingale parameter, represents the martingale parameter ratio factor. According to the properties of the martingale , solve the martingale expression parameters and , where represents the expectation operator; represents the arrival martingale process at time represents the arrival process from time slot 0 to time slot . It can be proved that and when is a martingale process;

[0130] If belongs to the order autoregressive (AR) process, its form is:

[0131] Equation 6: ;

[0132] Wherein: represents the autoregressive coefficient at the previous several moments; i represents the index of the lag term; represents the autoregressive process at the previous several moments; represents the constant expected value, which determines the overall offset of the sequence; represents the standard deviation; obeys the independent and identically distributed Gaussian distribution, with a mean of 0 and a variance of 1.

[0133] The present invention still constructs the arrival martingale of the -order autoregressive process by using the exponential supermartingale. On the time scale, the higher the time correlation, the greater the impact on the time delay. Therefore, the construction of the arrival martingale of the -order autoregressive arrival also needs to consider the influence of the order

[0134] Equation 7: ;

[0135] Wherein: j represents the time point; represents the autoregressive process at the previous moment; represents the martingale expression parameter, which is the service rate.

[0136] Then, using the properties of the martingale , solve the martingale expression parameter . will be closely related to the higher-order characteristics and frequency-domain characteristics of .

[0137] In addition, for other heavy-tailed arrival models such as the general ON-OFF process, construct the corresponding supermartingale process of the general ON-OFF heavy-tailed arrival according to the definition and properties of the supermartingale. The functional form of this supermartingale process is closely related to the probability distribution characteristics of the ON-state and OFF-state durations.

[0138] Step Four: Predict the service arrival process;

[0139] According to the prediction theory, the random variable is measurable, where represents algebra, which is a set of information; if the random variable is measurable, then there is:

[0140] Equation 8: ;

[0141] It can be known from the definition of conditional mathematical expectation that is measurable, where denotes algebra, which contains more information than ; if is measurable, according to the properties of the martingale it is deduced that , and finally solved to obtain , is equal to the cumulative arrival data packet traffic from the initial time to time slot .

[0142] If follows an independent and identically distributed Pareto distribution, according to the properties of the martingale, it can be known that the random variable is measurable. From Equation 5, it can be seen that the arrival martingale is measurable, that is is measurable.

[0143] Therefore, can be transformed into , that is:

[0144] Equation 9: ;

[0145] Finally solved to obtain:

[0146] Equation 10: ;

[0147] If belongs to order autoregressive (AR) process, then it is measurable, that is is measurable. From Equation 7, it can be seen that the arrival martingale is measurable, that is is measurable.

[0148] Therefore, can be transformed into , that is:

[0149] Equation 11: ;

[0150] Finally solved to obtain:

[0151] Equation 12: ;

[0152] Where: denotes the autoregressive process at the previous The value at a certain moment.

[0153] Step Five: Estimate the bandwidth of the service traffic;

[0154] Define the service rate as the bandwidth required by the traffic and represent the service as a service model with a constant rate.

[0155] If belongs to the order autoregressive (AR) process, in the form of Equation 6; for the service rate satisfies the autoregressive arrival model AR(p), let:

[0156] Equation 13: ;

[0157] Equation 14: ;

[0158] Where: represents the martingale parameter, a special value defined within the range of values of represents the variance; represents the delay violation probability coefficient; represents the autoregressive coefficient; represents the standard deviation of

[0159] Then the delay violation probability is:

[0160] Equation 15: ;

[0161] Where: represents the probability; represents the delay at time slot ; represents the delay bound;

[0162] Consider the special case of

[0163] Equation 16: ;

[0164] Then the variance is:

[0165] Equation 17: ;

[0166] Where: represents the variance of represents the variance symbol; represents the Gaussian process at time

[0167] Therefore:

[0168] Equation 18: ;

[0169] Equation 19: ;

[0170] Where: represents the mean value symbol; represents the correlation characteristic function of the arrival process, which can reflect the correlation between random variables; represents the correlation characteristic function of the service process;

[0171] Then the derivation of the delay violation probability is:

[0172] Equation 20: ;

[0173] Let the target delay violation probability , and use the bisection method to estimate the bandwidth C , the specific process is as follows:

[0174] (1) Initialize parameters;

[0175] Define the constants in the formula, set the range of the delay bound k as , and generate multiple k values.

[0176] (2) Define the bisection search interval;

[0177] For each k value, set the initial search range of the bandwidth as ..

[0178] (3) Bisection iteration;

[0179] Calculate the midpoint of the bandwidth :

[0180] Equation 21: ;

[0181] Calculate the intermediate value of the delay violation probability according to the formula:

[0182] Equation 22: ;

[0183] Judge the relationship between and the target delay violation probability :

[0184] If , the bandwidth is too large, and the search interval is reduced: ;

[0185] If If the bandwidth is too small, increase the search range: .

[0186] (4) Stop interval;

[0187] Stop the iteration when , where is the accuracy requirement, and the estimated value of the bandwidth is:

[0188] Equation 23: ;

[0189] Where: represent the minimum bandwidth and the maximum bandwidth respectively.

[0190] Example 1: Set the parameter values as shown in Table 1;

[0191]

[0192] When setting λ = to 10 Mbps, σ = 4 Mbps, change the value and observe the changing trend of the estimated bandwidth k under different delay bounds C . The simulation results are as shown in Figure 2 . The delay bound k sets the tolerance of the delay. As increases, the system's tolerance of the delay increases and the bandwidth requirement decreases. That is, the system can tolerate more requests with delay violations. Therefore, to meet a looser delay requirement, the system does not need a high bandwidth. When = 1 e -3, the system can tolerate a higher proportion of delay fluctuations, so the bandwidth requirement does not need to be as strict as when = 1 e -5, and the system still meets the requirements at a lower bandwidth. During the bandwidth estimation process, the bisection method is used for bandwidth search. The bisection method continuously adjusts the bandwidth according to the relationship between the current delay bound and the delay violation probability until the accuracy requirement is met. As the delay bound increases, the adjustment of the bandwidth becomes gradually slower, and finally the bandwidth approaches the expected value of the system λ .

[0193] When setting = 1 e -3, σ = 4 Mbps, change the λ value and observe the changing trend of the estimated bandwidth k under different delay bounds C . The simulation results are as shown in Figure 3 . When λ =When the speed is 5Mbps, the arrival volume per unit time is less, the load of the system is lighter, and the processing capacity of the system is relatively stronger. Therefore, under the same delay bound k , the system can handle more requests with a lower bandwidth. A larger λ means that the arrival volume of the system is higher and the load is heavier. The system needs a larger bandwidth to maintain a lower probability of delay violation. When the initial delay bound k increases, the system needs a larger bandwidth to cope with the higher probability of delay violation. Therefore, the bandwidth drops faster. As the delay bound increases, the system gradually stabilizes and the rate of bandwidth drop slows down.

[0194] When setting =1 e -3, λ = at 10Mbps, change the value, and observe the changing trend of the estimated bandwidth k under different delay bounds C . The simulation results are as Figure 4 shown. When the standard deviation σ = is 2Mbps, the volatility of the system is small, which means that the variation of the arrival process is relatively stable, the load of the system is relatively stable, and the curve drops slowly and approaches the mean value earlier. When the standard deviation is large, the volatility of the system is large, which means that the uncertainty of the arrival process is high, and the system needs a higher bandwidth to cope with these fluctuations. The curve drops rapidly at the beginning because the influence of noise is large, resulting in a strong response of the system. The larger the standard deviation, the stronger the initial reaction of the system. This indicates that the system is more sensitive to external disturbances, makes rapid adjustments at the beginning, but the system will gradually stabilize over time.

[0195] When setting σ = at 4Mbps, k= 20 ms and change the value, observe the changing trend of the estimated bandwidth λ under different C . The simulation results are as Figure 5 shown. As the expected value increases, the bandwidth also shows an upward trend. This indicates that as the arrival rate increases, the system needs more bandwidth to handle higher traffic. This is because a higher packet arrival rate requires more bandwidth resources to avoid delays or packet losses in the system due to insufficient bandwidth. =1 e -5 curve is at the top because at a lower probability of delay violation, the system must use a higher bandwidth to handle a larger request traffic to ensure that the delay does not exceed the set threshold.

[0196] When setting λ = at 10Mbps,k= 10 ms When, change the value, and observe the estimated bandwidth under different standard deviations C for its changing trend. The simulation results are as Figure 6 shown. =1 e The curve of =1 to -5 is at the top, meaning that at a lower delay violation probability, the system must provide a higher bandwidth to cope with the delay risk caused by increased noise or volatility. When the standard deviation increases, the bandwidth requirement grows faster because the system must ensure a lower delay violation probability to ensure that even with large fluctuations, the delay limit will not be exceeded.

[0197] The above is only the preferred embodiment of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicability of the patent.

Claims

1. A bandwidth estimation method for tactile teleoperation services, characterized in that It includes the following steps: Step 1: Modeling the tactile service arrival process; Analyze the autocorrelation and partial autocorrelation coefficients of the packet arrival rates from the master to the slave and from the slave to the master. According to the characteristics of the autocorrelation and partial autocorrelation coefficients, select a model for modeling: If it is independent and identically distributed, use maximum likelihood estimation to fit the candidate probability distribution; if it is first-order autocorrelated, adopt a Markov chain model; if it is p-order autocorrelated with p≥2, use a p-order autoregressive process for modeling. The probability distribution of the random variables involved in the autoregressive process uses the candidate distribution, and the parameters of the candidate distribution are fitted using maximum likelihood estimation; Step 2: Correlation analysis of the two-part arrival process; Calculate the time difference correlation coefficient of the service arrival processes from the master to the slave and from the slave to the master to measure the degree of correlation between them; Step 3: Martingale expression method for the tactile burst arrival process; Construct a martingale expression for the tactile service arrival process to reflect its burstiness and time correlation, specifically including: Independent and identically distributed Pareto distribution: Construct an exponential supermartingale, considering the impact of the tail index on the arrival martingale; p-order autoregressive process: Construct an exponential supermartingale, considering the impact of the order on the arrival martingale; Step 4: Predict the service arrival process; Use the properties of the martingale to predict the cumulative arrival packet traffic in future time slots, specifically including: Independent and identically distributed Pareto distribution: Predict through the martingale expression; p-order autoregressive process: Predict through the martingale expression; Step 5: Estimate the bandwidth of the service traffic; Define the service rate as the bandwidth and construct a constant-rate service model; for the autoregressive arrival model AR(p), calculate the delay violation probability; use the bisection method to estimate the bandwidth; The specific process of Step 3 is as follows: Let a(t) represent the arrival process, depicting the packet traffic arriving per unit time; A(t) represent the cumulative arrival process, and A(t) is equal to the cumulative packet traffic arriving from the initial time to time slot t; If a(t) follows an independent and identically distributed Pareto distribution, its probability distribution function is: Formula 4: Pr{a(t)>x}=(x / x min ) -α ; where: Pr represents the probability that the event a(t) > x occurs; x represents the value of the random variable; x min represents the lower bound of the random variable x; α represents the tail index; Let M A (t) denote the arrival martingale process. The arrival martingale of the tactile service is constructed as an exponential supermartingale. Considering the influence of the tail exponent α on the arrival martingale, according to the properties of the Pareto distribution, the expression construction of the arrival martingale corresponding to the Pareto distribution is: Formula 5: where: θ represents the martingale parameter, and γ represents the martingale parameter ratio factor; according to the properties of the martingale E[M A (t + 1)|α(0),…,α(t)] = M A (t), solve the martingale expression parameters θ and γ, where E represents the expectation operator; M A (t + 1) represents the arrival martingale process at time t + 1; α(0),…,α(t) represents the arrival process from time slot 0 to time slot t; prove that when γ = 1 and θ > 0, M A (t) is a martingale process; If a(t) belongs to a p-order autoregressive process, its form is: Formula 6: where: ω i represents the autoregressive coefficient at the previous i time instants; i represents the index of the lag term; a(t - i) represents the value of the autoregressive process a(t) at the previous i time instants; λ represents the constant expected value; σ represents the standard deviation; z(t) follows an independent and identically distributed Gaussian distribution with a mean of 0 and a variance of 1; Use the exponential supermartingale to construct the arrival martingale of the p-order autoregressive process, considering the impact of the order p, that is, the time-domain characteristics of the arrival process, and construct the arrival martingale expression as: Formula 7: where: j represents the time point; a(t - j + 1) represents the value of the autoregressive process a(t) at the previous j - 1 moment; C represents the martingale expression parameter, which is the service rate; Using the property of the martingale \(E[M A (t + 1)|\alpha(0),\ldots,\alpha(t)]=M A (t)\) to solve for the martingale expression parameter \(C\); The specific process of Step 5 is as follows: Define the service rate as the bandwidth required by the traffic and represent the service as a constant-rate service model; if a(t) belongs to a p-order autoregressive process, its form is Equation 6; for the autoregressive arrival model AR(p) with the service rate C satisfying C > λ, let: Formula 13: Formula 14: Where: θ * represents the martingale parameter, which is a special value defined within the range of values of θ; σ 2 represents the variance; κ represents the delay violation probability coefficient; ω represents the autoregressive coefficient; ν represents the standard deviation of ωa(t); Then the delay violation probability is: Formula 15: Wherein: represents probability; W represents the delay at time slot t; k represents the delay bound; Consider the special case of p = 1, that is: Equation 16: a(t) = ωa(t - 1) + (1 - ω)λ + (1 - ω)σz(t); Then the variance is: Formula 17: where: ν 2 represents the variance of ωa(t); represents the variance symbol; z(t + 1) represents the Gaussian process at time t + 1; Therefore: Formula 18: Formula 19: Wherein: represents the mean value symbol; h(a n ) represents the related characteristic function of the arrival process; h(C) represents the related characteristic function of the service process; Then the delay violation probability is derived as: Formula 20: Let the target delay violation probability Use the bisection method to estimate the bandwidth C. The specific process is as follows: Initialization parameters: Define the constants in the formula, set the range of the time delay bound k as [k min , k max , and generate multiple k values; Define the bisection search interval: For each value of k, set the initial search range of the bandwidth to be [C min , C max ; Bisection iteration includes: Calculate the midpoint C of the bandwidth mid : Formula 21: Calculate the median value ε of the delay violation probability according to the formula mid :[[]]END]] Formula 22: Determine ε mid Relationship with the target delay violation probability ε: If ε mid > ε, the bandwidth is too large, reduce the search range: C max = C mid ; If ε mid <ε, the bandwidth is too small, increase the search range: C min = C mid ; Stopping interval: Stop the iteration when |C max - C min | < tol, where tol is the precision requirement. Then the estimated value of the bandwidth is: Formula 23: where: C min , C max represent the minimum bandwidth and the maximum bandwidth respectively.

2. The bandwidth estimation method for haptic teleoperation services according to claim 1, in step 1, the calculation formulas for the autocorrelation coefficient and the partial autocorrelation coefficient are as follows: Suppose the time series data is M = {M1, M2,..., M n}, where M t represents the observed value of the business traffic at the t-th moment; Autocorrelation coefficient ρ k Used to measure the data M at time t t And the data M at the lagged time k t+k The correlation between them, and the calculation formula is: Formula 1: Among them, is the mean of the time series M; k is the lag period; n is the sample size of the time series, i.e., the total number of observations; Partial autocorrelation coefficient Used to measure the data M at time t t And the data M at lag k t+k The direct relationship between them, that is, the correlation between the two after removing the influence of the first k - 1 lags. The calculation formula is: Formula 2: Where: Cov represents the conditional covariance between the data M at the t-th moment and the data M at the lag k moment, given the data of the first k - 1 lag periods. t and the data M at the lag k moment t-k ; Var represents the conditional variance of the data M at the t-th moment t given the first k - 1 lag periods.

3. The bandwidth estimation method for haptic teleoperation services according to claim 1, the specific process of step 4 is as follows: According to the prediction theory, the random variable E{X|F1} is F1-measurable. If X is F1-measurable, there is: Equation 8: E{X|F1} = X; From the definition of conditional mathematical expectation, it is known that \(E\{X|\mathcal{F}\}\) is \(\mathcal{F}\)-measurable. If \(X\) is \(\mathcal{F}_1\)-measurable, according to the property of martingale \(E[M A (t + 1)|\alpha(0),\ldots,\alpha(t)]=M A (t)\) is deduced that \(M A (t + 1)=M A (t)\). Finally, by solving, \(A(t + 1)\) is obtained, and \(A(t + 1)\) is equal to the cumulative packet traffic arriving from the initial time to time slot \(t + 1\). If \(a(t)\) follows an independent and identically distributed Pareto distribution, according to the properties of martingales, the random variable \(E\{X|F_1\}\) is \(F_1\)-measurable. From Equation 5, it can be seen that the arrival martingale \(M A (t)\) is measurable, that is, \(X\) is measurable; Therefore, convert E[M A (t + 1)|α(0),…,α(t)] = M A (t) to M A (t + 1) = M A (t), that is: Formula 9: Finally, the solution is obtained: Formula 10: If \(a(t)\) belongs to a \(p\)-order autoregressive (AR) process, it is measurable, i.e., \(\mathcal{F}_1\)-measurable; as can be seen from Equation (7), the martingale \(M A (t)\) is measurable, i.e., \(X\) is measurable; Therefore, convert E[M A (t + 1)|α(0),…,α(t)] = M A (t) to M A (t + 1) = M A (t), that is: Formula 11: Finally, the solution is obtained: Formula 12: Wherein: a(t - j + 2) represents the value of the autoregressive process a(t) at the previous j - 2 time instants.

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