LEO-SN multi-hop multi-service end-to-end time delay analysis method based on yoke theory

Abstract

The invention discloses an LEO-SN multi-hop multi-service end-to-end time delay analysis method based on a yoke theory. According to the method, firstly, a transmission model based on inter-satellite link (ISL) utility is established by utilizing predictability of the LEO-SN so as to represent transmission characteristics of the LEO-SN; secondly, representing a multi-hop relay link as an equivalent queuing model through the definition of minimum plus convolution and residual service; meanwhile, by combining a yoke theory and an SNC framework, a satellite internal information processing system is modeled as a receiving, calculating and transmitting subsystem, and the processing process of the service flow in the satellite nodes is analyzed. Under the condition of considering propagation time delay and resource competition, a multi-hop multi-service hyper-yoke end-to-end (E2E) backlog and time delay boundary analysis model under a priority scheduling strategy is provided. And finally, through comparison with simulation data, the effectiveness of the proposed analysis model is verified.

Description

Technical Field

[0001] The present invention relates to the technical field of communication networks, and in particular to a method for analyzing LEO-SN multi-hop multi-service end-to-end delay based on martingale theory. Background Art

[0002] With the gradual integration of terrestrial Internet, mobile communication networks and space network services, building a unified space-ground integrated information network has become a key goal of the 6G network. As the core technology of 6G, the space-ground integrated information network aims to achieve wide-area intelligent interconnection of all things and global ubiquitous seamless access, providing safe and reliable unlimited connection services for "people, machines and things" anytime and anywhere. Among them, Starlink, Iridium and other low earth orbit satellite networks (LEO-SN, Low Earth Orbit-Satellite Network) have become an ideal choice for providing high reliability, low latency, and large bandwidth communication services with their advantages of low transmission delay, low link loss, flexible launch and low overall manufacturing cost.

[0003] In typical application scenarios of 6G, extremely reliable communications require that system design must guarantee multiple service qualities (QoS) to ensure the timeliness and reliability of communications. LEO-SN has a wide coverage area and diverse service types, ranging from wide-area coverage and emergency communications to emerging businesses such as artificial intelligence and smart cities, which put forward requirements for low latency, high reliability, high energy efficiency and ultra-high density connections on the network. In this context, outdated or unreliable data may lead to catastrophic consequences, so it is crucial to ensure strict standards for network QoS. In addition, LEO-SN has high construction costs, limited on-board resources and is not scalable. Therefore, it is urgent to build a compact delay reliability analysis framework in the early stage of design to ensure the QoS performance of service transmission and meet the strict requirements of 6G networks for extremely reliable satellite communications.

[0004] With the large-scale and high-density development of LEO-SN, in order to meet the needs of highly differentiated service carrying and consistent service experience, satellite networks need to provide end-to-end (E2E) global consistency delay and reliability guarantee mechanisms and indicator systems to ensure service transmission and user experience. However, the time-varying topology, highly dynamic and resource-constrained satellite-based nodes, and network loads that change dynamically over time increase the irregularity and uncertainty of the network, making it difficult to guarantee the QoS of LEO-SN services and to establish a reliability indicator system.

[0005] In addition, LEO-SN also has problems such as long inter-satellite communication distance and large link propagation delay. For example, the link delay between low-orbit satellites is at the millisecond level, which is far higher than the node-to-node delay in the ground wired network, affecting the E2E delay performance guarantee. In the process of service transmission, there are problems such as the interweaving of multiple serially connected satellite nodes and interference between different service flows, which leads to the entanglement of multiple random processes in the delay analysis process, making it difficult to perform accurate and systematic disassembly analysis, which brings challenges to LEO-SN delay analysis.

[0006] Existing network delay analysis methods include queuing theory, effective bandwidth, stochastic network calculus (SNC) and martingale theory. Queuing theory analyzes the data backlog process of node buffers in specific scenarios through mathematical models, and is the basis of E2E delay performance analysis. However, queuing theory is difficult to express in closed form for arrival and service processes that obey general distributions or have time correlation. Effective bandwidth is derived from the large deviation theory and is used to study key statistical indicators such as delay violation probability, queue length probability distribution, and data buffer capacity overflow in queuing systems.

[0007] However, the effective bandwidth method is difficult to use for statistical analysis of service performance in actual multi-node networks, and the calculation results are loose. SNC describes the service arrival and node service in the network with upper envelope and lower envelope respectively, and calculates the network queuing delay and queue backlog expressions through minimum plus convolution operation and minimum plus algebraic theory, thereby obtaining network performance information. However, the queue performance boundary obtained by using SNC theory to analyze network queuing performance has been questioned as not tight enough.

[0008] Martingale theory is an emerging theory that has attracted much attention in QoS analysis and assurance. It combines queuing theory and SNC to provide an effective mathematical framework for quantifying system delay. However, satellite communications have inherent propagation delays due to long-distance transmission, and multi-hop transmission will lead to the accumulation of propagation delays, which in turn affects the transmission of delay-sensitive information. Therefore, it is necessary to establish a new compact LEO-SN delay analysis model to accurately evaluate and optimize delay performance. Summary of the invention

[0009] To solve the above problems, the present invention discloses a LEO-SN multi-hop multi-service E2E delay analysis model based on martingale theory to address the problems of highly dynamic topology structure, significant propagation delay and increasingly prominent resource competition in LEO-SN. By constructing a time-varying topology structure, the highly dynamic LEO-SN transmission characteristics are characterized, and on the basis of considering propagation delay and resource competition, the E2E backlog and delay process of multi-service relay transmission in multi-hop satellite networks is studied, providing a service-oriented delay reliability analysis framework.

[0010] The present invention proposes a LEO-SN multi-hop multi-service end-to-end delay analysis method based on martingale theory. The method steps are as follows:

[0011] (1) Using the predictability of LEO-SN, a transmission model based on ISL utility is established to characterize the transmission characteristics of LEO-SN.

[0012] (2) Through the definition of minimum sum convolution and residual service, the multi-hop relay link is characterized as an equivalent queuing model.

[0013] (3) Split the satellite’s internal information processing system into a receiving subsystem, a computing subsystem, and a transmission subsystem to analyze the service process within the satellite;

[0014] (4) Taking into account propagation delay and resource contention, a multi-hop multi-service super-martingale E2E backlog and delay boundary analysis model is proposed under the priority scheduling strategy.

[0015] As a further preferred embodiment, step (1) proposes a time-varying topology model based on a discrete graph in combination with the predictability of the satellite network. The model can describe the state of the satellite network topology at different times and simulate the dynamic evolution of the topology structure over time.

[0016] As a further preferred embodiment, step (1) comprehensively considers the dynamic changes of the signal-to-noise ratio and the transmission rate caused by the time-varying characteristics of the LEO-SN, establishes a transmission model based on the ISL utility, and characterizes the transmission characteristics of the LEO-SN.

[0017] As a further optimization, step (2) takes into account the problem that the service link transmits multiple services at the same time and the non-service link occupies part of the storage, computing and transmission resources of the aggregation node, which has a negative impact on the service quality of the service link. Combined with the minimum convolution method, the equivalent expansion of service link i service k in the multi-hop queuing system with H satellite nodes is derived

[0018]

[0019] in Represents the propagation delay caused by the H-hop relay transmission process.

[0020] As a further optimization, step (3) takes into account that future satellite networks need to realize inter-satellite networking and on-orbit computing, and deploys integrated on-board storage and computing exchange to reduce communication overhead and improve service quality. To this end, a receiving, computing, and transmission subsystem is established to analyze the service process of the business flow inside the satellite node.

[0021] As a further optimization, the influence of access delay, calculation delay and transmission delay is considered in step (3). Since the delay caused by the receiving subsystem is mainly reflected in the martingale parameter, the delay caused by the calculation subsystem and the transmission subsystem is firstly concerned. The arrival process of the calculation subsystem is A a (n), each successfully accessed data packet needs to go through the computing service, and its service curve is represented by S a (n). Assume that the calculated service time follows an exponential distribution and the average service time is 1 / μ com , the corresponding probability density function is Taking into account the time-varying characteristics of ISL, the transmission subsystem is modeled as the system transmission model based on ISL utility established in step 1, and its arrival process is represented by A b (n), the service process is S b (n).

[0022] Using the correlation property of minimum convolution, the departure process of the satellite internal information processing system is:

[0023]

[0024] Therefore, the equivalent service curve of the satellite internal information processing system is

[0025] As a further preferred embodiment, step (4) constructs the arrival martingale and service martingale of the multi-hop satellite relay queuing system according to the martingale definition, and analyzes the impact of each subsystem on the satellite E2E delay. Since the satellite internal information processing system includes a receiving subsystem, a computing subsystem, and a transmission subsystem, among which the computing subsystem and the transmission subsystem have different service capabilities, the subsystem with weaker service capabilities becomes the key to limiting the E2E delay. Therefore, the martingale parameters of the subsystem with weaker service capabilities are selected to represent the service capabilities of the satellite information processing system.

[0026] As a further preferred embodiment, the arrival process of service k in service link i in step (4) All services except service k in service link i The arrival process is The arrival process of non-service link j at node h is: The computing service process and transmission service process of node h are and The corresponding supermartingale is In a multi-hop relay system, the upper bound of the E2E backlog unreliability of service k on service link i is

[0027]

[0028] in

[0029]

[0030]

[0031] As a further preferred embodiment, the upper bound of the multi-hop E2E delay unreliability of service k in service link i under different priority scheduling strategies is derived in step 4 as follows:

[0032]

[0033] in Represents the propagation delay caused by the H-hop relay transmission process.

[0034] Beneficial effects of the present invention:

[0035] The present invention proposes a delay analysis method applicable to LEO-SN, which provides a service-oriented delay reliability analysis framework. Because the propagation delay and resource competition problems that cannot be ignored in the satellite network are comprehensively considered, and the satellite internal information processing system is modeled as a receiving subsystem, a computing subsystem, and a transmission subsystem, a comprehensive analysis of the delay of each part will be closer to the future satellite network transmission mode. By comparing with simulation data, the analysis method of the present invention considers the influencing factors more comprehensively, and the analysis results are more in line with network characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is the LEO-SN transmission model;

[0037] Figure 2 This is a spatiotemporal evolution diagram of a satellite network based on topological snapshots ((a) static topological subgraph sequence; (b) spatiotemporal evolution);

[0038] Figure 3 It is a two-hop satellite relay service;

[0039] Figure 4 It is an H-hop satellite relay service;

[0040] Figure 5 It is the satellite’s internal information processing system;

[0041] Figure 6 The fitting accuracy of the E2E delay default probability of the LEO-SN multi-hop multi-service E2E delay analysis model in the range of 10-4 to 100 is shown. DETAILED DESCRIPTION

[0042] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0043] The end-to-end delay analysis method of LEO satellite network multi-hop multi-service based on martingale theory in this embodiment specifically includes the following steps:

[0044] 1. System Model

[0045] This section presents the system model, makes necessary assumptions on the network model, service arrival characteristics, construction of satellite network time-varying topology, and I SL utility-based transmission services, and establishes a framework for subsequent theoretical analysis.

[0046] 1.1. Network Model

[0047] This paper mainly studies the E2E delay of multi-hop multi-service transmission in LEO-SN, such as Figure 1 As shown. After the heterogeneous service flows are uploaded to the source satellite node, they need to be transmitted through a series of serially connected LEO satellite relays to reach the destination satellite node. This multi-hop LEO relay transmission path is called an E2E link. This paper abstracts the satellite data reception, calculation and transmission process into a queuing model, in which the satellite's memory is regarded as a queue in the queuing system, and the processor and transmitter in the satellite are regarded as servers in the queuing system, and then analyzes the multi-hop transmission process of multiple services in LEO-SN under different priority scheduling strategies. In addition, different E2E links may be interspersed or converged at the same satellite node. As shown Figure 1 As shown in Figure 1, link 1 and link 2 converge at satellite node C. At this time, the transmission of link 2 services will occupy some storage, computing, and transmission resources of node C, which may have a negative impact on the service quality of link 1. Therefore, this paper divides E2E links into service links and non-service links. The services transmitted by non-service links are interference services for service links and will affect the E2E delay of service links.

[0048] 1.2. Business arrival model

[0049] Since LEO-SN provides ubiquitous access capabilities for various types of services that are widely distributed around the world, it has spawned many applications with different delay sensitivity levels, such as IoT data collection, 3D games, and real-time search and rescue systems. These services have differentiated QoS requirements for satellite communication reliability and latency. In order to meet the latency requirements of different services and analyze the resource competition between different E2E links on the same satellite, this paper proposes two service flow modeling methods: Through Traffic and Cross Traffic.

[0050] 1) Through Traffic: Through traffic is the service flow transmitted by the service link. Network services are divided into M levels according to the sensitivity of the service to the delay index. The higher the level, the higher the delay sensitivity. The transmission priority is also increased accordingly to ensure that the more delay-sensitive services can be given priority. Figure 1 The transmission model is shown. Assume that the arrival process of service k is a k (n),k∈{1,…,M}, the cumulative arrival process is According to the arrival characteristics of network traffic, it is assumed that the service arrival model follows the state space The Markov process modulates the switching process, and the state transfer matrix T k As shown below

[0051]

[0052] Among them, p k is the probability of changing from state 0 to state 1, q k is the probability of the 1 state transferring to the 0 state. k Represents the number of data packets arriving per time slot for service k in state 1.

[0053] 2) Cross Traffic: Cross traffic is the traffic flow transmitted by non-serving links, and is mainly used to describe the scenario where non-serving links interfere with serving links. Figure 1 As shown in the figure, assuming that link 1 is a service link, the service transmitted by link 2 is Cross Traffic, which competes with link 1 for the resources of satellite node C. In multi-hop E2E service transmission, cross traffic is used to describe different interference states, including the arrival of non-interference flow, the arrival of service k as an interference service, or the situation where a combination of multiple services are interference sources. The Markov process can effectively capture the randomness of the arrival and departure process of interference services. Therefore, Cross Traffic is modeled as a Markov process. By constructing the state space of Cross Traffic, the state transition matrix T of the interference service can be obtained. o According to the transfer matrix T oThe steady-state distribution and the corresponding packet arrival rate R k , the arrival rate of aggregated interference services under different interference conditions can be calculated

[0054] 1.3. Satellite network time-varying topology model

[0055] In order to effectively analyze the E2E delay of LEO-SN, it is first necessary to build a network topology model that can accurately reflect its dynamic characteristics. Although the satellites are spatially symmetrically distributed in the constellation, forming a seemingly regular network structure, in fact, due to the influence of orbital dynamics, the distance and azimuth between satellites will continue to change. In order to capture this dynamicity, this paper combines the predictability of the satellite network and proposes a time-varying topology model based on discrete graphs. This model can describe the state of the satellite network topology at different times and simulate the dynamic evolution of the topology structure over time.

[0056] In order to introduce the time dimension parameter into the virtual topology description of LEO-SN, this paper adopts the theory of space-time evolution graph. Figure 2 As shown in (a), LEO-SN is expressed as G = (S, E, T). Using the periodicity and predictability of LEO-SN, the orbital period of the satellite is T = [t 0 ,t K ] is divided into K+1 topological snapshots, denoted as T = {τ 1 ,...,τ k ,τ K},τ k =[t k-1 ,t k ]. S={S 1 ,S 2 ,…,,S N} represents the set of satellite nodes, and E represents the set of I SLs. In the spatiotemporal evolution diagram, if within time t, any two satellites If there is a path between them, the graph is connected, indicating that any two satellites can transmit data during this period. This graph can simulate the change process of satellite topology over a period of time. Figure 2 As shown in (b), the source satellite S 1 With the target satellite S 4 Can be found from arrive The reachable path (in red) indicates that data can be transmitted between the source satellite and the destination satellite during this time period.

[0057] However, if the ISL state in each snapshot is simply defined as binary "on" or "off", it is impossible to fully quantitatively analyze the link properties dynamically, which will lead to inaccurate delay analysis due to untimely link state updates. Therefore, when constructing satellite network topology, it is necessary to quantify the impact of link state on the network transmission process.

[0058] 1.4. Transmission model based on ISL utility

[0059] The time-varying characteristics of LEO-SN will cause dynamic changes in the signal-to-noise ratio and transmission rate. The above factors together determine the feasibility of data transmission. This paper comprehensively considers the above factors and establishes a transmission model based on ISL utility to characterize the transmission characteristics of LEO-SN. Assuming that the number of data packets served between adjacent satellites in time slot n is s(n), the time for data packets to receive service follows a negative value distribution, and the service time distribution is

[0060]

[0061] The average number of packets served per time slot is p su (n)C(n), where C(n) is the transmission rate between adjacent satellites; p su (n) is the probability of successful data packet transmission. The specific parameters are introduced as follows:

[0062] 1) SNR: When the signal-to-noise ratio of the receiving satellite is less than the receiving threshold, network transmission is easily interrupted and the transmission quality of ISL cannot be guaranteed. Since LEO-SN uses laser links for intersatellite communication, the SNR of the intersatellite laser link will be affected by free space propagation losses, including path loss and pointing error. When the signal at the transmitter is x and the signal at the receiver is y, Where P t is the transmit power, γ is the path loss exponent, and n is the variance. is the Gaussian white noise, and L is the distance between satellites. Obviously, the statistical characteristics of the intersatellite laser link are mainly reflected in the link loss factor h.

[0063] In a free space link, the loss of the laser ISL includes the geometric loss due to tracking error and the path loss due to long-distance transmission. e When the beam divergence half width is ω 0 The link loss factor h is

[0064]

[0065] Among them, the probability density function constrained by the loss factor h is

[0066]

[0067] At any time slot n, the SNR of the ISL between satellites is

[0068]

[0069] According to the distribution law of h, we can conclude that |h(n)| 2 It follows a non-central chi-square distribution (χ 2 ), whose probability density function is

[0070]

[0071] When the ISL signal-to-noise ratio is less than the threshold α, transmission interruption may occur during data transmission, and the probability of the interruption event is

[0072]

[0073] That is, the probability of successful data packet transmission is p su (n) = 1 - P (n).

[0074] 2) Transmission rate: The achievable data rate of ISL in time slot n is expressed as

[0075]

[0076] Among them G t and G r are the gains of the transmitting and receiving antennas respectively, k is the Boltzmann constant, U s Represents the noise temperature of the entire system; (E b / N 0 ) req Defined as the ratio of the received energy required per bit to the noise density, A represents the link margin; L fsl (n) is the free space loss of ISL, which is calculated by

[0077]

[0078] Where c is the speed of light, S r (n) represents the tilt range in time slot n, and f represents the communication center frequency of ISL. 2. E2E delay analysis of multi-hop satellite network

[0079] E2E delay is a key QoS indicator for evaluating the queuing performance of LEO-SN. In order to obtain an analytical solution for this indicator, this section will first briefly introduce the basic queuing model, focusing on the impact of propagation delay on the delay performance of LEO-SN. Then, by introducing the concept of residual service, the competition interference phenomenon caused by the occupation of service link resources by non-service links in multi-hop LEO-SN networks is discussed. In addition, in order to deeply analyze the service process of the service inside the satellite node, this paper models the internal information processing system of the satellite into three subsystems: reception, calculation, and transmission, and analyzes the delay generated by each subsystem. Finally, by constructing the arrival martingale and service martingale of the multi-hop satellite queuing system, the E2E delay of LEO-SN is quantitatively analyzed.

[0080] 2.1. Queuing model based on propagation delay

[0081] exist Figure 1 In the multi-hop LEO satellite transmission scenario, it is assumed that time is discrete and Represents the arrival and departure process of service flow k at satellite node h. In terrestrial communication systems, since the propagation speed of electromagnetic waves is close to the speed of light, the propagation delay is usually in the microsecond order, which has a relatively small impact on system performance and is often ignored in queuing theory models. Relatively speaking, the propagation delay in LEO-SN may reach the millisecond order due to the long ISL distance. Ignoring the impact of propagation delay may lead to inaccurate model analysis results, especially in real-time communication or delay-sensitive scenarios. Therefore, it is necessary to consider the propagation delay in satellite communication systems with multi-hop relay services. Assume that the propagation delay between satellites is T P , where T P =L / c, c is the speed of light. Due to the influence of propagation delay, the relationship between the departure process of the previous node and the arrival process of the next node is Service Process h (n) represents the data packet service process of the satellite, which is used to describe various network functions such as node scheduling, computing and transmission.

[0082] For the sake of brevity, the subscript of this process is omitted when analyzing queue performance. SNC uses non-negative, non-decreasing binary functions to model arrival, service, and departure processes, providing a unified network queue algebra for a wide range of arrival / scheduling / service categories. Based on the consideration of propagation delay, the departure process is related to the arrival process and the service process in the form of minimum convolution

[0083]

[0084] Assume that the random processes of arrival and service are independent of each other. The delay process represents the total delay of a data packet in the system after it is sent in time slot n, which is intuitively represented as the horizontal distance between curves A(n) and D(n). Combined with the definition of the departure process in (10), the bound of the delay is

[0085]

[0086] Combined with the LEO-SN time-varying topology model in Chapter 2, when there is a reachable path between the arrival process and the service process, the complementary distribution of W(n) can be obtained. By utilizing the associative properties of the minimum plus algebra in SNC theory, the single-hop queuing model can be extended to the multi-hop relay queuing system.

[0087] 2.2. Multi-hop satellite relay service system

[0088] This paper takes service k transmitted in service link i as an example to analyze the E2E delay of multi-hop satellite relay transmission of this service under the influence of propagation delay. Since the service link may transmit multiple service flows at the same time, it is necessary to consider the other services in service link i. Impact on service k. In addition, the LEO-SN topology is complex, and service flows on different links may converge at the same satellite node. At this time, the non-service link (blue) will occupy part of the storage, computing and transmission resources of the aggregation node, which will have a negative impact on the service quality of the service link (red). Figure 3 As shown in the figure, in a two-hop satellite relay system, for service link i, non-service link j will divide the resources of satellite node 1 and satellite node 2, resulting in an increase in the E2E delay of service k in service link i. Therefore, it is necessary to analyze the resource competition problem caused by the non-service link occupying the service link resources.

[0089] When H = 2, according to the departure process (10), the service curve S 1 (n) is related to the arrival process and the departure process as follows:

[0090]

[0091] D 1 (τ 2 ) can be decomposed into service k transmitted by service link i, and all services except service k transmitted by service link i And the three-part departure process of the service transmitted by non-service link j

[0092]

[0093] By moving the departure process except for the service k transmitted by service link i to the right side of the equation, we can get

[0094]

[0095] because (14) can be rewritten as follows

[0096]

[0097] Rearranging the right side of the equation gives

[0098]

[0099] where [x] + It is expressed as the maximum value between 0 and x. Introducing the concept of residual service capacity, the residual service capacity of satellite node 1 for service link i is defined as

[0100]

[0101] Combining (16) and (17), we can get:

[0102]

[0103] For satellite node 2, its service curve S 2 (n) is related to the arrival process and the departure process as follows:

[0104]

[0105] Accordingly, Split into three parts

[0106]

[0107] The leaving process of service k in service link i can be expressed as

[0108]

[0109] Because of the relationship (21) can be expressed as

[0110]

[0111] Similarly, the remaining services of satellite node 2 serving link i service k are defined similarly:

[0112]

[0113] Due to the influence of propagation delay between satellite nodes, there is therefore,

[0114]

[0115] By observation, we can find that the service curve is stationary, so the above inequality can be further derived as

[0116]

[0117] From (25), we can see that for service k in service link i, the two-hop LEO satellite relay system can be represented by a single equivalent system It is expressed in the form of minimum plus convolution. Therefore, in Figure 4 In the multi-hop queuing system with H satellite nodes shown in the figure, the service curve of service k of service link i can be equivalently expanded using the minimum convolution form as

[0118]

[0119] in Represents the propagation delay generated by the H-hop relay transmission process. In the above way, the service process of the service link for the arriving service flow in the LEO-SN multi-hop relay system can be represented as a simple equivalent queuing model.

[0120] 2.3. Satellite internal information processing system

[0121] The existing LEO-SN uses a bent-pipe transmission method to forward user data to the ground cloud center, but the communication overhead is large and the latency is high, making it difficult to support latency-sensitive services. Therefore, future satellite networks need to realize inter-satellite networking and on-orbit computing, and deploy integrated onboard storage and computing to reduce communication overhead and improve service quality. To this end, this paper establishes the receiving, computing, and transmission subsystems to analyze the service process of the business flow inside the satellite node, such as Figure 5 As shown in the figure. The receiving subsystem first identifies and processes data packets of different priorities to ensure that mission-critical data can be processed in a timely manner, while efficiently managing services of different priorities under limited resources. The computing subsystem processes and analyzes data packets in real time, quantifying the delay caused by the satellite processing data packets under limited computing resources and energy supply. The transmission subsystem models the delay caused by the transmission of calculation results between satellite nodes, and needs to consider issues such as signal attenuation and the establishment of inter-satellite links.

[0122] Since the delay caused by the receiving subsystem is mainly reflected in the martingale parameter, we first focus on the delay caused by the computing subsystem and the transmission subsystem. The arrival process of the computing subsystem is A a (n), each successfully accessed data packet needs to go through the computing service, and its service curve is represented by S a (n). Assume that the calculated service time follows an exponential distribution and the average service time is 1 / μ com , the corresponding probability density function is Taking into account the time-varying characteristics of ISL, the transmission subsystem is modeled as the system transmission model based on ISL utility established in the system model in Chapter 2, that is, (2), and its arrival process is expressed as A b (n), the service process is S b (n).

[0123] Using the correlation property of minimum plus convolution, Figure 5 The departure process of the satellite internal information processing system is as follows:

[0124]

[0125] Therefore, the equivalent service curve of the satellite internal information processing system is Right now Figure 3 The service curve S inside satellite node 1 and node 2 1 (n) and S 2 (n) Solve by (27).

[0126] 2.4. Delay analysis of multi-hop relay system based on Martingale

[0127] Martingale theory can transform different random processes into the same martingale process through a reasonable martingale construction method, thereby introducing the martingale analysis method into the analysis of multi-hop multi-service arrival queue systems. In a multi-arrival queue system, by exploring the construction of the martingale process and modeling and analyzing the queue's cache behavior in the martingale domain, it is possible to avoid the calculation of complex probability distribution superposition. This section will construct the arrival martingale and service martingale of a multi-hop satellite relay queue system based on the martingale definition, and analyze the impact of each subsystem on the satellite E2E delay.

[0128] Definition 1 (supermartingale): A random process X(n) is a continuous-time supermartingale that satisfies

[0129]

[0130] According to the definition of upper martingale, the arrival martingale envelope and service martingale envelope of M types of business flows can be constructed.

[0131] Definition 2 (Martingale on Arrival Process): If there is an exponential decay factor θ, θ>0, the martingale parameter K A (θ) and the monotonically increasing function h related to {a(n), n≥0} A (a(n)), then the arrival supermartingale of the arrival process {a(n),n≥0} is

[0132]

[0133] According to the Perron-Frobenius theorem, the element T in the state transfer matrix T of the Markov modulation process X(n) i,jPerform exponential transformation The matrix T θ , T θ The spectral radius is h A is the corresponding right eigenvector, that is, both satisfy T θ h A =ρ(T θ )h A . Arriving at the martingale parameter h A (x(n)) is h A The x(n)th element of A (θ) The selection range is K A (θ)≥lnρ(T θ ) / θ. Definition 3 (Martingale on the service process): If there is an exponential decay factor θ, θ>0, the martingale parameter K S (θ) and the monotonically increasing function h related to {s(n), n≥0} S (s(n)), then the service supermartingale of the service process {s(n),n≥0} is

[0134]

[0135] Among them, the martingale parameter K S The value range of (θ) is For independent and identically distributed service processes, h S (s(n)) is defined as a constant. Since the satellite internal information processing system includes the receiving subsystem, computing subsystem and transmission subsystem, the computing subsystem and the transmission subsystem have different service capabilities, and the subsystem with weaker service capabilities becomes the key to limiting the E2E delay. Therefore, this paper selects the martingale parameter of the subsystem with weaker service capabilities to represent the service capability of the satellite information processing system.

[0136] Theorem 1 (Upper bound of multi-hop E2E backlog unreliability): Assume that the arrival process of service k in service link i is All services except service k in service link i The arrival process is The arrival process of non-service link j at node h is: The computing service process and transmission service process of node h are and The corresponding supermartingale is In a multi-hop relay system, the upper bound of the E2E backlog unreliability of service k on service link i is

[0137] in

[0138]

[0139] Theorem 2 (Upper bound of multi-hop E2E delay unreliability): The upper bound of multi-hop E2E delay unreliability of service link i service k under different priority scheduling strategies is

[0140]

[0141] represents the propagation delay generated by the H-hop relay transmission process. The specific proof process is shown in the Appendix. From Theorem 1 and Theorem 2, it can be seen that the upper bound of the E2E delay of the multi-hop system under different priority scheduling methods is affected by the service capacity of the H server and other business traffic.

[0142] 3. Simulation analysis

[0143] This section analyzes and evaluates the effectiveness of the proposed LEO-SN multi-hop multi-service E2E delay analysis model. First, a low-orbit satellite network simulation environment is established using the Satellite Tool Kit (STK), and then the corresponding theoretical formulas and simulation programs are written using MATLAB software.

[0144] 3.1. Simulation Configuration

[0145] This paper uses a 6×11 Iridium constellation to verify the effectiveness of the proposed LEO-SN multi-hop multi-service E2E delay analysis model in sending services from Beijing to London. First, the Satellite ToolKit (STK) is used to create a geometric scenario of the satellite network, which includes establishing a satellite constellation, adding intersatellite links, and performing orbit analysis to provide the necessary physical parameters. Subsequently, theoretical formulas and simulation programs are written in MATLAB for verification. The LEO-SN service level M is set to 2, and the services are divided into delay-tolerant services (DTS) and delay-sensitive services (DSS). Table 1 details the specific satellite-related parameters used in the simulation, and the service-related parameters are listed in Table 2.

[0146] Table 1 Satellite parameter settings

[0147]

[0148]

[0149] Table 2 Service parameter settings

[0150] parameter Value Time slot size 5ms Number of service levels M 2 <![CDATA[State transition probability p from state 0 to state 1 for delay-sensitive services s > 0.1 <![CDATA[State transition probability q from state 1 to state 0 for latency-sensitive services s > 0.9 <![CDATA[Arrival rate R of latency-sensitive services s > 16 packets / time slot <![CDATA[State transition probability p from state 0 to state 1 of delay-tolerant service t > 0.2 <![CDATA[State transition probability q from delay-tolerant service state 1 to state 0 t > 0.6 <![CDATA[The arrival rate R of delay-tolerant services t > 7 packets / time slot <![CDATA[Calculating the average service time of the subsystem 1 / μ com > 0.2ms

[0151] 3.2. Simulation analysis

[0152] Figure 6 The LEO-SN multi-hop multi-service E2E delay analysis model is shown in 10 -4 to 10 0The fitting accuracy of E2E delay default probability within the range. By comparing the simulation and analysis results, it is found that the E2E delay default probability analysis results of DTS and DSS are very close to the simulation results and have the same decay rate, which verifies the accuracy of the analysis model.

[0153] 4. Appendix

[0154] The probability that the end-to-end delay of traffic is greater than ω is

[0155]

[0156] Taking traffic k in service link i as an example, the E2E delay distribution is

[0157]

[0158] According to the equivalent service curve (26) of the H-hop network under the influence of propagation delay, substituting it into (36) we can get

[0159]

[0160] in Represents the propagation delay caused by the H-hop relay transmission process.

[0161] when When , combined with the definition of remaining service capacity (17)(23), we can get

[0162]

[0163] Since the satellite internal information processing system consists of access, computing and transmission subsystems, combined with (27), there is

[0164]

[0165] For the convenience of calculation, it is assumed that the service curves of the H-hop computing subsystem and the transmission subsystem are independent and identically distributed, then x∈{a,b}, since the subsystem with weak service capability in the satellite internal information processing system is the key to limiting the delay reliability, the parameter θ is defined * ,θ * >0, and

[0166]

[0167] (39) can be further transformed into

[0168]

[0169] because

[0170]

[0171] From (41)(42) we can conclude that

[0172]

[0173] From the definition of the upper martingale, combined with the above formula, we can consider the martingale and H-jump service martingale h=1,…H

[0174]

[0175] According to (43), the upper martingale is multiplied in the time domain. Can get

[0176]

[0177] In this scenario, the backlog process can be expressed as

[0178]

[0179] Define the stop time N as the time when the backlog process first exceeds the threshold σ

[0180]

[0181] According to the definition of the backlog process, we can get P(B(n)≥σ)=P(N<∞). Since the stopping time N is unbounded, {N→∞} may occur. We need to define a new stopping time N^T:=min{N,T}. ω (n) Using the stopping time theorem, we can get the above formula (50)

[0182]

[0183] in

[0184]

[0185] Therefore, based on (51), the distribution function of the backlog can be obtained as

[0186]

[0187] According to (36)(43), the upper bound of the end-to-end delay of service k in service link i is

[0188] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above technical features.

Claims

1. A LEO-SN multi-hop multi-service end-to-end delay analysis method based on the martingale theory is characterized by: The specific steps include: Step (1) In order to address the high dynamic characteristics of LEO-SN and realize the quantitative dynamic analysis of ISL properties, a transmission model based on ISL utility is proposed; Step (2) characterizes the multi-hop relay link as an equivalent queuing model through the definition of minimum plus convolution and residual service; Step (3) splitting the satellite internal information processing system into a receiving subsystem, a computing subsystem and a transmission subsystem to analyze the service process of the business inside the satellite; Step (4) considers propagation delay and resource contention, and uses the martingale theory and SNC framework to derive the boundary expressions of network backlog and delay.

2. The method for analyzing the end-to-end delay of LEO-SN multi-hop multi-service based on the martingale theory according to claim 1, characterized in that: The step (1) specifically includes the following: Step 11: Use the space-time evolution graph theory to express LEO-SN as G = (S, E, T). Using the periodicity and predictability of LEO-SN, the orbital period of the satellite is T = [t0, t K ] is divided into k+1 topological snapshots, denoted as T = {τ1,…,τ k ,…τ K },τ k =[t k-1 ,t k ]; S = {S1, S2, ..., S N } represents the satellite node set, E represents the ISLs set; in the spatiotemporal evolution diagram, if within time t, any two satellites If there is a path between them, the graph is connected, indicating that any two satellites can transmit data during this period; the graph can simulate the change process of satellite topology structure over a period of time; Step 12: Establish a transmission model based on ISL utility to characterize the transmission characteristics of LEO-SN; define the number of data packets served between adjacent satellites in time slot n as s(n), the time for data packets to receive service follows a negative value distribution, and the service time distribution is The average number of packets served per time slot is p su (n)C(n), where C(n) is the transmission rate between adjacent satellites; p su (n) is the probability of successful data packet transmission.

3. The method for analyzing the end-to-end delay of LEO-SN multi-hop multi-service based on the martingale theory according to claim 2, characterized in that: The specific parameters of step 12 are as follows: SNR: When the signal-to-noise ratio of the receiving satellite is less than the receiving threshold, the network transmission is easily interrupted and the transmission quality of the ISL cannot be guaranteed; when the ISL signal-to-noise ratio is less than the threshold α, transmission interruption may occur during data transmission; when the tracking error angle is θ e When , for a Gaussian beam with a beam divergence half-width of ω0, the probability of an interruption event is That is, the probability of successful data packet transmission is p su (n) = 1-P(n); where P t is the transmit power, γ is the path loss exponent, and n is the variance. Gaussian white noise, L is the distance between satellites; Transmission rate: The achievable data rate of an ISL in time slot n is expressed as Among them G t and G r are the gains of the transmitting and receiving antennas respectively, k is the Boltzmann constant, U s Represents the noise temperature of the entire system; (E b / N0) req Defined as the ratio of the received energy required per bit to the noise density, A represents the link margin; L fsl (n) is the free space loss of ISL.

4. The method for analyzing the end-to-end delay of LEO-SN multi-hop multi-service based on the martingale theory according to claim 1, characterized in that: According to the definition of minimum convolution and residual service, step (2) deduces that in a multi-hop queuing system with H hop satellite nodes, the service curve of service link i service k can be equivalently expanded to: in Represents the propagation delay generated by the H-hop relay transmission process; through the above method, the service process of the service link for the arriving service flow in the LEO-SN multi-hop relay system is represented as a simple equivalent queuing model.

5. The method for analyzing the end-to-end delay of LEO-SN multi-hop multi-service based on the martingale theory according to claim 1, characterized in that: The step (3) models the satellite internal information processing system into receiving, computing and transmitting subsystems to analyze the service process of the business flow inside the satellite node; The delay caused by the receiving subsystem is mainly reflected in the martingale parameter; the arrival process of the computing subsystem is A a (n), each successfully accessed data packet needs to go through the computing service, and its service curve is represented by S a (n); Assume that the calculated service time follows an exponential distribution and the average service time is 1 / μ com , the corresponding probability density function is The transmission subsystem is modeled as a system transmission model based on ISL utility, and its arrival process is represented by A b (n), the service process is S b (n); Using the correlation property of minimum convolution, the departure process of the satellite internal information processing system is: Therefore, the equivalent service curve of the satellite internal information processing system is 6. The method for analyzing the end-to-end delay of LEO-SN multi-hop multi-service based on the martingale theory according to claim 1, characterized in that: The step (4) specifically includes the following: Step 41: construct the arrival martingale and service martingale of the multi-hop satellite relay queuing system according to the martingale definition, analyze the impact of each subsystem on the satellite E2E delay, and select the martingale parameters of the subsystem with weaker service capability to represent the service capability of the satellite information processing system; Step 42: Assume the arrival process of service k in service link i All services except service k in service link i The arrival process is The arrival process of non-service link j at node h is: The computing service process and transmission service process of node h are and The corresponding supermartingale is In a multi-hop relay system, the upper bound of the E2E backlog unreliability of service k on service link i is in The upper bound of the multi-hop E2E delay unreliability of service link i service k under different priority scheduling strategies is: represents the propagation delay generated by the H-hop relay transmission process. From the results, it can be seen that the upper bound of the E2E delay of the multi-hop system under different priority scheduling methods is affected by the service capacity of the H server and other business traffic.

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