An end-to-end delay modeling method and system for a TSN-5G cross-domain fusion network

Abstract

The application discloses a kind of TSN-5G cross-domain fusion network's end-to-end delay modeling method and system, belong to deterministic network communication technical field.This method includes: constructing TSN-5G cross-domain fusion network;Random arrival process model and random service process model of 5G domain service flow are constructed, and then the probability delay upper bound of service flow in 5G domain is calculated;Based on SPI-DCM cross-domain parameter mapping mechanism, the statistical characteristic parameters of service flow are mapped into deterministic arrival curve of TSN domain;End-to-end service curve is constructed for TSN domain node, and is combined with deterministic arrival curve, and the deterministic delay upper bound of service flow in TSN domain is calculated;Finally, based on the probability delay upper bound of 5G domain, cross-domain link transmission delay and the deterministic delay upper bound of TSN domain, the end-to-end delay theoretical upper bound of service flow is obtained.The application provides analyzable, verifiable theoretical basis for end-to-end deterministic transmission in industrial internet.

Description

Technical Field

[0001] This invention belongs to the field of deterministic network communication technology, and in particular relates to an end-to-end latency modeling method and system for TSN-5G cross-domain converged networks. Background Technology

[0002] With the rapid development of Industry 4.0 and intelligent manufacturing, the Industrial Internet has placed higher demands on communication networks for end-to-end low latency, high reliability, and deterministic guarantees. To meet these demands, the wired network field has proposed Time-Sensitive Networking (TSN), which achieves microsecond-level deterministic transmission through mechanisms such as gating scheduling, time synchronization, and frame preemption. The wireless network field, relying on the URLLC (Ultra-reliable & Low-latency Communication) capabilities of 5G, provides millisecond-level high-reliability communication through technologies such as network slicing and scheduling-free access. In practical industrial systems, TSN and 5G often need to work together to form a cross-domain converged network to achieve end-to-end communication coverage.

[0003] In such cross-domain converged networks, network calculus theory is commonly used in the industry to conduct rigorous theoretical analysis and safeguards against end-to-end latency. Among these, the technologies based on deterministic network calculus (DNC) for analyzing the TSN domain and on stochastic network calculus (SNC) for analyzing the 5G domain are relatively mature. However, the two computational theories differ fundamentally in their modeling paradigms, leading to the following problems with existing technologies in TSN–5G cross-domain scenarios: First, there is a lack of a unified cross-domain latency modeling mechanism. TSN primarily uses deterministic network calculus (DNC) for worst-case latency analysis, while 5G relies on stochastic network calculus (SNC) for probabilistic latency modeling. The mathematical forms of the two are incompatible, making it difficult to directly combine and derive the end-to-end latency upper bound. Second, existing methods typically use an approximate linearization approach to map SNC outputs to the DNC framework, lacking rigorous theoretical support, resulting in overly conservative latency estimates and insufficient accuracy. Furthermore, traditional modeling does not fully consider the scheduling differences and interference effects between multiple priority service flows (such as periodic, aperiodic, and bursty flows), making it difficult to achieve refined analysis. Finally, as network scale increases or path multi-hops increase, the computational complexity of existing methods rises sharply, resulting in poor scalability and making them unsuitable for practical industrial deployments. Although existing standards have proposed interfaces such as TSNTranslator and TSN AF to achieve protocol interoperability, there is still a lack of theoretical methods to support unified modeling of cross-domain latency, which restricts the reliable application of TSN-5G converged networks in industrial automation and control scenarios. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an end-to-end latency modeling method and system for TSN-5G cross-domain converged networks, so as to achieve high-precision and analytical calculation of the end-to-end latency upper bound, solve the problems of inconsistent modeling, overly conservative latency upper bound, and inability to accurately analyze multi-priority services in the prior art, and provide deterministic assurance for industrial applications.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention provides an end-to-end latency modeling method for TSN-5G cross-domain converged networks, comprising:

[0007] Construct a TSN-5G cross-domain converged network, and formally describe and classify the service flows in the TSN-5G cross-domain converged network;

[0008] Based on the theory of random network calculus, a random arrival process model and a random service process model of service flow in the 5G domain are constructed, and the upper bound of the probability delay of service flow in the 5G domain is calculated based on the random arrival process model and the random service process model.

[0009] Statistical feature parameters of the business flow are extracted, and based on the SPI-DCM cross-domain parameter mapping mechanism, the statistical feature parameters are mapped to deterministic arrival curves in the TSN domain.

[0010] Based on deterministic network calculus theory, end-to-end service curves are constructed for TSN domain nodes, and based on the deterministic arrival curves and end-to-end service curves, the upper bound of the deterministic delay of the service flow in the TSN domain is calculated.

[0011] Based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of cross-domain links, and the deterministic latency upper bound of the TSN domain, the theoretical upper bound of the end-to-end latency of the service flow is obtained.

[0012] Preferably, the construction of the TSN-5G cross-domain converged network includes:

[0013] The TSN-5G cross-domain converged network is abstracted as a weighted directed graph. ,in Represents the set of all network nodes. , The number of network nodes. It represents the set of all directed links in the network; the TSN-5G cross-domain converged network includes at least one TSN domain and one 5G domain;

[0014] The service flows in the TSN-5G cross-domain converged network are formally described and classified, including:

[0015] When there is When a business flow request arrives, use To indicate the first Each business flow Defined using a six-tuple:

[0016] ,

[0017] in, Indicates the first Average arrival rate of each business flow Indicates the first The maximum burst volume of a business flow Indicates the first The priority of each business flow Indicates the first The latency default probability threshold for each business flow. Indicates the first The network domain identifier injected into the service flow of each service flow. Indicates the first The upper bound of the end-to-end latency for each service flow;

[0018] The business flow is divided into three types: periodic control flow, non-periodic state flow, and burst monitoring flow, and an initial priority is assigned to each type of business flow.

[0019] Preferably, the construction of the random arrival process model for service flows within the 5G domain includes:

[0020] For burst monitoring streams, the random arrival process model adopts a state modulation model with a discrete time slot backoff mechanism, defining the burst monitoring stream within the time interval. Cumulative arrivals within for: ,in, This refers to the amount of data that is successfully reported in a single time slot during a burst of monitoring. For independent Bernoulli variables,

[0021] The corresponding moment generating function is:

[0022] ,

[0023] in, Cumulative arrivals The generating function of the moment, For the free parameters of the generating function of the moment mother, For sudden monitoring flow in the first The actual burst probability of each time slot The time slot number, , Time interval The number of complete time slots included;

[0024] For periodic control flow and aperiodic state flow, the random arrival process model adopts the periodic arrival model and the Poisson arrival model, respectively, and the corresponding moment generating functions are derived.

[0025] Preferably, constructing a stochastic service process model for service flows within the 5G domain includes: constructing a unified service process model and constructing a residual service process model.

[0026] The construction of a unified service process model includes:

[0027] For a wireless link, its service capacity is a random process, occurring over time intervals. Within, the cumulative service volume provided by the wireless link is The sum of multiple independent random service variables in a single time slot Internal, service volume It is a random variable: ,in, This represents the proportion of available resources on the link. For bandwidth, The instantaneous signal-to-noise ratio follows a Gamma distribution. , It is a large-scale fading factor. Random variables characterizing small-scale fading;

[0028] Service volume The generating function of the moment mother Represented as: ;in, It is the shape parameter of the Gamma distribution. For Tricomi confluence hypergeometry functions, ;

[0029] Then the entire time interval Within, cumulative service volume The generating function of the moment mother Represented as: ;

[0030] For wired links, their service capacity is a deterministic process, and the service process is constructed based on a constant service rate. , is represented as: ,in, It is the first The scheduling weight of each service flow It is the sum of the weights of all active flows. It refers to the service rate of the wired link;

[0031] The service process is obtained using the expectation operator. The generating function of the moment mother Represented as; ;

[0032] For burst monitoring streams, the actual service obtained is the total service process. Therefore, if the current network node is a wireless node, the service process obtained by the burst monitoring stream corresponds to the service process of the wireless link. Its moment generating function is as follows: If the current network node is a wired node, the service process obtained from the burst monitoring flow corresponds to the service process of the wired link. Its moment generating function is as follows: ;

[0033] Construct a model for the remaining service process, including:

[0034] For periodic control flows, affected by high-priority burst monitoring flows, let the high-priority burst monitoring flows be within a time interval. The cumulative arrivals within are Then the remaining service process of the periodic control flow Represented as:

[0035] ,in, Indicates the network node in the time interval The total cumulative service volume that can be provided within;

[0036] Remaining service process The generating function of the moment mother The upper bound is estimated based on Boole's inequality and the independence of the MGF, and is expressed as: ,in, Represents total cumulative service volume The generating function of the moment, Cumulative arrivals The generating function of the moment;

[0037] For aperiodic state flows, which are influenced by both burst monitoring flows and periodic control flows, let's assume the medium-priority periodic control flow occurs within a time interval. The cumulative arrivals within are The remaining service process of the aperiodic state flow Represented as:

[0038] ,

[0039] Remaining service process The generating function of the moment mother The estimate is: , Cumulative arrivals The moment generating function.

[0040] Preferably, calculating the probabilistic upper bound of service flow latency in the 5G domain based on the random arrival process model and the random service process model includes:

[0041] For any Time-delay random variable Exceeding a given threshold value probability Satisfy the following upper bound:

[0042] ;

[0043] in, This indicates that the expression within the curly braces is... Within the range, take the exact boundary. It is the first The moment generator function for the random arrival process of a business flow. It is the first The matrix generating function of the remaining service process actually obtained by each business flow;

[0044] Substitute the corresponding moment generating function into the Chernoff bound formula, and then... Optimize to obtain the first The upper bound of probabilistic latency for individual service flows in the 5G domain , is represented as:

[0045] ,

[0046] in For the first The threshold for the probability of delay default for each business flow.

[0047] Preferably, the step of extracting statistical feature parameters of the service flow and mapping these parameters to a deterministic arrival curve in the TSN domain based on the SPI-DCM cross-domain parameter mapping mechanism includes:

[0048] Statistical characteristic parameters extracted from the business flow include: average arrival rate. Variance of the arrival process Delay default probability threshold Priority and periodic perturbation function ,

[0049] Design the SPI-DCM mapping function:

[0050] ,

[0051] in, This represents the SPI-DCM mapping function. Indicates time, A rate adjustment factor based on business type. It is the adjustment coefficient of the disturbance correction term. , It is the basic adjustment coefficient. The priority weighting coefficient, It is a business type adjustment coefficient;

[0052] The statistical characteristic parameters are mapped to a deterministic arrival curve in the TSN domain based on the SPI-DCM mapping function, as follows:

[0053] ;

[0054] ,

[0055] in, For the first Deterministic arrival curves for individual service flows entering the TSN domain. For the first Equivalent cumulative arrival volume of each business flow For the first The maximum burst volume of each business flow is determined by the mapping function. The intercept at that time can be determined by fitting.

[0056] Preferably, the step of constructing end-to-end service curves for TSN domain nodes based on deterministic network calculus theory includes:

[0057] TSN domain nodes employ time-aware shapers, and their baseline service curves... A slope is the link rate A linear function, expressed as: ;

[0058] Introducing elastic service curves :

[0059] ;

[0060] in, Due to inherent scheduling delay, It is the link service rate of the TSN domain node. This indicates the initial attenuation of service capacity within the deterministic domain. Indicates the recovery rate of service capabilities within the deterministic domain;

[0061] Constructing the Remaining Service Curve Represented as:

[0062] ,

[0063] in, This indicates that all priorities higher than the current one are... A collection of business flows for each business flow. () is a high-priority business flow The deterministic arrival curve Indicates taking a non-negative value;

[0064] End-to-end service curve of service flow transmitted along the path within the TSN domain It is the minimum convolution of the remaining service curves of all nodes on the path.

[0065] Preferably, based on the deterministic arrival curve and the end-to-end service curve, the upper bound of the deterministic delay of the service flow in the TSN domain is calculated, including:

[0066] upper bound of deterministic latency of service flows in the TSN domain It is a deterministic arrival curve End-to-end service curve The maximum horizontal distance between them.

[0067] Preferably, based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of the cross-domain link, and the deterministic latency upper bound of the TSN domain, the theoretical upper bound of the end-to-end latency of the service flow is obtained, expressed as:

[0068] ,

[0069] in, This is the theoretical upper bound for the end-to-end latency of the service flow. This refers to the fixed transmission delay for cross-domain links.

[0070] This invention also provides an end-to-end latency modeling system for a TSN-5G cross-domain converged network, used to implement the above-mentioned end-to-end latency modeling method for a TSN-5G cross-domain converged network, the system comprising:

[0071] The converged network construction module is used to construct a TSN-5G cross-domain converged network and to formally describe and classify the service flows in the TSN-5G cross-domain converged network.

[0072] The probability delay calculation module is used to construct a random arrival process model and a random service process model of service flows in the 5G domain based on the random network calculus theory, and to calculate the upper bound of the probability delay of service flows in the 5G domain based on the random arrival process model and the random service process model.

[0073] The mapping module is used to extract statistical feature parameters of the business flow and, based on the SPI-DCM cross-domain parameter mapping mechanism, map the statistical feature parameters to the deterministic arrival curve of the TSN domain.

[0074] The deterministic delay calculation module is used to construct end-to-end service curves for TSN domain nodes based on deterministic network calculus theory, and to calculate the upper bound of the deterministic delay of the service flow in the TSN domain based on the deterministic arrival curves and end-to-end service curves.

[0075] The end-to-end latency calculation module is used to obtain the theoretical upper bound of the end-to-end latency of the service flow based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of the cross-domain link, and the deterministic latency upper bound of the TSN domain.

[0076] The beneficial effects of this invention are as follows:

[0077] This invention provides an end-to-end latency modeling method for TSN-5G cross-domain converged networks. It utilizes the moment generating function of stochastic network calculus to characterize the random arrival and service processes of various service flows in the 5G domain. Through the SPI-DCM (Stochastic Parameter Interface-Deterministic Conversion Mapping) mechanism, it maps the SNC statistical characteristic parameters to an analytically resolvable arrival curve from deterministic network calculus. It constructs a unified service model of the residual service curve and elastic service curve within the converged domain. Based on minimum addition algebraic convolution, it derives the theoretical upper bound of cross-domain end-to-end latency. This invention achieves a theoretical connection between the SNC and DNC modeling systems, enabling unified and compact latency upper bound analysis for time-sensitive flows crossing TSN and 5G domains. This effectively improves modeling accuracy and reduces conservatism, providing an analytical and verifiable theoretical foundation for end-to-end deterministic transmission in the Industrial Internet. Attached Figure Description

[0078] Figure 1 This is a diagram of the TSN-5G converged network system architecture based on SPI-DCM in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of the end-to-end latency modeling method for TSN-5G cross-domain converged network provided in an embodiment of the present invention;

[0080] Figure 3 This is a flowchart of the SPI-DCM cross-domain mapping mechanism provided in an embodiment of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0082] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0083] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0084] It should also be noted that, unless otherwise specified, the term "connection" in this article can refer not only to a direct connection, but also to an indirect connection involving an intermediary.

[0085] In the following description, embodiments of the invention will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0086] It should be emphasized here that the step markers mentioned below are not a limitation on the order of the steps, but should be understood as meaning that the steps can be executed in the order mentioned in the embodiments, or in a different order than in the embodiments, or several steps can be executed simultaneously.

[0087] This invention provides an end-to-end latency modeling method for TSN-5G cross-domain converged networks, based on, for example... Figure 1 The deterministic network convergence system architecture shown is implemented. The system adopts a layered design and mainly includes a terminal access layer, a network domain, a network core layer, and an application layer.

[0088] Terminal access layer: used to connect various industrial terminal devices to the corresponding network domain according to service flow type;

[0089] Network domain: refers to the heterogeneous data transmission environment composed of the TSN wired domain and the 5G wireless domain;

[0090] The network core layer is used to run the SPI-DCM (Stochastic Parameter Interface-Deterministic Conversion Mapping) mapping mechanism, enabling unified conversion and control of cross-domain parameters. Its core functional modules include:

[0091] Mapping processor: Used to execute the SPI-DCM cross-domain parameter mapping mechanism;

[0092] Stream classifier: Used to classify and identify input business streams;

[0093] Parameter extractor: Used to extract key statistical feature parameters from random delay modeling results in the 5G wireless domain;

[0094] Application layer: Used to receive data after cross-domain scheduling and execute the final industrial application tasks.

[0095] Based on the above system architecture, the end-to-end latency modeling method for TSN-5G cross-domain converged networks provided by this invention is described in [reference needed]. Figure 2 Specifically, it includes the following steps:

[0096] Step S1: Construct the TSN-5G cross-domain converged network and model the service flow;

[0097] Step S1 is the foundation for cross-domain analysis. This step defines the cross-domain network topology, which includes the Time-Sensitive Network (TSN) domain and the 5G domain, and formally describes and classifies the service flows in the network.

[0098] Building a TSN-5G cross-domain converged network includes: abstracting the TSN-5G cross-domain converged network into a weighted and directed graph. ,in Represents the set of all network nodes. , The number of network nodes. This represents the set of all directed links in the network. The TSN-5G cross-domain converged network comprises at least one TSN domain and one 5G domain, interconnected via cross-domain links, connecting network nodes belonging to different domains. and Cross-domain links, denoted as ,and The bandwidth of a wired link within the TSN domain is expressed as... 5G domain wireless link bandwidth representation Each network node possesses specific processing capabilities and cache resources for running scheduling algorithms and storing and forwarding data packets.

[0099] Modeling the business flow specifically involves, when there is When a business flow request arrives, use To indicate the first Individual business flows. Defined using a six-tuple:

[0100] ,

[0101] in, Indicates the first Average arrival rate of each business flow Indicates the first The maximum burst volume of a business flow Indicates the first The priority of each business flow Indicates the first The latency default probability threshold for each business flow. Indicates the first The network domain identifier injected into the service flow of each service flow. Indicates the first The upper bound of the end-to-end latency for each service flow.

[0102] Then, based on the real-time and reliability requirements of the business flow, it is divided into three types: periodic control flow, non-periodic state flow, and burst monitoring flow, and an initial priority is assigned to each type of business flow. The periodic control flow has a fixed arrival period and is used to transmit critical instructions such as PLC control commands; the non-periodic state flow has a variable arrival interval and is used to transmit sensor feedback data such as temperature and pressure; the burst monitoring flow generates a large amount of data when an event is triggered and is used to transmit data such as images captured by industrial cameras, and is extremely sensitive to initial latency.

[0103] Step S2: Perform stochastic delay modeling on the 5G nondeterministic domain;

[0104] This step S2 is based on the theory of random network calculus. It constructs a random arrival process model and a random service process model for service flows in the 5G nondeterministic domain, and derives and calculates their probabilistic delay upper bound.

[0105] This step categorizes service flows into high, medium, and low priorities, and constructs the remaining service processes for medium and low priority service flows. Specifically, the remaining service process for medium-priority flows is obtained by subtracting the arrival process of high-priority flows from the total network service process, while the remaining service process for low-priority flows is obtained by subtracting the arrival processes of both high-priority and medium-priority flows from the total network service process. Details are as follows:

[0106] Step S21: For the different types of business flows, establish their random arrival process models respectively.

[0107] For burst monitoring streams, a state modulation model with a discrete time slot backoff mechanism is used for characterization. It is set that a burst monitoring stream is allowed at most one reporting action within a unit time slot. The probability of sudden occurrence is The cumulative arrival amount is: ,in For independent Bernoulli variables, Its moment generator function is:

[0108] ,

[0109] in: For sudden monitoring flow in the first The actual burst probability of each time slot; The initial burst probability (base probability) of the burst monitoring stream in the first time slot; The decay factor for the probability of sudden occurrence satisfies This is used to control the rate at which the probability of a sudden event decays over time. The time slot number, ; For sudden monitoring streams within a time interval Cumulative arrivals within; These are the start and end points of the time interval. ; Time interval The number of complete time slots included. ,in The length of a single time slot; This refers to the amount of data that a burst monitoring stream successfully reports within a single time slot (i.e., the size of the data packets generated in each burst). For the first Bernoulli random variables in time slots, This indicates that there is an emergency report in that time slot. It indicates that no emergencies were reported, and ; Cumulative arrivals The generating function of the moment; For the free parameters of the generating function of the moment mother, In subsequent derivation of the upper bound of delay, it is usually taken as ; For mathematical expectation operators; is a natural constant and the base of the exponential function.

[0110] For periodic control flow and aperiodic state flow, periodic arrival model and Poisson arrival model are used respectively, and their corresponding moment generating functions are derived. and .

[0111] Step S22: Construct a unified service process model for the 5G domain.

[0112] The service process in the 5G domain needs to distinguish between wireless and wired links. For wireless links, their instantaneous service capability is affected by channel fading, and a Gamma-distributed signal-to-noise ratio model is used for statistical modeling. Let the link... The instantaneous signal-to-noise ratio (SNR) is ,in, It is a large-scale fading factor. The random variable characterizing small-scale fading follows a normalized Gamma distribution (i.e., the shape parameter is...). The scale parameter is Its probability density function is:

[0113] ,

[0114] in: For random variables The value of represents the instantaneous gain of small-scale fading (dimensionless). The shape parameter of the Gamma distribution (also known as the fading factor) in the Nakagami fading channel, Usually taken ≥1 / 2 is used to describe the severity of channel fading. The larger the value, the less fading occurs, and the more stable the channel. The Gamma function is a generalization of factorial operations over the real number field, defined as follows: This is used to ensure that the integral of the entire probability density function over its domain is equal to 1 (i.e., the normalization constant).

[0115] Therefore, instantaneous signal-to-noise ratio It also follows a Gamma distribution, with its probability density function being... .

[0116] Taking into account factors such as control signaling overhead and beam scanning, the proportion of available resources of the link is denoted as... Its typical value range is Based on Shannon's formula and considering actual coding and modulation efficiency, the link... Signal-to-noise ratio at a certain instant The instantaneous service rate under the given conditions is ,in This refers to the system bandwidth.

[0117] Average service rate of wireless links It is a statistical average of instantaneous rate over channel fading:

[0118] ,

[0119] This average service rate It characterizes the long-term average service capability of a wireless link.

[0120] To perform stochastic network calculus analysis, we need to characterize the stochasticity of the service process. This is defined within a time interval. Within, the cumulative service volume provided by the wireless link is In a block fading channel, assuming each time slot length... If the channel states within remain unchanged and are independently and identically distributed, then It can be modeled as the sum of multiple independent random service variables. Within a single time slot... Internal, service volume It is a random variable: .

[0121] The moment generating function (MGF) is key to the analysis, especially for negative parameters. Single time slot Internal service volume The derivation of the moment generating function MGF is as follows:

[0122] ,

[0123] ,

[0124] ,

[0125] and then,

[0126] ,

[0127] The integral expression can be solved in closed form using special functions. This can be achieved using integral identities. (in (For the Tricomi confluence hypergeometry function), substitute into , , We can obtain:

[0128] ,

[0129] This closed-form moment generator function MGF lays a rigorous mathematical foundation for the subsequent analytical calculation of the upper bound of the time delay.

[0130] Because the time slots are independent, throughout the entire time interval Inside (including) (each time slot), the moment generating function MGF for the cumulative service process is:

[0131] .

[0132] For wired links, we consider links within the TSN domain or other links with stable transmission characteristics (such as fiber optic cables, dedicated Ethernet, etc.). The channel quality of such links does not fluctuate randomly, and their service capacity can be considered constant.

[0133] For a service rate of A wired link, which in a time interval The amount of deterministic services that can be provided internally is Under Weighted Fair Queuing (WFQ) scheduling, the dedicated service process obtained by the business flow on this link can be characterized as follows:

[0134] ,

[0135] in, It is the first The scheduling weight of each service flow It is the sum of the weights of all active flows. It is a tiny service offset used to characterize extremely fine-grained scheduling initialization overhead. This indicates that a non-negative value is taken. In practical analysis, if ignored... Then the service process can be simplified to .

[0136] Due to the service process It is deterministic (or approximately deterministic, with much less randomness than a wireless link), and its moment generating function (MGF) can be directly obtained from the expectation operator. For the parameters... The derivation of its moment generating function MGF is as follows:

[0137] ,

[0138] neglect ,

[0139] ,

[0140] This result indicates that the MGF of the wired link service process is an exponential function, with the exponential part being allocated by the link to the first... Equivalent Deterministic Service Rate for Each Business Flow and time interval A joint decision.

[0141] Compared to the complex integral form of the MGF for wireless links, the MGF for wired link service processes has a concise exponential form. This qualitative difference accurately reflects the essential difference in service determinism between the two types of links: the service capability of a wireless link is a stochastic process, requiring a probability distribution (and its MGF) for complete description; while the service capability of a wired link is a deterministic process, with its MGF degenerating into a deterministic exponential function determined by the service rate. In the cross-domain framework of this invention, the stochastic service MGF of wireless links is the core of SNC analysis, while the deterministic MGF of wired links can be regarded as a special case of the former under the condition of no random fluctuations in service.

[0142] Step S23: Model the remaining service process.

[0143] This step, based on a weighted fair queue scheduling strategy, constructs the actual remaining service process obtained by business flows of different priorities and derives the corresponding matrix generator function.

[0144] In random network calculus, it is necessary to strictly distinguish the following two concepts:

[0145] Service process : refers to the time interval of a network node (or the entire system). The total cumulative service volume that can theoretically be provided. It reflects the inherent processing capacity of a node and is affected by link bandwidth, scheduling algorithms, and channel conditions (such as wireless fading), but does not consider how much service a specific flow actually consumes.

[0146] Remaining service process : Refers to the target business flow in scenarios where multiple flows compete for resources. In the time interval The actual cumulative service volume that can be obtained within the process. It equals the total service volume remaining after deducting the service volume occupied by all higher priority flows.

[0147] The core difference between the two is that the service process is an inherent attribute of the system, while the remaining service process is the actual result of a specific flow in a competitive environment.

[0148] Let the overall service process of the network node be as follows: Under weighted fair queue scheduling, assume there are three priority service types: burst monitoring flow. (High priority), periodic control flow (Medium priority), aperiodic state flow (Low priority), priority relationship is > > The remaining service processes for each type of flow are modeled as follows:

[0149] 1) High-priority flow (burst monitoring flow) )

[0150] Since high-priority flows are not affected by other flows, the service they actually receive is the total service process:

[0151] ,

[0152] Its moment generator function is:

[0153] ,

[0154] Wherein: the parameters of the moment generating function for the arrival process are used Defined as The parameters of the matrix generator function used in the service process Defined as ,in, This indicates the process of arrival. This notation originates from the basic form of Chernoff boundaries.

[0155] Indicates the network node in the time interval The total cumulative service volume that can be provided within.

[0156] Its specific form is given by the wireless / wired link service process model established in step S22:

[0157] If the current node is a wireless node: The corresponding wireless link service process in step S22 Its moment generator function has been derived in step S22 as follows: ,in The number of time slots within the time interval. For Tricomi confluence hypergeometry functions, Channel fading factor , It is a large-scale fading factor.

[0158] If the current node is a wired node: The corresponding step S22 is the wired link service process. Its moment generator function is: ,in It is the first The scheduling weight of each service flow It is the sum of the weights of all active flows. The service rate for the link.

[0159] To simplify the expression, the following derivations will use the same term. and This represents the overall network service process and its matrix generator function. The specific values ​​can be substituted into the corresponding expressions above according to the node type.

[0160] 2) Medium priority flow (periodic control flow) )

[0161] Medium-priority flows need to have their service usage deducted from that of high-priority flows. Let the cumulative arrival count of high-priority flows be... The remaining service process for the medium-priority flow is as follows:

[0162] ,

[0163] Its moment generating function The upper bound can be estimated using Boole's inequality and the independence of the MGF: ,

[0164] in, To indicate high-priority burst monitoring streams within a time interval The cumulative arrivals within, It is the cumulative arrival amount The moment generator function, based on the modeling results of the arrival process of the burst monitoring stream in step S21, is expressed as follows:

[0165] ,

[0166] The corresponding moment generating function (using) The form has been derived in step S21 as follows: .

[0167] 3) Low-priority flow (aperiodic state flow) )

[0168] Low-priority flows need to have all the service usage of higher-priority flows (high and medium) deducted. Let the cumulative arrival amount of medium-priority flows be... The remaining service process for the low-priority flow is as follows:

[0169] ,

[0170] Its moment generating function Similarly, it can be estimated as follows:

[0171] .

[0172] in, This indicates that the medium-priority periodic control flow is within the time interval. The cumulative arrivals within a given period. According to the periodic arrival model, its expression is:

[0173] ,

[0174] in The average arrival rate of the periodic control flow.

[0175] Cumulative arrivals The generating function of the moment mother for:

[0176] .

[0177] The product form of the above-described moment generating function is based on a key assumption: the service process is independent of the arrival processes of flows with different priorities. In practical wireless networks, this assumption is generally reasonable because channel fading (affecting the service process) and packet arrival processes are determined by different physical mechanisms. If a correlation exists, it can be corrected using Boole's inequality or more complex joint bounds, which will not be detailed here.

[0178] Step S24: Derivation of the upper bound of 5G domain probabilistic latency based on SNC:

[0179] Based on the moment generating functions of the arrival process and remaining service process of various service flows obtained in the preceding steps, this step uses the Chernoff bound to derive the upper bound of the probabilistic delay of each service flow in the 5G domain. For any Time-delay random variable Exceeding a given threshold probability Satisfy the following upper bound:

[0180] ,

[0181] in, This indicates that the expression within the curly braces is... The minimum value is taken within the range. Because It is a free optimization parameter, which is found by finding the parameter that minimizes the upper bound. The value can provide the most accurate upper bound for the time delay probability; It is the first The moment generator function for each business flow arrival process is adopted. Form, defined as ; It is the first The moment generator function of the remaining service process actually obtained by each business flow is adopted. Form, defined as ,in, It is the first The arrival process of each business flow, It is the first The remaining service process of each business flow.

[0182] Substitute the corresponding moment generating function into the Chernoff bound formula, and then... By optimizing, we can obtain the first... The upper bound of probabilistic latency for each service flow in the 5G domain :

[0183] ,

[0184] in For the first The threshold for the probability of delay default for each business flow.

[0185] Step S3: Implement the SPI-DCM cross-domain parameter mapping mechanism;

[0186] Step S3 is a crucial bridge connecting the random domain and the deterministic domain. Specifically, starting from the 5G domain probabilistic delay upper bound expression obtained in step S24, key statistical feature parameters that can characterize the randomness of service flows are extracted. Then, these parameters are converted into deterministic arrival curves that can be processed in the TSN domain using the SPI-DCM mapping function. For detailed implementation, please refer to [link to implementation details]. Figure 3 ,include:

[0187] Step S31, SNC parameter extraction: From the results of step S2, extract key statistical feature parameters for each service flow: average arrival rate. Variance of the arrival process Delay default probability threshold Priority and periodic perturbation function .

[0188] in: For the first Each business flow at time The periodic disturbance intensity is used to characterize the arrival characteristic fluctuations caused by 5G domain scheduling mechanisms (such as radio frame period, scheduling timing, etc.); The initial disturbance amplitude is a normal number representing the disturbance intensity at the moment of entering the TSN domain (t=0). Its value is related to factors such as the scheduling cycle of the 5G domain and the priority of service flows. The disturbance attenuation coefficient is a positive real number that controls the rate at which the disturbance decays over time. The larger the value, the faster the disturbance decays, indicating that the impact of 5G domain scheduling on the TSN domain weakens rapidly over time;

[0189] Step S32, SPI-DCM Mapping Function: A cross-domain parameter mapping function based on probability statistics and priority awareness is designed to map the statistical characteristic parameters of the service flow obtained from Stochastic Network Calculus (SNC) modeling to token bucket parameters that can be processed by Deterministic Network Calculus (DNC). This mapping function consists of three parts: an equivalent rate term, a burst compensation term based on Chernoff bounds, and a disturbance correction term related to priority and service type. Through this mapping, the deterministic arrival curve of the service flow entering the TSN domain can be obtained, thereby achieving the connection between the SNC and DNC modeling systems at the parameter level.

[0190] The SPI-DCM mapping function is expressed as follows:

[0191] ,

[0192] in, This represents the SPI-DCM mapping function. Indicates time,

[0193] The first item after the equals sign is the equivalent cumulative arrival amount based on the business type. This is a rate adjustment factor based on service type, used to reserve a certain service margin for the TSN domain. This represents the average arrival rate (a constant).

[0194] The second term after the equals sign is the Chernoff boundary burst compensation term: the derivation of this term is one of the core innovations of SPI-DCM. It stems from the arrival process... Apply Chernoff bounds. Assume... The moment generating function has an upper bound. (For example, for the Gaussian approximation or the boundaries of some known distributions). According to the Chernoff bound, we have:

[0195] ,

[0196] For the index part about Taking the derivative and setting it to zero yields the optimal value. Substituting, we get:

[0197] ,

[0198] Let the upper bound of this probability be equal to the time delay default probability threshold. ,Right now Solving for Therefore, in probability Down, This is the theoretical basis for emergency compensation items.

[0199] The third term after the equals sign is the perturbation correction term: .in, It is the adjustment coefficient of the disturbance correction term. It is the basic adjustment coefficient, which controls the overall magnitude of the disturbance correction term. ; The priority weighting coefficient controls the priority. The degree of influence on the correction term, ; This is a business type adjustment coefficient, related to the business flow type, used to compensate for behavioral differences between different flow types in cross-domain scheduling. This is a heuristic design, aiming to compensate for these differences through a time-decreasing function. This provides additional burst tolerance for low-priority services in the initial phase to compensate for transient service unfairness that may be encountered during cross-domain scheduling and not fully captured in the SNC model. The lower the priority, the more... The smaller, but Item makes it in The proportion of middle class has decreased, while Setting large values ​​for low-priority streams collectively leads to low-priority streams... The larger the value, the larger the correction term, ensuring the robustness of the model.

[0200] Step S33, Deterministic Arrival Curve Output: Output the SPI-DCM mapping formula from step S32. This is organized into a standard token bucket model for compatibility with deterministic network calculus toolchains within the TSN domain. Specifically, the standard token bucket model is represented as:

[0201] ,

[0202] in, For the first The equivalent cumulative arrival amount of each business flow, i.e.:

[0203] ,

[0204] For the first Maximum burst volume of each business flow: Take the mapping function at... The intercept at time t, or determined through fitting. According to the mapping formula:

[0205] ,

[0206] In practical calculations, it is also possible to let Substituting (at a typical time granularity) into the mapping formula and solving inversely. ,Right now:

[0207] ,

[0208] This mapping mechanism enables the mapping from random statistical characteristic parameters. To determine the curve parameters The resolvable transformation provides a compatible input for subsequent deterministic delay analysis in the TSN domain.

[0209] It should be noted that although the final output has a deterministic arrival curve Only the average arrival rate is explicitly included in the form. and maximum burst volume ,but (Variance of arrival process) and (Default probability threshold) has been passed through the burst compensation term in the SPI-DCM mapping formula. The burst was implicitly "absorbed". The possible values ​​are as follows. Specifically, It is not a simple original burst quantity, but an equivalent burst quantity obtained by solving an optimization problem, the magnitude of which implies variance. and probability constraints The impact. Therefore, and Although not in The expression appears explicitly at the end, but it has been fully passed to the latency analysis in the TSN domain through the mapping mechanism.

[0210] Output That is, the first The deterministic arrival curves of each service flow entering the TSN domain are used for TSN domain latency modeling in the subsequent step S4.

[0211] Step S4: Perform deterministic delay modeling on the deterministic domain of TSN;

[0212] In step S4, based on deterministic network calculus theory within the TSN domain, an end-to-end service curve is constructed for the TSN domain nodes. The aforementioned deterministic arrival curve is then combined with this end-to-end service curve to calculate the upper bound of the deterministic latency of the service flow within the TSN domain. The specific implementation process is as follows:

[0213] Step S41, Baseline Service Curve Construction: TSN domain nodes employ a time-aware shaper. Its ideal baseline service curve... A slope is the link rate A linear function, i.e. .

[0214] Step S42, Elastic Service Curve Modeling: To more accurately characterize the service latency that non-periodic / burst services may encounter at the start of scheduling, this invention introduces an elastic service curve. :

[0215] ,

[0216] in, This refers to the link service rate of a TSN domain node. For a single link node, Equal to the bandwidth of the wired link within the TSN domain defined in step S1 For nodes that support Time-Aware Integer (TAS), This indicates the equivalent service rate of the node within the gated time slot allocated to the current service flow. This represents the initial attenuation of service capacity within the deterministic domain (TSN domain). Physically, it represents the instantaneous service capacity gap caused by gating waiting, queue switching, and other mechanisms at the start of scheduling (around t=0). The larger this value, the more significant the service delay in the initial stage. This represents the recovery rate of service capacity within the deterministic domain (TSN domain). Physically, it represents how quickly the system recovers from its initial decay state to its steady-state service capacity. A larger value indicates faster service capacity recovery and a more rapid decay of the exponential decay term.

[0217] Derivation Explanation: This model is a correction to the ideal linear service curve. Due to inherent scheduling delay, This item is used to simulate the dynamic recovery of service capabilities. At that time, the service capacity is (Before taking a positive value), this indicates insufficient initial service capacity. Over time... Increase, exponential term decay, service capacity Gradually approaching the ideal .parameter Controlling recovery speed. This model is superior to a simple rate-latency service curve. It can more precisely describe the nonlinear characteristics of the service startup phase in a real system.

[0218] Step S43, Residual Service Curve Construction: For a certain node on the path, the actual service of the business flow is interfered with by higher-priority flows. Its residual service curve... By subtracting all higher priority flows from the total service curve The sum of the arrival curves yields:

[0219] ,

[0220] in, It is a high-priority business flow The deterministic arrival curve, given by step S33, takes the standard form of the token bucket model. ,in For equivalent cumulative arrival amount, The maximum burst volume; This indicates that all priorities higher than the current one are... The set of business flows for each business flow; this formula is the standard method for handling aggregation scheduling in DNC, ensuring that even under worst-case interference, the first business flow... The lower bound of services that a business flow can obtain.

[0221] Step S44, Calculation of the upper bound of the TSN domain delay: A service flow along the path within the TSN domain Transmission, its end-to-end service curve It is the minimum convolution of the remaining service curves of all nodes on the path:

[0222] ,

[0223] in, For the first Each business flow at the node The remaining service curve, , The minimum convolution operator has the physical significance of connecting the service guarantees of each node on the path. The service capacity of the entire path depends on the combination of the "bottleneck" of the service capacity of all nodes.

[0224] Finally, the first upper bound of deterministic latency for individual service flows in the TSN domain It is a deterministic arrival curve End-to-end service curve Maximum horizontal distance between:

[0225] ,

[0226] This is the core theorem of DNC: the upper bound of deterministic delay is determined by the maximum horizontal distance between the deterministic arrival curve and the service curve.

[0227] Step S5: Calculate the cross-domain end-to-end unified latency;

[0228] Step S5 is the final stage of this modeling method. It aims to synthesize all the results from previous steps, calculate the unified end-to-end theoretical upper bound of the service flow's latency, and complete the analysis loop. This step combines the calculated upper bounds of the 5G domain probabilistic latency, cross-domain link transmission latency, and TSN domain deterministic latency to obtain the theoretical upper bound of the end-to-end latency of the service flow. The specific implementation process is as follows:

[0229] Step S51: Calculate the upper bound of end-to-end latency: For a given service flow, the upper bound of the total latency it experiences after traversing the 5G domain, cross-domain links, and TSN domain. It is given by the following formula:

[0230] ,

[0231] in, From step S24, the service flow within the 5G domain, based on its random arrival and service process, is subject to a default probability. The upper bound of 5G domain probabilistic latency derived under constraints. The fixed transmission delay of a cross-domain link is a constant determined by the physical characteristics of the link. From step S44.

[0232] This accumulation formula achieves a unified synthesis of the probabilistic delay upper bound and the deterministic delay upper bound, forming a complete end-to-end delay analysis model.

[0233] Step S52, Calculation result output: The upper bound of the end-to-end delay calculated above. This is the core output of this method. This value quantitatively characterizes the maximum latency that a service flow may experience from its source to its destination under a given network configuration and service characteristics. This result directly serves the theoretical evaluation of network performance, providing a quantitative theoretical basis for determining whether the network design meets the latency deterministic requirements of the service.

[0234] Through the above-mentioned technical means, this invention realizes the theoretical connection between SNC and DNC modeling systems, enabling time-sensitive flows to achieve unified and tight latency upper bound analysis when crossing TSN and 5G domains, effectively improving modeling accuracy and reducing conservatism, and providing a resolvable and verifiable theoretical basis for end-to-end deterministic transmission in the Industrial Internet.

[0235] Based on the above-mentioned inventive concept, the present invention also provides an end-to-end latency modeling system for a TSN-5G cross-domain converged network, used to implement the above-mentioned end-to-end latency modeling method for a TSN-5G cross-domain converged network. The system includes:

[0236] The converged network construction module is used to construct a TSN-5G cross-domain converged network and to formally describe and classify the service flows in the TSN-5G cross-domain converged network.

[0237] The probability delay calculation module is used to construct a random arrival process model and a random service process model of service flows in the 5G domain based on the random network calculus theory, and to calculate the upper bound of the probability delay of service flows in the 5G domain based on the random arrival process model and the random service process model.

[0238] The mapping module is used to extract statistical feature parameters of the business flow and, based on the SPI-DCM cross-domain parameter mapping mechanism, map the statistical feature parameters to the deterministic arrival curve of the TSN domain.

[0239] The deterministic delay calculation module is used to construct end-to-end service curves for TSN domain nodes based on deterministic network calculus theory, and to calculate the upper bound of the deterministic delay of the service flow in the TSN domain based on the deterministic arrival curves and end-to-end service curves.

[0240] The end-to-end latency calculation module is used to obtain the theoretical upper bound of the end-to-end latency of the service flow based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of the cross-domain link, and the deterministic latency upper bound of the TSN domain.

[0241] It is worth noting that the system embodiment corresponds to the above method embodiment. The implementation methods of the above method embodiments are all applicable to the system embodiment and can achieve the same or similar technical effects, so they will not be described in detail here.

[0242] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0243] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0244] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0245] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0246] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. An end-to-end latency modeling method for a TSN-5G cross-domain converged network, characterized in that, include: Construct a TSN-5G cross-domain converged network, and formally describe and classify the service flows in the TSN-5G cross-domain converged network; Based on the theory of random network calculus, a random arrival process model and a random service process model of service flow in the 5G domain are constructed, and the upper bound of the probability delay of service flow in the 5G domain is calculated based on the random arrival process model and the random service process model. Statistical feature parameters of the business flow are extracted, and based on the SPI-DCM cross-domain parameter mapping mechanism, the statistical feature parameters are mapped to deterministic arrival curves in the TSN domain. Based on deterministic network calculus theory, end-to-end service curves are constructed for TSN domain nodes, and based on the deterministic arrival curves and end-to-end service curves, the upper bound of the deterministic delay of the service flow in the TSN domain is calculated. Based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of cross-domain links, and the deterministic latency upper bound of the TSN domain, the theoretical upper bound of the end-to-end latency of the service flow is obtained.

2. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 1, characterized in that, The construction of the TSN-5G cross-domain converged network includes: The TSN-5G cross-domain converged network is abstracted as a weighted directed graph. ,in Represents the set of all network nodes. , The number of network nodes. It represents the set of all directed links in the network; the TSN-5G cross-domain converged network includes at least one TSN domain and one 5G domain; The service flows in the TSN-5G cross-domain converged network are formally described and classified, including: When there is When a business flow request arrives, use To indicate the first Each business flow Defined using a six-tuple: ， in, Indicates the first Average arrival rate of each business flow Indicates the first The maximum burst volume of a business flow Indicates the first The priority of each business flow Indicates the first The latency default probability threshold for each business flow. Indicates the first The network domain identifier injected into the service flow of each service flow. Indicates the first The upper bound of the end-to-end latency for each service flow; The business flow is divided into three types: periodic control flow, non-periodic state flow, and burst monitoring flow, and an initial priority is assigned to each type of business flow.

3. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 2, characterized in that, The construction of the random arrival process model for service flows within the 5G domain includes: For burst monitoring streams, the random arrival process model adopts a state modulation model with a discrete time slot backoff mechanism, defining the burst monitoring stream within the time interval. Cumulative arrivals within for: ,in, This refers to the amount of data that is successfully reported in a single time slot during a burst of monitoring. For independent Bernoulli variables, The corresponding moment generating function is: ， in, Cumulative arrivals The generating function of the moment, For the free parameters of the generating function of the moment mother, For sudden monitoring flow in the first The actual burst probability of each time slot The time slot number, , Time interval The number of complete time slots included; For periodic control flow and aperiodic state flow, the random arrival process model adopts the periodic arrival model and the Poisson arrival model, respectively, and the corresponding moment generating functions are derived.

4. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 3, characterized in that, Constructing a stochastic service process model for service flows within the 5G domain includes: constructing a unified service process model and constructing a residual service process model. The construction of a unified service process model includes: For a wireless link, its service capacity is a random process, occurring over time intervals. Within, the cumulative service volume provided by the wireless link is The sum of multiple independent random service variables in a single time slot Internal, service volume It is a random variable: ,in, This represents the proportion of available resources on the link. For bandwidth, The instantaneous signal-to-noise ratio follows a Gamma distribution. , It is a large-scale fading factor. Random variables characterizing small-scale fading; Service volume The generating function of the moment mother Represented as: ;in, It is the shape parameter of the Gamma distribution. For Tricomi confluence hypergeometry functions, ; Then the entire time interval Within, cumulative service volume The generating function of the moment mother Represented as: ; For wired links, their service capacity is a deterministic process, and the service process is constructed based on a constant service rate. , is represented as: ,in, It is the first The scheduling weight of each service flow It is the sum of the weights of all active flows. It refers to the service rate of the wired link; The service process is obtained using the expectation operator. The generating function of the moment mother Represented as; ; For burst monitoring streams, the actual service obtained is the total service process. Therefore, if the current network node is a wireless node, the service process obtained by the burst monitoring stream corresponds to the service process of the wireless link. Its moment generating function is as follows: If the current network node is a wired node, the service process obtained from the burst monitoring flow corresponds to the service process of the wired link. Its moment generating function is as follows: ; Construct a model for the remaining service process, including: For periodic control flows, affected by high-priority burst monitoring flows, let the high-priority burst monitoring flows be within a time interval. The cumulative arrivals within are Then the remaining service process of the periodic control flow Represented as: ,in, Indicates the network node in the time interval The total cumulative service volume that can be provided within; Remaining service process The generating function of the moment mother The upper bound is estimated based on Boole's inequality and the independence of the MGF, and is expressed as: ,in, Represents total cumulative service volume The generating function of the moment, Cumulative arrivals The generating function of the moment; For aperiodic state flows, which are influenced by both burst monitoring flows and periodic control flows, let's assume the medium-priority periodic control flow occurs within a time interval. The cumulative arrivals within are The remaining service process of the aperiodic state flow Represented as: ， Remaining service process The generating function of the moment mother The estimate is: , Cumulative arrivals The moment generating function.

5. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 4, characterized in that, The upper bound of the probabilistic latency of service flows in the 5G domain is calculated based on the aforementioned random arrival process model and random service process model, including: For any Time-delay random variable Exceeding a given threshold value probability Satisfy the following upper bound: ； in, This indicates that the expression within the curly braces is... Within the range, take the exact boundary. It is the first The moment generator function for the random arrival process of a business flow. It is the first The matrix generating function of the remaining service process actually obtained by each business flow; Substitute the corresponding moment generating function into the Chernoff bound formula, and then... Optimize to obtain the first The upper bound of probabilistic latency for individual service flows in the 5G domain , is represented as: ， in For the first The threshold for the probability of delay default for each business flow.

6. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 5, characterized in that, The step of extracting statistical feature parameters from the service flow and mapping these parameters to a deterministic arrival curve in the TSN domain based on the SPI-DCM cross-domain parameter mapping mechanism includes: Statistical characteristic parameters extracted from the business flow include: average arrival rate. Variance of the arrival process Delay default probability threshold Priority and periodic perturbation function , Design the SPI-DCM mapping function: ， in, This represents the SPI-DCM mapping function. Indicates time, A rate adjustment factor based on business type. It is the adjustment coefficient of the disturbance correction term. , It is the basic adjustment coefficient. The priority weighting coefficient, It is a business type adjustment coefficient; The statistical characteristic parameters are mapped to a deterministic arrival curve in the TSN domain based on the SPI-DCM mapping function, as follows: ； ， in, For the first Deterministic arrival curves for individual service flows entering the TSN domain. For the first Equivalent cumulative arrival volume of each business flow For the first The maximum burst volume of each business flow is determined by the mapping function. The intercept at that time can be determined by fitting.

7. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 6, characterized in that, The method for constructing end-to-end service curves for TSN domain nodes based on deterministic network calculus theory includes: TSN domain nodes employ time-aware shapers, and their baseline service curves... A slope is the link rate A linear function, expressed as: ; Introducing elastic service curves : ； in, Due to inherent scheduling delay, It is the link service rate of the TSN domain node. This indicates the initial attenuation of service capacity within the deterministic domain. Indicates the recovery rate of service capabilities within the deterministic domain; Constructing the Remaining Service Curve Represented as: ， in, This indicates that all priorities higher than the current one are... A collection of business flows for each business flow. () is a high-priority business flow The deterministic arrival curve Indicates taking a non-negative value; End-to-end service curve of service flow transmitted along the path within the TSN domain It is the minimum convolution of the remaining service curves of all nodes on the path.

8. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 7, characterized in that, Based on the deterministic arrival curve and the end-to-end service curve, the upper bound of the deterministic latency of the service flow in the TSN domain is calculated, including: upper bound of deterministic latency of service flows in the TSN domain It is a deterministic arrival curve End-to-end service curve The maximum horizontal distance between them.

9. The end-to-end latency modeling method for TSN-5G cross-domain converged network according to claim 8, characterized in that, Based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of cross-domain links, and the deterministic latency upper bound of the TSN domain, the theoretical upper bound of the end-to-end latency of the service flow is obtained, expressed as: ， in, This is the theoretical upper bound for the end-to-end latency of the service flow. This refers to the fixed transmission delay for cross-domain links.

10. An end-to-end latency modeling system for a TSN-5G cross-domain converged network, characterized in that, The system for implementing the end-to-end latency modeling method for the TSN-5G cross-domain converged network as described in claim 1 includes: The converged network construction module is used to construct a TSN-5G cross-domain converged network and to formally describe and classify the service flows in the TSN-5G cross-domain converged network. The probability delay calculation module is used to construct a random arrival process model and a random service process model of service flows in the 5G domain based on the random network calculus theory, and to calculate the upper bound of the probability delay of service flows in the 5G domain based on the random arrival process model and the random service process model. The mapping module is used to extract statistical feature parameters of the business flow and, based on the SPI-DCM cross-domain parameter mapping mechanism, map the statistical feature parameters to the deterministic arrival curve of the TSN domain. The deterministic delay calculation module is used to construct end-to-end service curves for TSN domain nodes based on deterministic network calculus theory, and to calculate the upper bound of the deterministic delay of the service flow in the TSN domain based on the deterministic arrival curves and end-to-end service curves. The end-to-end latency calculation module is used to obtain the theoretical upper bound of the end-to-end latency of the service flow based on the probabilistic latency upper bound of the 5G domain, the fixed transmission latency of the cross-domain link, and the deterministic latency upper bound of the TSN domain.

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