A martingale-based end-to-end delay analysis method for multi-mode cognitive networks

Abstract

The application discloses a kind of based on martingale theory's multi-mode perception network end-to-end delay analysis method, belongs to communication network technical field;Including the following steps: constructing the overall network topology of multi-mode perception model, define end-to-end delay calculation formula;Arriving flow is divided into different service flow, the state transition matrix of service flow is initialized;Obtain arriving martingale model;Interlink interference analysis is carried out, and the interference cumulative quantity of node service is obtained;Service process analysis is carried out, and the probability distribution of service process is obtained;Obtain the end-to-end time violation probability under stable condition.The application is mapped to martingale domain by martingale theory and is analyzed to time-domain arriving flow, time-domain service flow, respectively selects three traffic characteristics service flow as arriving flow, fully considers the influence of priority scheduling strategy on end-to-end delay;Make the analysis framework constructed have compact delay, improve the reliable line of analysis result simultaneously, optimize network deployment and resource scheduling.

Description

Technical Field

[0001] This invention belongs to the field of communication network technology, specifically relating to an end-to-end delay analysis method for multimode sensing networks based on martingale theory. Background Technology

[0002] In recent years, the development of the Internet of Things (IoT) has propelled networks towards an era of ubiquitous connectivity. Terminals of various standards access networks to transmit information and interact with protocols on demand, building specific intelligent services between these devices. However, existing networks struggle to handle the complex environments in which these terminals operate. End-to-end service flow transmission involves multiple interconnected network nodes. In complex multi-mode sensing networks, multiple network links are intertwined, and the service capability of each node is affected by factors such as overall network routing and transmission modes, thus interfering with the latency analysis of each end-to-end link. Furthermore, end-to-end latency is influenced by uncertainties such as service traffic characteristics, priority scheduling strategies, and the scale and queue status of network nodes, leading to multiple intertwined stochastic processes in mathematical modeling, making precise decomposition and analysis difficult.

[0003] Serial queuing theory is the traditional mathematical foundation for analyzing end-to-end delay. However, the novel traffic characteristics in multimode sensing networks and the selection and scheduling mechanisms for multimode transmission lines complicate the analysis process, making it difficult to obtain the accurate probability distribution of end-to-end delay. The statistical properties of the upper boundary of end-to-end delay can offer a new perspective, and SNC theory can analyze this effectively. However, the use of joint bound inequalities in SNC-based end-to-end delay performance analysis can induce a time-violation boundary with significant errors.

[0004] The statistical characteristics of the upper boundary of end-to-end latency can serve as a new perspective, and SNC theory can analyze this effectively. However, the use of joint bound inequalities in SNC-based end-to-end latency performance analysis can induce a latency boundary with significant errors. To achieve a reasonable assessment of service latency requirements, different service traffic models need to be established for different service characteristics, which is a challenge in end-to-end latency analysis. QoS guarantee theory is used for spectrum resource allocation based on reliability and latency (based on power control) to maximize system throughput. Packet arrival and service characteristics are analyzed based on latency QoS, but the latency boundary is relatively loose for bursty, low-volume services. This leads to resource waste during network resource allocation, and low-volume services are common in multi-mode sensing networks.

[0005] Existing research shows that traditional latency calculation methods are insufficient for analyzing end-to-end transmission latency of various traffic characteristics in modern services, and they suffer from loose latency boundaries. Martingale theory-based latency analysis abstracts the complex queuing and interference processes and provides tighter latency boundaries. However, current martingale frameworks do not adequately meet the needs of multi-mode sensing networks. First, the routing and retransmission strategies for data packet transmission and reception in multi-mode networks differ from those in traditional networks. Second, arrival flow analysis and construction are required for sensing services with different traffic characteristics in IoT environments. Furthermore, current applications of martingale theory in end-to-end latency analysis consider a single link and do not account for cross-interference between data flows across different links in the overall network, which is inconsistent with reality.

[0006] Therefore, how to solve the problem of cross-interference between data streams on different links in the overall network, thereby optimizing network deployment and resource scheduling, is the technical problem that this invention aims to solve. Summary of the Invention

[0007] The purpose of this invention is to provide an end-to-end delay analysis method for multimodal sensing networks based on martingale theory, so as to solve the problems mentioned in the background art.

[0008] The objective of this invention is achieved as follows: A method for end-to-end delay analysis of multimodal sensing networks based on martingale theory, characterized by the following steps:

[0009] Step S1: Construct the overall network topology of the multimodal sensing model and define the end-to-end latency calculation formula;

[0010] Constructing the overall network topology of the multimodal perception model, and a... Time Link Model; derived using SNC theory, combined with cumulative arrival flow and service flow, to obtain the overall departure process. This allows us to obtain the end-to-end latency of the business flow. ;

[0011] Step S2: For arrival flows with different characteristics, divide the arrival flows into different service flows; based on the state transition probability, arrival rate, and active / idle probability of different service flows, initialize the state transition matrix of the service flows, and perform an exponential column transformation on the state transition matrix of the service flows.

[0012] The arrival flow is divided into three different service flows, including mixed interleaved service flow, emergency data service flow, and highly synchronized service flow;

[0013] Step S3: Construct martingales for the arrival process of different business flows according to the definition of martingale to obtain the arrival martingale model;

[0014] Step S4: For the three different intersection scenarios of service flows, perform inter-link interference analysis to obtain the cumulative amount of interference experienced by the node serving different service flows;

[0015] Step S5: Based on the state of different nodes, perform service process analysis to obtain the probability distribution of the service process;

[0016] Step S6: Obtain the end-to-end time violation probability under steady-state conditions. .

[0017] Preferably, the overall network topology of the multimodal sensing model adopts... It means that among them Represents a node in a network. Indicates in The communication link at any given moment;

[0018] include EN, There are one RN and one MN, where EN represents the end sensing node, RN represents the routing aggregation node, and MN represents the central master control node;

[0019] ;

[0020] in, Indicates in time and The communication link between them , This indicates a power line carrier communication link. Indicates the radio frequency link; Shown time and Between A pattern communication link exists, and vice versa.

[0021] Preferably, in step S1, the overall departure process is obtained by deriving the SNC theory and combining the cumulative arrival flow and service flow. This allows us to obtain the end-to-end latency of the business flow. The specific steps are as follows:

[0022] Will reach the flow The last hop in the E2E link The cumulative departure process is regarded as the departure process of the entire link, and is represented as:

[0023] ;

[0024] in, express From time slot Time slot The cumulative number of data packets received;

[0025] express From time slot Time slot The cumulative number of data packets served;

[0026] express From time slot Time slot The total number of packets that have left the network;

[0027] End-to-end latency of the business flow Represented as:

[0028] .

[0029] Preferably, the initialization of the state transition matrix of the service flow in step S2 is performed as follows:

[0030] Step S2-1: Solve for the state transition torques of the mixed interleaved service flow and the emergency data service flow, and model the highly synchronized service flow using the Beta / M / 1 model;

[0031] The specific steps for calculating the state transition torques of the mixed interleaved service flow and the emergency data service flow are as follows:

[0032] The hybrid interleaved service flow refers to the data service flows with different characteristics at different stages in the multimodal awareness model, which alternately arrive at the routing aggregation node; the multimodal awareness model is represented as a Markov chain as follows: ;

[0033] in, describe Service arrival status of time-slot data streams; }describe Status of time-slot services; express Time slot services Has a data packet arrived?

[0034] The state space representation of the hybrid interleaved service flow Markov chain is as follows:

[0035] ;

[0036] in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is ;

[0037] The formula used for the emergency data service flow It means that, among them, Indicates in Time slot arrives at service link Emergency data services The number of data packets; the emergency data service flow refers to the service information flow reported in the multi-modal perception model for sudden states, indicating equipment failure or emergency events. The emergency data service flow is usually in an idle state, but once an emergency event occurs, it arrives in batches and must be processed with priority.

[0038] The multimodal sensing model is represented as a two-dimensional Markov chain, as follows: , , Indicates being in The status of time-slot emergency data services Indicates being in The arrival status of time-slot data packets, if ,but If probability 1 holds true, the state transition matrix of the emergency data service flow is represented as follows:

[0039] ;

[0040] in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. This represents the probability of data packet arrival.

[0041] The Beta / M / 1 model is used to model highly synchronous service flows. The specific steps are as follows:

[0042] The highly synchronous service flow refers to a large number of MTC devices in the multi-mode sensing network accessing the network in a highly concurrent manner, with signaling flow having the highest priority; it is modeled using the Beta / M / 1 model, and the analytical expression of the Beta distribution MGF is:

[0043] ;

[0044] in, To represent the ascending factorial, if If it is an integer, then ; The parameter is The first kind of confluence hypergeometry function;

[0045] Step S2-2: Based on the state transition torque of the hybrid interleaved service flow and the state transition torque of emergency data service flows Perform exponential transformation.

[0046] Preferably, in step S2-2, the state transition torque based on the hybrid interleaved service flow... and the state transition torque of emergency data service flows To perform exponential column transformation, the specific steps are as follows:

[0047] The state space matrix of the hybrid interleaved service flow Performing the corresponding exponential transformation yields:

[0048] ;

[0049] in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is ;

[0050] The state transition torque of the emergency data service flow Performing the corresponding exponential transformation yields:

[0051] ;

[0052] in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. The probability of data packet arrival. For the number of arrivals.

[0053] Preferably, in step S3, martingales are constructed for the arrival process of different service flows according to the definition of martingales to obtain arrival martingale models. The specific operation is as follows:

[0054] Step S3-1: Convert the state transition of the mixed interleaved service flow into a matrix. After performing the corresponding exponential transformation, we get State transition matrix for emergency data service flows After performing the corresponding exponential transformation, we get ,right , Calculate the corresponding spectral radius , ;

[0055] Step S3-2: Determine the function for the hybrid interleaved traffic flow to reach the martingale. , And the function for emergency data service flows to reach the martingale. ,parameter ;

[0056] Step S3-3: When satisfy ;

[0057] ;

[0058] satisfy ;

[0059] ;

[0060] Then, the martingale arrival process of the mixed and intertwined business flow is represented as:

[0061] ;

[0062] in, for The One element; for The One element; For martingale parameters, For mixed and intertwined business flows Time slot to Cumulative arrivals of time-slot data packets;

[0063] The martingale arrival process of an emergency data service flow is represented as follows:

[0064] ;

[0065] in, for The One element; for The One element; For martingale parameters, For emergency data service flow Time slot to Cumulative arrivals of time-slot data packets;

[0066] Step S3-4: For high-concurrency service flows occurring during the network setup phase The corresponding Wald martingale is constructed using its moment generating function. The martingale arrival process of highly synchronized business flows is represented as follows:

[0067] ;

[0068] in, The analytical expression of the Beta distribution MGF For highly synchronized services Time slot to Cumulative arrivals of time-slot data packets.

[0069] Preferably, in step S4, inter-link interference analysis is performed for the three different convergence scenarios of service flows to obtain the cumulative interference experienced by the node serving different service flows. The specific operation is as follows:

[0070] Step S4-1: For non-service links and service links that appear... Analyze three possible intersection scenarios;

[0071] Representation and service link At the node They meet, but their next hop nodes are different. This will affect the service chain. It causes interference;

[0072] Representing business flow and service links At the node Convergence, and the next hop is also a node. , This will affect the service chain. It causes interference;

[0073] Represents a node This is the last hop in the current business flow. No service is required for this business flow. No impact on service links It causes interference;

[0074] Step S4-2: Obtain the node pairs of the three different service flows in the non-service link and the service link. Interference;

[0075] The interference of the hybrid interleaved service flow is represented as follows:

[0076] ;

[0077] Among them, for those from Mixed and intertwined business flows, recorded from of Type of business flow at node The probability of being processed is denoted as ; This represents data packets for mixed interleaved service flows, emergency data service flows, and highly synchronized service flows. express middle The percentage of the three types of data packets in the cumulative number of nodes leaving; express Cumulative arrivals at nodes; express Middle node Does the next jump occur? Inside, if This indicates that business flows have converged, otherwise they have not. Indicates at node All of the convergence , A collection of type links;

[0078] Disruptions to emergency service flows are represented as follows:

[0079]

[0080] Among them, for those from Emergency data service flow, recorded from of Type of business flow at node The probability of being processed is denoted as ;

[0081] The interference of the highly synchronized service flow is represented as

[0082]

[0083] Among them, for those from Highly synchronized business flow, recording from of Type of business flow at node The probability of being processed is denoted as ;

[0084] Step S4-3: Based on the nodes The actual cumulative service volume is obtained by measuring the actual interference to the three different business flows in the service link.

[0085] The actual cumulative service volume is:

[0086] ;

[0087] in, Represents a node from Time slot to Cumulative service volume per time slot; Indicates for Type of business flow, non-service link to service link from Time slot to Cumulative interference in time slots.

[0088] Preferably, in step S5, service process analysis is performed based on the states of different nodes to obtain the probability distribution of the service process. Specifically, the operation is as follows:

[0089] Consider node status from three perspectives: time slot allocation, multimode transmission, and packet loss retransmission.

[0090] From the perspective of packet loss retransmission and multimode transmission: assuming each time slot arrive Successfully transmitted data packets are For each data packet, there are two possibilities: successful transmission or failure.

[0091] Assuming FHPLC and wireless channel transmission modes arrive The success rates of data packet transmission are respectively , Based on the differences between the channel models of FHPLC and wireless communication, using express arrive FHPLC link signal-to-noise ratio express arrive The signal-to-noise ratio of the wireless link is expressed as follows:

[0092] ;

[0093] in, This represents the average energy of the signal. Indicates the fading gain of the FHPLC channel. This represents the noise ratio of IMN to BGN;

[0094] ;

[0095] in, Indicates the fading gain of the wireless channel. This represents the noise ratio of IMN to BGN. express The transmission power, Represents the channel fading coefficient. express arrive The distance;

[0096] According to Shannon's formula, the transmission rates of FHPLC mode and wireless communication mode are expressed as follows:

[0097] ;

[0098] ;

[0099] in, For nodes With nodes The channel bandwidth of the communication link between them; In FHPLC mode, the nodes With nodes The transmission rate of the link; In RF mode, the node With nodes The transmission rate of the link;

[0100] Assuming each data packet has a length of 1000 kbps The transmission times for a single data packet in the two different modes are as follows:

[0101] ;

[0102] ;

[0103] in, Transmission time of a single data packet in FHPLC mode; The transmission time of a single data packet in wireless communication mode;

[0104] Assuming in the pattern Down, and The transmission success rate of the link between them is A data packet is considered successfully transmitted only if both data transmission and the ACK response are successfully transmitted. The probability of an error during data packet transmission is [missing information]. Assuming in Time slot and When there are no transmission failures, the maximum number of transmissions that can be sent is [number]. Each data packet is represented as:

[0105] ;

[0106] in, express Time slot in mode Down and The expected access latency of the link between them;

[0107] From the perspective of time slot allocation: [The following is a possible interpretation:] Divided into inter-node contention latency and inter-business competition latency ;

[0108] Node contention latency This refers to the same time slot at different nodes. Transmission preemption of the channel for mixed interleaved service flows If the node is in a contention time slot, i.e. Access requires contention; if a collision is detected, a random backoff period is required.

[0109] Assuming time slots The number of nodes that preempt this channel is expressed as Follows a Poisson distribution:

[0110] ;

[0111] in, This represents the average number of competing nodes per unit of time; if it is in its own dedicated time slot, that is... Then there is It directly occupies the channel; if ,but If backoff is necessary, then the node contention delay can be calculated as follows:

[0112] ;

[0113] in, This indicates the number of time slots that other nodes are avoiding when they have exclusive access to the time slots.

[0114] Business competition delay This means that if a node receives a data packet with a higher priority than the packet at the head of the queue during the initial listening time of a time slot, the current service data packet needs to be backed up to a time slot; assuming that the occurrence of high-priority services follows a Poisson distribution and the number is... It follows a Poisson distribution:

[0115] ;

[0116] The probability distribution of avoidance delay is expressed as follows:

[0117] ;

[0118] in, This indicates the maximum number of data packets that a service with priority continuous channel access can send in a unit time slot;

[0119] For urgent data service flows and highly synchronous services, the types and quantities of services that need to be avoided follow different distributions, thus calculating the backoff delay;

[0120] Time slot The access latency is:

[0121] ;

[0122] in, Indicates node contention latency; Indicates delays due to business competition;

[0123] Assumption Of the data packets, the retransmitted data packets are: There is one retransmission only for each failed data packet, indicating that... The transmission failed. The transmission is considered successful only when both the data packet and the ACK response are successfully transmitted simultaneously; therefore, in Number of retransmissions in transmission mode The probability distribution is as follows:

[0124] ;

[0125] in, These represent FHPLC mode and wireless communication mode, respectively. express Transmission mode and The transmission success rate of the link between them; Represented as Transmission mode and between The average number of data packets transmitted per time slot;

[0126] The number of data packets actually transmitted in a time slot is expressed as: ,when At that time, the actual number of data packets received The probability distribution is modeled as follows:

[0127] ;

[0128] In summary, based on the state of the node { The service process of obtaining different types of data packets for each time slot, including their hop probabilities and conditional distributions. probability distribution:

[0129] ;

[0130] Here, it is assumed that each time slot and each transmission mode follows a Bernoulli distribution. This indicates the probability that the current time slot will use the FHPLC mode transmission link; This indicates the probability that the current time slot will use wireless communication mode to transmit the link; express Time slot and Cumulative service volume between; Indicates the actual number of data packets arriving in FHPLC mode. The probability of; Indicates the actual number of data packets arriving in the wireless communication mode. The probability of.

[0131] Preferably, in step S6, the end-to-end time violation probability under stable conditions is obtained. The specific steps are as follows:

[0132] Step S6-1: Initialize martingale parameters based on arrival process analysis and service martingale definition. Related functions ;

[0133] Based on interference analysis, the actual service flow process in the service link is represented as follows: ,in, ;

[0134] The cumulative service process is recorded as ,,in For nodes Interference from non-service links; based on martingale parameters Related functions ,structure The service duct is:

[0135] ;

[0136] Among them, martingale parameters Related functions Take them as follows:

[0137] ;

[0138] ;

[0139] According to the service process The service flow distribution derived from the probability distribution is obtained. ;

[0140] remember Then the random process Represented as:

[0141] ;

[0142] in, Represented as a service link and between Actual cumulative service volume during the time slot;

[0143] Step S6-2: Based on the arrival flow With service flow The martingale domain model will concatenate descriptors Defined as:

[0144] ;

[0145] in, This represents the sum of the three service flows, i.e. ;

[0146] From the perspective of mixed and intertwined business flows, the overall arrival of the martingale Represented as:

[0147] ;

[0148] in, ;

[0149] ;

[0150] From the perspective of emergency business data packets, the overall arrival time is... Represented as:

[0151] ;

[0152] For highly synchronous services, the overall arrival martingale remains unchanged;

[0153] E2E link The corresponding serial queuing system Service capabilities describe:

[0154] ;

[0155] , This reflects the characteristics of the sequential collaborative service mode of E2E links; based on the characteristics of the sequential collaborative service mode of E2E links, the expressions for arrival martingale and service martingale are summarized as follows:

[0156] ;

[0157] ;

[0158] in, ,because The necessary and sufficient condition for it to be true is:

[0159] ;

[0160] remember Let be the maximum average arrival rate that a serial queuing system in the martingale domain can support; denoted as , regarded as a node The minimum average service rate that needs to be provided; therefore, This can be understood as a condition for the stability of a queuing system.

[0161] Step S6-3: Calculate the end-to-end time violation probability under steady-state conditions based on the supremum property and the deviation value. ;

[0162] According to the supremum property, the link is end-to-end delay The unreliability is calculated using the following formula:

[0163] ;

[0164] in, express Number of routing aggregation nodes on the link; This indicates the arrival flow of the serial queuing system. Service capabilities; Indicates the maximum time-lapse boundary; express The moment generating function; This represents the lower boundary of end-to-end delay reliability. Indicates end-to-end delay; express The collection of service capabilities of all nodes on the link.

[0165] Compared with the prior art, the present invention has the following improvements and advantages: 1. By using martingale theory to map the time-domain arrival flow and time-domain service flow to the martingale domain for analysis, and selecting three types of traffic flows with traffic characteristics, namely mixed interleaved service flow, urgent data service flow and highly synchronous service flow, as arrival flows, the impact of priority scheduling strategy on end-to-end latency is fully considered; this makes the constructed analysis framework have tight latency, while improving the reliability of analysis results and optimizing network deployment and resource scheduling.

[0166] 2. Interference analysis was conducted on the intertwined non-service links and service links in the network. The service capabilities of nodes at different stages were analyzed to obtain service flow. A martingale was constructed to obtain the time violation probability formula. Compared with the traditional delay calculation method, which is difficult to analyze the end-to-end transmission delay of various traffic characteristics of current services and has the problem of loose delay boundaries, the analysis method of this invention abstracts the complex queuing and interference process and has a tighter delay boundary. Attached Figure Description

[0167] Figure 1 This is the overall flowchart of the present invention.

[0168] Figure 2 This is a structural diagram of a multi-mode sensing network communication system.

[0169] Figure 3 This is a time-slot analysis diagram between two nodes.

[0170] Figure 4 This is a structural diagram of the arrival process of mixed interleaved service flows, emergency data service flows, and highly synchronized service flows.

[0171] Figure 5 This is a service process analysis diagram.

[0172] Figure 6 This is a diagram illustrating interference analysis of non-service link data.

[0173] Figure 7 Diagram showing PLC links and RF links as the backbone communication links of a multimode communication network.

[0174] Figure 8 This is a diagram illustrating the end-to-end latency characteristics of mixed interleaved service flows.

[0175] Figure 9 This graph shows the increase in the probability of time violation after backoff from interference by high-priority services, when the same latency threshold is met.

[0176] Figure 10 This is a diagram illustrating the end-to-end latency characteristics of emergency data service flows.

[0177] Figure 11 This is a diagram illustrating the end-to-end latency characteristics of highly synchronized service flows.

[0178] Figure 12 This is a comparison chart showing the results of the time violation probability formula derived through martingale theory with the actual simulated data packet transmission and reception results.

[0179] Figure 13 This is a graph showing the impact of the number of online dual-mode nodes in the network on the overall end-to-end latency.

[0180] Figure 14 This diagram illustrates the impact of hop count on overall end-to-end latency in an end-to-end link.

[0181] Figure 15 This is a graph showing the relationship between the number of data packets arriving within a time slot and the latency.

[0182] Figure 16 This is a graph showing the impact of wireless transmission success rate on retransmission latency.

[0183] Figure 17 This is a diagram showing the queuing delay analysis when the arrival rate is less than 200kb / s. Detailed Implementation

[0184] The invention will be further summarized below with reference to the accompanying drawings.

[0185] by Figure 2 Taking the multi-mode sensing network communication system shown as an example, a compact latency and reliability analysis framework is established to optimize network deployment and resource scheduling:

[0186] like Figure 1 As shown, an end-to-end latency analysis method for multimodal sensing networks based on martingale theory is presented. This method includes the following steps:

[0187] Step S1: Construct the overall network topology of the multimodal sensing model and define the end-to-end latency calculation formula;

[0188] Constructing the overall network topology of the multimodal perception model, and a... Time Link Model; derived using SNC theory, combined with cumulative arrival flow and service flow, to obtain the overall departure process. This allows us to obtain the end-to-end latency of the business flow. ;

[0189] First, the overall network topology of the multimodal sensing model adopts It means that among them Represents a node in a network. Indicates in The communication link at any given moment;

[0190] include EN, There are one RN and one MN, where EN represents the end sensing node, RN represents the routing aggregation node, and MN represents the central master control node;

[0191] in, Indicates in time and The communication link between them , This indicates a power line carrier communication link. Indicates the radio frequency link; Indicates in This link must always be present, otherwise it must not be present.

[0192] Furthermore, denote all ENs as a set. ; Assumption Generate a data stream, which passes through multiple serial... , passed on This multi-hop path is called an end-to-end (E2E) link; for , record it in The link at any time is , A set containing multiple nodes is denoted as . ,in express , express .

[0193] make Indicates link In the time slot The number of arriving data packets, express In the time slot The number of data packets served; the number of packets arriving in the stream. The last hop in the E2E link The cumulative departure process is considered as the departure process of the entire link, and is derived as follows:

[0194] ;

[0195] in, express From time slot Time slot The total number of data packets received. express From time slot Time slot The cumulative number of data packets served. express From time slot Time slot The cumulative number of outgoing data packets; therefore, the service flow end-to-end delay Represented as:

[0196] .

[0197] Step S2: For arrival flows with different characteristics, divide the arrival flows into different service flows; based on the state transition probability, arrival rate, and active / idle probability of different service flows, initialize the state transition matrix of the service flows, and perform an exponential column transformation on the state transition matrix of the service flows.

[0198] The incoming flow is divided into three different service flows, including mixed interleaved service flows, emergency data service flows, and highly synchronized service flows;

[0199] In step S2, the state transition matrix of the business flow is initialized. The specific operation is as follows:

[0200] Step S2-1: Solve for the state transition torques of the mixed interleaved service flow and the emergency data service flow, and model the highly synchronized service flow using the Beta / M / 1 model;

[0201] Solve for the state transition torques of the mixed interleaved service flow and the emergency data service flow:

[0202] Hybrid interleaved service flows refer to the data service flows with different characteristics at different stages in a multimodal awareness model, which alternately arrive at the routing aggregation node; the multimodal awareness model is represented as a Markov chain. ;

[0203] in, describe Service arrival status of time-slot data streams; }describe The status of time-slot services This indicates that the service is in a normal state (normal transmission and reception rate) during the time slot when data packets arrive. This indicates that the service is in a busy state (high-frequency transmission and reception rate) during the time slot when data packets arrive. express Time slot services Is there a data packet arrival status? This indicates that a data packet has arrived. This indicates that no data packets have arrived;

[0204] Therefore, the state space of a Markov chain is represented as:

[0205] ;

[0206] The state space representation of a Markov chain of mixed and intertwined business flows is as follows:

[0207] ;

[0208] in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is .

[0209] Formula for emergency data service flow It means that, among them, Indicates in Time slot arrives at service link Emergency data services The number of data packets; the emergency data service flow represents the service information flow reported in the multi-modal perception model for sudden states, indicating equipment failure or emergency events. Emergency data service flows are normally idle, but arrive in batches and must be processed with priority once an emergency occurs; to describe the emergency data service flow, we use... , This indicates whether the emergency data service is in an idle or active state, and represents the arrival status of the data packet as follows: ,state This indicates that the service is active and data packets are arriving; Status This indicates that the service is active, but no data packets have arrived; Status This indicates that the service is in an idle state and no data packets have arrived.

[0210] In summary, the multimodal sensing model can be represented as a two-dimensional Markov chain, as follows: , , Indicates being in The status of time-slot emergency data services Indicates being in The arrival status of time-slot data packets, if ,but If probability 1 is true, then the state of the emergency data service flow is:

[0211] ;

[0212] The state transition matrix of the emergency data service flow is represented as follows:

[0213] ;

[0214] in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. This represents the probability of data packet arrival.

[0215] Highly synchronous service flows indicate that a large number of MTC devices in a multimode sensing network access the network in a highly concurrent manner, with signaling flows having the highest priority. We use the Beta / M / 1 model for modeling, and the analytical expression for the Beta distribution MGF is:

[0216] ;

[0217] in, To represent the ascending factorial, if If it is an integer, then ; The parameter is The first type of merging hypergeometric function; for this type of high-concurrency business flow, we set .

[0218] Step S2-2: Based on the state transition torque of the hybrid interleaved service flow and the state transition torque of emergency data service flows Perform exponential transformation;

[0219] Based on the state transition torque of the mixed interleaved business flow and the state transition torque of emergency data service flows To perform exponential column transformation, the specific steps are as follows:

[0220] State space matrix of hybrid interwoven business flows Performing the corresponding exponential transformation yields:

[0221] ;

[0222] in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is ;

[0223] State transition torque of emergency data service flow Performing the corresponding exponential transformation yields:

[0224] ;

[0225] in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. The probability of data packet arrival. For the number of arrivals.

[0226] Step S3: Construct martingales for the arrival process of different business flows according to the definition of martingale to obtain the arrival martingale model;

[0227] According to the definition of the martingale, for the transition matrix , Perform an exponential transformation to obtain , Then calculate the transformed spectral radius. and Determine the relevant functions for reaching the martingale. , With parameters , ; Obtain the mapping of the time-domain model in the martingale domain based on the parameters. and .against Construct the corresponding Wald martingale and obtain .

[0228] Step S3-1: Convert the state transition of the mixed interleaved service flow into a matrix. After performing the corresponding exponential transformation, we get State transition matrix for emergency data service flows After performing the corresponding exponential transformation, we get ,right , Calculate the corresponding spectral radius , ;

[0229] According to the martingale parameter theorem, for Performing an exponential transformation yields have: ;in, This represents the corresponding element of the Markov transition matrix. , for The state of the time slot; The spectral radius is expressed as , For the corresponding right eigenvector, the martingale parameter is reached. Determined as The One element, The selection range is: .

[0230] Step S3-2: Determine the function for the hybrid interleaved traffic flow to reach the martingale. , And the function for emergency data service flows to reach the martingale. ,parameter ;

[0231] Step S3-3: When satisfy ;

[0232] ;

[0233] satisfy ;

[0234] ;

[0235] Then, the martingale arrival process of the mixed and intertwined business flow is represented as:

[0236] ;

[0237] in, for The One element; for The One element; For martingale parameters, For mixed and intertwined business flows Time slot to Cumulative arrivals of time-slot data packets;

[0238] The martingale arrival process of an emergency data service flow is represented as follows:

[0239] ;

[0240] in, for The One element; for The One element; For martingale parameters, For emergency data service flow Time slot to Cumulative arrivals of time-slot data packets;

[0241] Step S3-4: For high-concurrency service flows occurring during the network setup phase The corresponding Wald martingale is constructed using its moment generating function. The martingale arrival process of highly synchronized business flows is represented as follows:

[0242] ;

[0243] in, The analytical expression of the Beta distribution MGF For highly synchronized services Time slot to Cumulative arrivals of time-slot data packets.

[0244] Step S4: For the three different intersection scenarios of service flows, perform inter-link interference analysis to obtain the cumulative amount of interference experienced by the node serving different service flows;

[0245] Based on the cumulative arrival of interference packets at the aggregation node and the separation node and the proportion of service flow data packets with different priorities. To obtain the cumulative amount of interference experienced by different business flows in the node service: , ;

[0246] Due to the complex topology of multimodal sensing networks, data flows on different links may intersect or converge at a certain routing aggregation node; for example... Figure 6 As shown, in In the event of an aggregation, the current service link Passing through the node The next jump is For non-service links, there may be issues. Three types; specific operations are as follows:

[0247] Step S4-1: For non-service links and service links that appear... Analyze three possible intersection scenarios;

[0248] Representation and service link At the node They meet, but their next hop nodes are different. This will affect the service chain. It causes interference;

[0249] Representing business flow and service links At the node Convergence, and the next hop is also a node. , This will affect the service chain. It causes interference;

[0250] Represents a node This is the last hop in the current business flow. No service is required for this business flow. No impact on service links It causes interference;

[0251] Therefore, when calculating end-to-end latency on a service link, in addition to the data packets arriving at the end-sensing node of the service link, it is also necessary to consider the data packets transmitted from other non-service links to the junction node that need to be processed; recorded at the node All of the convergence , The set of type links is ,for Place Time slot to The cumulative data volume of arriving flows across all non-service flow links in a time slot is expressed as follows: ;

[0252] Based on the FIFO principle and priority scheduling strategy, this analysis takes emergency business data flow as an example. Assuming... middle In the cumulative number of departing nodes, the proportions of the three types of data packets are as follows: .remember express Middle node Does the next jump occur? Inside, if This indicates that data stream convergence has occurred, otherwise it has not; packets of the same priority are processed according to the FIFO principle. For packets from... Emergency data stream, recorded from Data flow in nodes The probability of being processed is denoted as ,in This represents three different types of data packets, at which point there are .

[0253] At the node The cumulative total arrivals from non-service links are as follows:

[0254] ;

[0255] At the node The cumulative total arrivals from non-service links are as follows:

[0256] ;

[0257] in, In summary, the results at the node are as follows: The cumulative interference from non-service links that needs to be addressed is as follows:

[0258] Therefore, we will discuss interference in different scenarios, and the nodes... Non-service links interfere with mixed interleaved service flows, emergency service flows, and highly synchronized service flows.

[0259] Step S4-2: Obtain the node pairs of the three different service flows in the non-service link and the service link. Interference;

[0260] Interference in mixed and interleaved service flows is represented as follows:

[0261]

[0262] Among them, for those from Mixed and intertwined business flows, recorded from of Type of business flow at node The probability of being processed is denoted as ; This represents data packets for mixed interleaved service flows, emergency data service flows, and highly synchronized service flows. express middle The percentage of the three types of data packets in the cumulative number of nodes leaving; express Cumulative arrivals at nodes; express Middle node Does the next jump occur? Inside, if This indicates that business flows have converged, otherwise they have not. Indicates at node All of the convergence , A collection of type links;

[0263] Disruptions to emergency service flows are represented as follows:

[0264]

[0265] Among them, for those from Emergency data service flow, recorded from of Type of business flow at node The probability of being processed is denoted as ;

[0266] Interference in highly synchronized service flows is represented as

[0267]

[0268] Among them, for those from Highly synchronized business flow, recording from of Type of business flow at node The probability of being processed is denoted as ;

[0269] Step S4-3: Based on the nodes The actual cumulative service volume is obtained by measuring the actual interference to the three different business flows in the service link.

[0270] The actual cumulative service volume is:

[0271] ;

[0272] in, Represents a node from Time slot to Cumulative service volume per time slot; Indicates for Type of business flow, non-service link to service link from Time slot to Cumulative interference in time slots.

[0273] Step S5: Based on the state of different nodes, perform service process analysis to obtain the probability distribution of the service process;

[0274] Consider node status from three perspectives: time slot allocation, multimode transmission, and packet loss retransmission.

[0275] From the perspective of packet loss retransmission and multimode transmission: assuming each time slot arrive Successfully transmitted data packets are For each data packet, there are two possibilities: successful transmission or failure.

[0276] Assuming FHPLC and wireless channel transmission modes arrive The success rates of data packet transmission are respectively , Based on the differences between the channel models of FHPLC and wireless communication, using express arrive FHPLC link signal-to-noise ratio express arrive The signal-to-noise ratio of the wireless link is expressed as follows:

[0277] ;

[0278] in, This represents the average energy of the signal. Indicates the fading gain of the FHPLC channel. This represents the noise ratio of IMN to BGN;

[0279] ;

[0280] in, Indicates the fading gain of the wireless channel. This represents the noise ratio of IMN to BGN. express The transmission power, Represents the channel fading coefficient. express arrive The distance;

[0281] According to Shannon's formula, the transmission rates of FHPLC mode and wireless communication mode are expressed as follows:

[0282] ;

[0283] ;

[0284] in, For nodes With nodes The channel bandwidth of the communication link between them; In FHPLC mode, the nodes With nodes The transmission rate of the link; In RF mode, the node With nodes The transmission rate of the link;

[0285] Assuming each data packet has a length of 1000 kbps The transmission times for a single data packet in the two different modes are as follows:

[0286] ;

[0287] ;

[0288] in, Transmission time of a single data packet in FHPLC mode; The transmission time of a single data packet in wireless communication mode;

[0289] Assuming in the pattern Down, and The transmission success rate of the link between them is A data packet is considered successfully transmitted only if both data transmission and the ACK response are successfully transmitted. The probability of an error during data packet transmission is [missing information]. Assuming in Time slot and When there are no transmission failures, the maximum number of transmissions that can be sent is [number]. Each data packet is represented as:

[0290] ;

[0291] in, express Time slot in mode Down and The expected access latency of the link between them;

[0292] From the perspective of time slot allocation: [The following is a possible interpretation:] Divided into inter-node contention latency and inter-business competition latency ;

[0293] Node contention latency This refers to the same time slot at different nodes. Transmission preemption of the channel for mixed interleaved service flows If the node is in a contention time slot, i.e. Access requires contention; if a collision is detected, a random backoff period is required.

[0294] Assuming time slots The number of nodes that preempt this channel is expressed as Follows a Poisson distribution:

[0295] ;

[0296] in, This represents the average number of competing nodes per unit of time; if it is in its own dedicated time slot, that is... Then there is It directly occupies the channel; if ,but If backoff is necessary, then the node contention delay can be calculated as follows:

[0297] ;

[0298] in, This indicates the number of time slots that other nodes are avoiding when they have exclusive access to the time slots.

[0299] Business competition delay This means that if a node receives a data packet with a higher priority than the packet at the head of the queue during the initial listening time of a time slot, the current service data packet needs to be backed up to a time slot; assuming that the occurrence of high-priority services follows a Poisson distribution and the number is... It follows a Poisson distribution:

[0300] ;

[0301] The probability distribution of avoidance delay is expressed as follows:

[0302] ;

[0303] in, This indicates the maximum number of data packets that a service with priority continuous channel access can send in a unit time slot;

[0304] For urgent data service flows and highly synchronous services, the types and quantities of services that need to be avoided follow different distributions, thus calculating the backoff delay;

[0305] Time slot The access latency is:

[0306] ;

[0307] in, Indicates node contention latency; Indicates delays due to business competition;

[0308] Assumption Of the data packets, the retransmitted data packets are: There is one retransmission only for each failed data packet, indicating that... The transmission failed. The transmission is considered successful only when both the data packet and the ACK response are successfully transmitted simultaneously; therefore, in Number of retransmissions in transmission mode The probability distribution is as follows:

[0309] ;

[0310] in, These represent FHPLC mode and wireless communication mode, respectively. express Transmission mode and The transmission success rate of the link between them; Represented as Transmission mode and between The average number of data packets transmitted per time slot;

[0311] The number of data packets actually transmitted in a time slot is expressed as: ,when At that time, the actual number of data packets received The probability distribution is modeled as follows:

[0312] ;

[0313] In summary, based on the state of the node { The service process of obtaining different types of data packets for each time slot, including their hop probabilities and conditional distributions. probability distribution:

[0314] ;

[0315] Here, it is assumed that each time slot and each transmission mode follows a Bernoulli distribution. This indicates the probability that the current time slot will use the FHPLC mode transmission link; This indicates the probability that the current time slot will use wireless communication mode to transmit the link; express Time slot and Cumulative service volume between; Indicates the actual number of data packets arriving in FHPLC mode. The probability of; Indicates the actual number of data packets arriving in the wireless communication mode. The probability of.

[0316] Step S6: Obtain the end-to-end time violation probability under steady-state conditions. Construct the overall network topology of the multimodal sensing model, and then define the end-to-end latency calculation formula;

[0317] In step S6, the end-to-end time violation probability under steady-state conditions is obtained. The specific steps are as follows:

[0318] Step S6-1: Initialize martingale parameters based on arrival process analysis and service martingale definition. Related functions ;

[0319] Based on interference analysis, the actual service flow process in the service link is represented as follows: ,in, ;

[0320] The cumulative service process is recorded as ,in For nodes Interference from non-service links; based on martingale parameters Related functions ,structure The service duct is:

[0321] ;

[0322] Among them, martingale parameters Related functions Take them as follows:

[0323] ;

[0324] ;

[0325] According to the service process The service flow distribution derived from the probability distribution is obtained.

[0326] ;

[0327] remember Then the random process Represented as:

[0328] ;

[0329] in, Represented as a service link and between Actual cumulative service volume during the time slot;

[0330] Step S6-2: Based on the arrival flow With service flow The martingale domain model will concatenate descriptors Defined as:

[0331] ;

[0332] in, This represents the sum of the three service flows, i.e. ;

[0333] From the perspective of mixed and intertwined business flows, the overall arrival of the martingale Represented as:

[0334] ;

[0335] in, ;

[0336] ;

[0337] From the perspective of emergency business data packets, the overall arrival time is... Represented as:

[0338] ;

[0339] For highly synchronous services, the overall arrival martingale remains unchanged;

[0340] E2E link The corresponding serial queuing system Service capabilities describe:

[0341] ;

[0342] , This reflects the characteristics of the sequential collaborative service mode of E2E links; based on the characteristics of the sequential collaborative service mode of E2E links, the expressions for arrival martingale and service martingale are summarized as follows:

[0343] ;

[0344] ;

[0345] in, ,because The necessary and sufficient condition for it to be true is:

[0346] ;

[0347] remember Let be the maximum average arrival rate that a serial queuing system in the martingale domain can support; denoted as , regarded as a node The minimum average service rate that needs to be provided; therefore, This can be understood as a condition for the stability of a queuing system.

[0348] Step S6-3: Calculate the end-to-end time violation probability under steady-state conditions based on the supremum property and the deviation value. ;

[0349] According to the supremum property, the link is end-to-end delay The unreliability is calculated using the following formula:

[0350] ;

[0351] in, express Number of routing aggregation nodes on the link; This indicates the arrival flow of the serial queuing system. Service capabilities; Indicates the maximum time-lapse boundary; express The moment generating function; This represents the lower boundary of end-to-end delay reliability. Indicates end-to-end delay; express The collection of service capabilities of all nodes on the link.

[0352] Working Principle: Considering two transmission media—power line carrier communication and radio frequency communication—three traffic characteristics are selected as arriving flows: mixed interleaved traffic flow, urgent data traffic flow, and highly synchronized traffic flow. The paper analyzes the impact of priority scheduling strategies on end-to-end latency. Furthermore, interference analysis is conducted for the interleaving of non-service and service links in the network. Service flows are obtained by analyzing the service capabilities of nodes at different stages, and a martingale is constructed to obtain the timing violation probability formula. Compared to traditional latency calculation methods, which struggle to analyze the end-to-end transmission latency of various traffic characteristics and suffer from loose latency boundaries, this analytical method abstracts the complex queuing and interference processes and achieves tighter latency boundaries.

[0353] Simulation experiment:

[0354] The invention uses MATLAB simulation to evaluate the analytical capability of the above model in end-to-end delay analysis in a dual-mode sensing network. It assumes the overall network layout has an area of... In the distribution network of the transformer substation, the network consists of a central control node, a routing aggregation node, and end sensing nodes.

[0355] Assuming the end-point sensing nodes are low-power devices powered by batteries or induction, their access points can be either a central control node or a routing aggregation node. The central control node and routing aggregation nodes use power lines and wireless as transmission media, forming a mesh network structure centered on the central control node. For example... Figure 7 As shown, the multimode communication network consists of two types of links: PLC links and RF links. PLC links use power lines as the transmission medium, while RF links use 470MHz wireless as the transmission method. Together, the PLC and RF links form the backbone communication links of the multimode network. The network primarily carries services including device data acquisition, priority-based service transmission, and power outage reporting.

[0356] Assuming the maximum transmission rate of the PLC link is 1.1 Mbps and the 470 MHz RF transmission rate is 100 / 200 kbps, the simulation delays in this paper were all performed on MATLAB R2021a. The node parameters for the simulation experiments are shown in Table 1.

[0357] Table 1 shows the node parameters for the simulation experiment.

[0358]

[0359] Assume there are three types of service flows with different arrival characteristics and priorities in the network, and analyze the end-to-end latency characteristics. The performance parameter values ​​for mixed-interleaved service flows, urgent data service flows, and highly synchronized services are shown in Table 2.

[0360] Table 2 shows the performance parameter values ​​for hybrid interleaved service flows, emergency data service flows, and highly synchronized services.

[0361]

[0362] like Figure 8 As shown, the arrival rate of mixed-interleaved service flows is relatively stable, indicating periodic reporting services in the network. These services have the lowest priority and need to be backed up when higher-priority service flows arrive, such as... Figure 9 As shown, at the same latency threshold, the probability of time violation increases after backing off from interference from high-priority services. Figure 10 Emergency data traffic is characterized by sporadic arrivals; most of the time, this type of traffic does not exist in the network. It arises when a device malfunctions or other emergency occurs, and has a medium priority. Figure 11 As shown, emergency data traffic is not affected by mixed and interleaved traffic, but the probability of time-lapse increases when highly synchronized traffic arrives. Figure 8 Highly synchronized services do not occur normally in the network. They arise when a large number of devices experience power outages and reconnections, generating a large amount of data within a short period. These services have the highest priority. Figure 10 As shown, it is not affected by low-priority services, but its failure probability increases as the number of end-to-end hops increases.

[0363] like Figure 12 As shown, comparing the results of the time violation probability formula derived through martingale theory with the actual simulated data packet transmission and reception results reveals that the overall curve trends are the same. Under conditions where random delay backoff is required without interference from high-priority services, the two formulas fit well. However, when interference occurs, due to the limited number of random samples in the simulation, the statistical service capacity in the formula will differ from the actual service capacity of each node. Therefore, a certain deviation will occur when the time violation requirement is high; the error will decrease with a larger sample size.

[0364] like Figure 13The diagram illustrates the impact of the number of online dual-mode nodes on overall end-to-end latency. As the number of network nodes increases, interference from non-service links becomes more significant. Furthermore, the latency due to contention for access between nodes also increases with the number of network nodes. Therefore, the actual service capacity of each node decreases, and the end-to-end latency of service links increases with the network size. When the number of online nodes reaches a certain threshold, the links will struggle to handle the load, resulting in significant latency accumulation.

[0365] like Figure 14 The figure shows the impact of the number of hops in the end-to-end link on the overall end-to-end latency in the time violation probability formula. Here, we choose a time violation probability of 1. A time threshold is used to truncate the data. It can be observed that the average latency increases with the number of hops per node. Furthermore, adopting a dual-mode transmission routing method prioritizing minimum latency can effectively reduce the average latency and improve the service capacity of each node. Compared with the actual simulation curve, the fit is better when the number of link nodes is small; as the number of nodes increases, some error will occur, but the overall growth trend remains consistent.

[0366] Figure 15 The graph shows the relationship between the number of data packets arriving within an average of 100 time slots and the latency. It can be seen that the latency probability curve derived from martingale theory is largely consistent with the actual average latency trend. When the amount of data arriving within 100 time slots is small, the average latency of the three routing methods is not significantly different. When the cumulative arrival volume reaches 4kb or more, the latency increase is more gradual in the dual-mode transmission routing method that prioritizes minimum latency, and it is much lower than the latency of single-mode transmission.

[0367] Since martingale theory analyzes the overall end-to-end delay, it cannot calculate the specific five parts of delay mentioned in Section 3 of the paper separately. Therefore, it is necessary to analyze the delay of each part through other calculation methods.

[0368] Figure 16 This illustrates the impact of wireless transmission success rate on retransmission latency. Since PLC transmission success rate is high and stable, we analyze the changes in wireless transmission success rate. It can be seen that for a PLC-first routing strategy, changes in transmission success rate have almost no impact on retransmission latency. For a dual-mode routing strategy prioritizing minimum latency, when the success rate is low, the retransmission latency is high, so the route prioritizes PLC link transmission. At this point, the curve does not change significantly. When the success rate rises to a certain level, wireless transmission will be selected, and the retransmission latency will decrease as the success rate increases.

[0369] To analyze the time it takes for a data packet to travel from entering the node queue to becoming the head of the queue and waiting to be sent, we use traditional queuing theory to calculate this time. We analyze the service rate of each node based on the service process to obtain the impact of different routing strategies and data arrival rates on the average queuing delay. For example... Figure 17 As shown, when the arrival rate is less than 200kb / s, the queuing delay increases slowly. When the arrival rate is greater than 250kb / s, the queuing delay of the network will increase significantly, and the service capacity of the nodes will be unable to meet the rate requirements of the business.

[0370] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for end-to-end delay analysis of multimodal sensing networks based on martingale theory, characterized in that: The method includes the following steps: Step S1: Construct the overall network topology of the multimodal sensing model and define the end-to-end latency calculation formula; Constructing the overall network topology of the multimodal perception model, and a... Time Link Model; derived using SNC theory, combined with cumulative arrival flow and service flow, to obtain the overall departure process. This allows us to obtain the end-to-end latency of the business flow. ; Step S2: For arrival flows with different characteristics, divide the arrival flows into different service flows; based on the state transition probability, arrival rate, and active / idle probability of different service flows, initialize the state transition matrix of the service flows, and perform an exponential column transformation on the state transition matrix of the service flows. The arrival flow is divided into three different service flows, including mixed interleaved service flow, emergency data service flow, and highly synchronized service flow; Step S3: Construct martingales for the arrival process of different business flows according to the definition of martingale, and obtain the arrival martingale model. The specific operation is as follows: Step S3-1: Convert the state transition of the mixed interleaved service flow into a matrix. After performing the corresponding exponential series transformation, we get State transition matrix for emergency data service flows After performing the corresponding exponential series transformation, we get ,right , Calculate the corresponding spectral radius , ; Step S3-2: Determine the function for the hybrid interleaved service flow to reach the martingale. , And the function for emergency data service flows to reach the martingale ,parameter ; Step S3-3: When satisfy ; ； satisfy ; ； Then, the martingale arrival process of the mixed and intertwined business flow is represented as: ； in, for The One element; for The One element; For martingale parameters, For mixed and intertwined business flows Time slot to Cumulative arrivals of time-slot data packets; The martingale arrival process of an emergency data service flow is represented as follows: ； in, for The One element; for The One element; For martingale parameters, For emergency data service flow Time slot to Cumulative arrivals of time-slot data packets; Step S3-4: For high-concurrency service flows occurring during the network setup phase The corresponding Wald martingale is constructed using its moment generating function. The martingale arrival process of highly synchronized business flows is represented as follows: ； in, The analytical expression of the Beta distribution MGF For highly synchronized services Time slot to Cumulative arrivals of time-slot data packets; Step S4: For the three different intersection scenarios of service flows, perform inter-link interference analysis to obtain the cumulative amount of interference experienced by the node serving different service flows; Step S5: Based on the state of different nodes, perform service process analysis to obtain the probability distribution of the service process; Step S6: Obtain the end-to-end time violation probability under steady-state conditions. .

2. The end-to-end delay analysis method for multi-mode sensing networks based on martingale theory according to claim 1, characterized in that: The overall network topology of the multimodal sensing model adopts... It means that among them Represents a node in a network. Indicates in The communication link at any given moment; include EN, One RN and one MN, where EN represents the end sensing node, RN represents the routing aggregation node, and MN represents the central master control node; ； in, Indicates in time and The communication link between them , Indicates a power line carrier communication link. Indicates the radio frequency link; Shown time and Between A pattern communication link exists, and vice versa.

3. The end-to-end delay analysis method for multi-mode sensing networks based on martingale theory according to claim 1, characterized in that: In step S1, the overall departure process is obtained by deriving the SNC theory and combining the cumulative arrival flow and service flow. This allows us to obtain the end-to-end latency of the business flow. The specific steps are as follows: Will reach the flow The last hop in the E2E link The cumulative departure process is regarded as the departure process of the entire link, and is represented as: ； in, express From time slot Time slot The cumulative number of data packets received; express From time slot Time slot The cumulative number of data packets served; express From time slot Time slot The total number of packets that have left the network; End-to-end latency of the business flow Represented as: 。 4. The end-to-end delay analysis method for multi-mode sensing networks based on martingale theory according to claim 1, characterized in that: In step S2, the state transition matrix of the service flow is initialized, and the specific operation is as follows: Step S2-1: Solve for the state transition torques of the mixed interleaved service flow and the emergency data service flow, and model the highly synchronized service flow using the Beta / M / 1 model; The specific steps for calculating the state transition torques of the mixed interleaved service flow and the emergency data service flow are as follows: The hybrid interleaved service flow refers to the data service flows with different characteristics at different stages in the multimodal awareness model, which alternately arrive at the routing aggregation node; the multimodal awareness model is represented as a Markov chain as follows: ; in, describe Service arrival status of time-slot data streams; }describe Status of time-slot services; express Time slot services Has a data packet arrived? The state space representation of the hybrid interleaved service flow Markov chain is as follows: ； in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is ; The formula used for the emergency data service flow It means that, among them, Indicates in Time slot arrives at service link Emergency data services The number of data packets; the emergency data service flow refers to the service information flow reported in the multi-modal perception model for sudden states, indicating equipment failure or emergency events. The emergency data service flow is usually in an idle state, but once an emergency event occurs, it arrives in batches and must be processed with priority. The multimodal sensing model is represented as a two-dimensional Markov chain, as follows: , , Indicates being in The status of time-slot emergency data services Indicates being in The arrival status of time-slot data packets, if ,but If probability 1 holds true, the state transition matrix of the emergency data service flow is represented as follows: ； in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. This represents the probability of data packet arrival. The Beta / M / 1 model is used to model highly synchronous service flows. The specific steps are as follows: The highly synchronous service flow refers to a large number of MTC devices in the multi-mode sensing network accessing the network in a highly concurrent manner, with signaling flow having the highest priority; it is modeled using the Beta / M / 1 model, and the analytical expression of the Beta distribution MGF is: ； in, To represent the ascending factorial, if If it is an integer, then ; The parameter is The first kind of confluence hypergeometry function; Step S2-2: Based on the state transition torque of the hybrid interleaved service flow and the state transition torque of emergency data service flows Perform exponential transformation.

5. The end-to-end delay analysis method for multimodal sensing networks based on martingale theory according to claim 4, characterized in that: In step S2-2, the state transition torque of the hybrid interleaved service flow is used as a reference. and the state transition torque of emergency data service flows To perform exponential column transformation, the specific steps are as follows: The state space matrix of the hybrid interleaved service flow Performing the corresponding exponential transformation yields: ； in, The jump probabilities are respectively expressed as ; The jump probabilities are respectively expressed as , The jump probabilities are respectively expressed as ; , This indicates that the current time slot service is in a normal state. With busy state Transition probability, per time slot The probability of data packet arrival is ; The state transition torque of the emergency data service flow Performing the corresponding exponential transformation yields: ； in, , This indicates that emergency data services are in either idle or active states. and These represent the probabilities of the idle and active states, respectively. The probability of data packet arrival. For the number of arrivals.

6. The end-to-end delay analysis method for multi-mode sensing networks based on martingale theory according to claim 1, characterized in that: In step S4, inter-link interference analysis is performed for the three different convergence scenarios of service flows to obtain the cumulative interference experienced by the node serving different service flows. The specific operation is as follows: Step S4-1: For non-service links and service links that appear... Analyze three possible intersection scenarios; Representation and service link At the node They meet, but their next hop nodes are different. This will affect the service chain It causes interference; Representing business flow and service links At the node Convergence, and the next hop is also a node. , This will affect the service chain It causes interference; Represents a node This is the last hop in the current business flow. No service is required for this business flow. No impact on service links It causes interference; Step S4-2: Obtain the node pairs of the three different service flows in the non-service link and the service link. Interference; The interference of the hybrid interleaved service flow is represented as follows: ； Among them, for those from Mixed and intertwined business flows, recorded from of Type of business flow at node The probability of being processed is denoted as ; This represents data packets for mixed interleaved service flows, emergency data service flows, and highly synchronized service flows. express middle The percentage of the three types of data packets in the cumulative number of nodes leaving; express Cumulative arrivals at nodes; express Middle node Does the next jump occur? Inside, if This indicates that business flows have converged, otherwise they have not. Indicates at node All of the convergence , A collection of type links; The interference with the emergency data service flow is represented as follows: ； Among them, for those from Emergency data service flow, recorded from of Type of business flow at node The probability of being processed is denoted as ; The interference of the highly synchronized service flow is represented as ； Among them, for those from Highly synchronized business flow, recording from of Type of business flow at node The probability of being processed is denoted as ; Step S4-3: Based on the nodes The actual cumulative service volume is obtained by measuring the actual interference to the three different business flows in the service link. The actual cumulative service volume is: ； in, Represents a node from Time slot to Cumulative service volume per time slot; Indicates for Type of business flow, non-service link to service link from Time slot to Cumulative interference in time slots.

7. The end-to-end delay analysis method for multimodal sensing networks based on martingale theory according to claim 1, characterized in that: In step S5, service process analysis is performed based on the states of different nodes to obtain the probability distribution of the service process. The specific operation is as follows: Consider node status from three perspectives: time slot allocation, multimode transmission, and packet loss retransmission. From the perspective of packet loss retransmission and multimode transmission: assuming each time slot arrive The successfully transmitted data packet is For each data packet, there are two possibilities: successful transmission or failure. Assuming FHPLC and wireless channel transmission modes arrive The success rates of data packet transmission are respectively , Based on the differences between the channel models of FHPLC and wireless communication, using express arrive FHPLC link signal-to-noise ratio express arrive The signal-to-noise ratio of the wireless link is expressed as follows: ； in, This represents the average energy of the signal. Indicates the fading gain of the FHPLC channel. This represents the noise ratio of IMN to BGN; ； in, Indicates the fading gain of the wireless channel. This represents the noise ratio of IMN to BGN. express The transmission power, Represents the channel fading coefficient. express arrive The distance; According to Shannon's formula, the transmission rates of FHPLC mode and wireless communication mode are expressed as follows: ； ； in, For nodes With nodes The channel bandwidth of the communication link between them; In FHPLC mode, the nodes With nodes The transmission rate of the link; In RF mode, the node With nodes The transmission rate of the link; Assuming each data packet has a length of 1000 kbps The transmission times for a single data packet in the two different modes are as follows: ； ； in, Transmission time of a single data packet in FHPLC mode; The transmission time of a single data packet in wireless communication mode; Assuming in the pattern Down, and The transmission success rate of the link between them is A data packet is considered successfully transmitted only if both data transmission and the ACK response are successfully transmitted. The probability of an error during data packet transmission is [missing information]. ; Assuming in Time slot and When there are no transmission failures, the maximum number of transmissions that can be sent is [number]. Each data packet is represented as: ； in, express Time slot in mode Down and The expected access latency of the link between them; From the perspective of time slot allocation: [The following is a possible interpretation:] Divided into inter-node contention latency and inter-business competition latency ; Node contention latency This refers to the same time slot at different nodes. Transmission preemption of the channel for mixed interleaved service flows If the node is in a contention time slot, that is... Access requires contention; if a collision is detected, a random backoff period is required. Assuming time slots The number of nodes that preempt this channel is expressed as Follows a Poisson distribution: ； in, This represents the average number of competing nodes per unit of time; if it is in its own dedicated time slot, that is... Then there is It directly occupies the channel; if ,but If backoff is necessary, then the node contention delay is calculated as follows: ； in, This indicates the number of time slots that other nodes are avoiding when they have exclusive access to the time slots. Business competition delay This means that if a node receives a data packet with a higher priority than the packet at the head of the queue during the initial listening time of a time slot, the current service data packet needs to be backed up to a time slot; assuming that the occurrence of high-priority services follows a Poisson distribution and the number is... It follows a Poisson distribution: ； The probability distribution of avoidance delay is expressed as follows: ； in, This indicates the maximum number of data packets that a service with priority continuous channel access can send in a unit time slot; For urgent data service flows and highly synchronous services, the types and quantities of services that need to be avoided follow different distributions, thus calculating the backoff delay; Time slot The access latency is: ； in, Indicates node contention latency; Indicates delays due to business competition; Assumption Of the data packets, the retransmitted data packets are: There is one retransmission only for each failed data packet, indicating that... The transmission failed. The transmission is considered successful only when both the data packet and the ACK response are successfully transmitted simultaneously; therefore, in Number of retransmissions in transmission mode The probability distribution is as follows: ； in, These represent FHPLC mode and wireless communication mode, respectively. express Transmission mode and The transmission success rate of the link between them; Represented as Transmission mode and between The average number of data packets transmitted per time slot; The number of data packets actually transmitted in a time slot is expressed as: ,when At that time, the actual number of data packets received The probability distribution is modeled as follows: ； In summary, based on the state of the node { The service process of obtaining different types of data packets for each time slot, including their hop probabilities and conditional distributions. probability distribution: ； Here, it is assumed that each time slot and each transmission mode follows a Bernoulli distribution. This indicates the probability that the current time slot will use the FHPLC mode transmission link; This indicates the probability that the current time slot will use wireless communication mode to transmit the link; express Time slot and Cumulative service volume between; Indicates the actual number of data packets arriving in FHPLC mode. The probability of; Indicates the actual number of data packets arriving in the wireless communication mode. The probability of.

8. The end-to-end delay analysis method for multimodal sensing networks based on martingale theory according to claim 1, characterized in that: In step S6, the end-to-end time violation probability under stable conditions is obtained. The specific steps are as follows: Step S6-1: Initialize martingale parameters based on arrival process analysis and service martingale definition. Related functions ; Based on interference analysis, the actual service flow process in the service link is represented as follows: ,in, ; The cumulative service process is recorded as ,in For nodes Interference from non-service links; based on martingale parameters Related functions ,structure The service duct is: ； Among them, martingale parameters Related functions Take them as follows: ； ； According to the service process The service flow distribution derived from the probability distribution is obtained. ; remember Then the random process Represented as: ； in, Represented as a service link and between Actual cumulative service volume during the time slot; Step S6-2: Based on the arriving flow With service flow The martingale domain model will concatenate descriptors Defined as: ； in, This represents the sum of the three service flows, i.e. ; From the perspective of mixed and intertwined business flows, the overall arrival of the martingale Represented as: ； in, ; ； From the perspective of emergency business data packets, the overall arrival time is... Represented as: ； For highly synchronous services, the overall arrival martingale remains unchanged; E2E link The corresponding serial queuing system Service capabilities describe: ； , This reflects the characteristics of the sequential collaborative service mode of E2E links; based on the characteristics of the sequential collaborative service mode of E2E links, the expressions for arrival martingale and service martingale are summarized as follows: ； ； in, ,because The necessary and sufficient condition for it to be true is: ； remember Let be the maximum average arrival rate that a serial queuing system in the martingale domain can support; denoted as , regarded as a node The minimum average service rate that needs to be provided; therefore, This can be understood as a condition for the stability of a queuing system. Step S6-3: Calculate the end-to-end time violation probability under steady-state conditions based on the supremum property and the deviation value. ; According to the supremum property, the link is end-to-end delay The unreliability is calculated using the following formula: ； in, express Number of routing aggregation nodes on the link; This indicates the arrival flow of the serial queuing system. Service capabilities; Indicates the maximum time-lapse boundary; express The moment generating function; This represents the lower boundary of end-to-end delay reliability. Indicates end-to-end delay; express The collection of service capabilities of all nodes on the link.

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