Method, device and medium for end-to-end latency analysis of mobile cyber-physical systems

Abstract

The embodiment of the application relates to the technical field of wireless network control, in particular to a kind of end-to-end delay analysis method, equipment and medium of mobile cyber-physical system, which comprises the following steps: defining arrival process and service process respectively, obtaining arrival cumulative quantity and cumulative service quantity;Respectively, scaling processing is carried out to arrival cumulative quantity and cumulative service quantity;Arrival cumulative quantity and cumulative service quantity after scaling processing are projected to signal-to-noise ratio domain, and network calculus is carried out under signal-to-noise ratio domain, to obtain calculus result;Simplification processing is carried out to calculus result, to obtain simplified formula;Based on lemma, inequality is obtained;And based on simplified formula and inequality, the end-to-end delay limit of stable perception is obtained.The embodiment of the application provides an end-to-end delay analysis method of mobile cyber-physical system, which can at least solve the problem that network calculus cannot be carried out due to the violation of traffic conservation law by mobile cyber-physical system.

Description

Technical Field

[0001] This application relates to the field of wireless network control technology, and in particular to an end-to-end delay analysis method, device and medium for mobile cyber-physical systems. Background Technology

[0002] Mobile Cyber-Physical Systems (M-CPS) utilize device mobility and wireless communication capabilities to achieve ubiquitous sensing, communication, and control functions over a wide area. Their ability to closely integrate and coordinate information and physical resources has led to their widespread application in various fields such as manufacturing, healthcare, shipbuilding, transportation, military, and infrastructure construction. They have gradually become one of the key technologies in the field of wireless network control.

[0003] Network calculus, as a network performance analysis tool, can be divided into deterministic network calculus and stochastic network calculus. Deterministic network calculus is relatively simple, aiming to obtain the worst-case boundary of network performance. Currently, the theory and research of deterministic network calculus are mature, but its analytical capabilities are limited. Stochastic network calculus aims to provide stochastic quality of service guarantees for networks. It must consider the random bursts and self-identity characteristics of network data flows, as well as factors such as access congestion and physical channel fading. Therefore, its application is relatively more complex, and different mathematical methods and expressions are often used to extend stochastic network calculus.

[0004] Currently, the analysis of local latency in Mobile Cyber-Physical Systems (M-PPS) typically employs stochastic geometry-based Mobile Edge Computing (MEC) vehicular ad hoc networks. However, since this analysis is based on the law of flow conservation, which is violated in M-PPS with edge computing, the existing analytical results cannot be directly extended to M-PPS. Summary of the Invention

[0005] This application provides an end-to-end delay analysis method, device, and medium for mobile cyber-physical systems, which solves the problem of network computation being impossible due to mobile cyber-physical systems violating the law of flow conservation.

[0006] To address the aforementioned technical problems, embodiments of this application provide an end-to-end delay analysis method for mobile cyber-physical systems, comprising: defining an arrival process and a service process respectively, and obtaining an arrival cumulative quantity and a cumulative service quantity; the cumulative service quantity includes edge computing cumulative service quantity, wireless channel cumulative service quantity, and remote control cumulative service quantity; scaling the arrival cumulative quantity and the cumulative service quantity respectively; projecting the scaled arrival cumulative quantity and the cumulative service quantity into the signal-to-noise ratio domain, and performing network calculations in the signal-to-noise ratio domain to obtain calculation results; simplifying the calculation results to obtain a simplified formula; obtaining an inequality based on a lemma; and obtaining a stable-aware end-to-end delay limit based on the simplified formula and the inequality.

[0007] In some exemplary embodiments, the arrival process and the service process are defined respectively to obtain the arrival accumulation and the cumulative service amount, including: defining the end-to-end delay respectively to obtain the limit of the cumulative arrival process; obtaining the wireless channel cumulative service amount based on the limit of the cumulative arrival process and the service rate in the time slot; obtaining the edge computing cumulative service amount based on the waiting time and the output rate of the edge computing processing delay; and obtaining the remote control cumulative service amount based on the indicator function and the output rate of the processing delay in the remote controller.

[0008] In some exemplary embodiments, end-to-end delays are defined to obtain the limits of the cumulative arrival process, including: defining the transmission delay of the wireless channel from the sensing device to the edge computing device, the processing delay of the edge computing, the transmission delay of the wireless channel from the edge computing device to the remote controller, the processing delay in the remote controller, and the transmission delay of the wireless channel from the remote controller to the actuator, respectively denoted as the first service node, the second service node, the third service node, the fourth service node, and the fifth service node, and represented by S1, S2, S3, S4, and S5 respectively; assuming that the sensing device periodically generates raw data at a rate of b frames / timeslot, with each frame containing L bits, the limits of the cumulative arrival process are obtained as shown in the following formula:

[0009]

[0010] Where A1(τ, t) represents the cumulative arrival and service process of the first service node during the interval [τ, t);

[0011] The service rate in a time slot is shown in the following formula:

[0012]

[0013] The cumulative service volume of the wireless channel is shown in the following formula:

[0014]

[0015] Where S1(τ,t) represents the cumulative service volume of the wireless channel; t represents the time slot; h(t) represents the wireless channel coefficient in time slot t; it is assumed that h(t) remains constant in each time slot t; B represents the channel bandwidth; N0 represents the power density of Gaussian white noise; p represents the transmit power from the transmitter to the receiver.

[0016] In some exemplary embodiments, the waiting time is as follows:

[0017]

[0018] Among them, T w This represents the waiting time; assuming each frame of raw data contains L bits, and processing is only performed after the entire frame has completely entered the edge computing device, the waiting time is obtained.

[0019] When the edge computing device receives a complete frame, it takes T seconds. p The time required to obtain device status information; assuming each frame of device status information contains bits, and the output rate of edge computing processing latency is frames / second, the cumulative service volume of edge computing is obtained as shown in the following formula:

[0020]

[0021] Where S2(τ, t) represents the cumulative service volume of edge computing; η represents the number of bits per frame representing device status information. d T is a constant representing the output rate of edge computing processing latency, measured in frames per second; d =T w +T p Tp is a constant, T w It is a random variable related to the time-varying wireless channel capacity, and T is obtained. d Distribution function:

[0022]

[0023] Among them, T d The distribution function follows a Gaussian distribution.

[0024] The cumulative service volume for remote control is:

[0025]

[0026] Where S4(τ, t) represents the cumulative service volume of remote control; Indicates the number of bits contained in each frame of the control signal; η r The output rate represents the processing latency in the remote controller, in frames per second; Tr represents the waiting time before processing, and Tr is a constant.

[0027] In some exemplary embodiments, scaling processing is performed on the arrival cumulative volume and cumulative service volume, including: reducing the initial incoming traffic based on a first scaling factor to obtain a reduced incoming traffic; scaling the cumulative service volume of the first service node and the cumulative service volume of the second service node to obtain a first scaled cumulative service volume and a second scaled cumulative service volume; reducing the reduced incoming traffic based on a second scaling factor, and scaling processing is performed on the first scaled cumulative service volume, the second scaled cumulative service volume, the cumulative service volume of the third service node, and the cumulative service volume of the fourth service node; before the second service node S2, data flows in the network at a size of L bits / frame, but after the second service node S2 provides service, the frame size is...

[0028] The first scaling factor is:

[0029]

[0030] make Reduce the initial incoming flow A1(τ, t);

[0031] make The cumulative service volume of the first service node and the cumulative service volume of the second service node are scaled to obtain the first scaled cumulative service volume and the second scaled cumulative service volume.

[0032] The second proportional factor is:

[0033]

[0034] The following formula is used to scale the incoming traffic, the first scaled cumulative service volume, the second scaled cumulative service volume, the third service node's cumulative service volume, and the fourth service node's cumulative service volume.

[0035]

[0036]

[0037]

[0038]

[0039] in,

[0040] In some exemplary embodiments, the arrival and service processes of each service node in the signal-to-noise ratio domain are as follows:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where g1(γ)=(1+γ) μB , g5(γ)=(1+γ) B as well as

[0048] In some exemplary embodiments, the calculation results are simplified by Merlin transform to obtain a simplified formula;

[0049] make The calculation results are simplified as shown in the following formula:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] in, And [ι] + =max{0, ι};

[0057] By connecting all service nodes in series, the system's service curve is as follows:

[0058]

[0059] Among them, the operator It is a (min, ×) convolution, defined as:

[0060]

[0061] In some exemplary embodiments, the lemma includes a first lemma and a second lemma;

[0062] Let x1(τ,t) and χ2(τ,t) be two independent nonnegative random processes; for s < 1 Merlin transform satisfies

[0063] The inequality leads to the first lemma:

[0064]

[0065] Define a system where the arrival process and the service process are represented as A(τ, t) and S(τ, t), respectively, and the corresponding signal-to-noise ratio (SNR) domain projection processes are respectively... and The delay probability satisfies the inequality Pr(D(t)>ω) ε )≤ε;

[0066] Where, ω ε Is ω satisfied? The minimum value yields the second lemma:

[0067]

[0068] Based on the first and second lemmas, we obtain the inequality:

[0069]

[0070]

[0071] The probability of a boundary violation due to marginal delay is shown in the following formula:

[0072]

[0073] The end-to-end delay bound for stable sensing is calculated using the delay violation probability; the bound for the delay violation probability is expressed as:

[0074]

[0075] In addition, embodiments of this application also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the aforementioned end-to-end latency analysis method for mobile cyber-physical systems.

[0076] In addition, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned end-to-end latency analysis method for mobile cyber-physical systems.

[0077] The technical solution provided in this application has at least the following advantages:

[0078] This application addresses the problem that existing local delay analysis methods for mobile cyber-physical systems (Mobile Cyber-Physical Systems) cannot be directly extended to Mobile Cyber-Physical Systems. This application provides an end-to-end delay analysis method, device, and medium for Mobile Cyber-Physical Systems. The method includes the following steps: defining an arrival process and a service process to obtain an arrival accumulation and a service accumulation; scaling the arrival accumulation and service accumulation; projecting the scaled arrival accumulation and service accumulation onto the signal-to-noise ratio (SNR) domain and performing network calculations in the SNR domain to obtain calculation results; simplifying the calculation results to obtain a simplified formula; obtaining an inequality based on a lemma; and obtaining a stable-aware end-to-end delay limit based on the simplified formula and the inequality.

[0079] This application provides an end-to-end latency analysis method for mobile cyber-physical systems (Mobile Cyber-Physical Systems). On one hand, it addresses the problem of network computation being impossible due to Mobile Cyber-Physical Systems violating the law of flow conservation. On the other hand, Mobile Cyber-Physical Systems with edge computing are multi-node networks containing wireless channels, edge computing nodes, and remote control nodes; this application solves the problem of calculating latency limits in multi-hop networks. Furthermore, as a control system, Mobile Cyber-Physical Systems require a stable, perceived latency limit; this application provides a stable, perceived latency limit through an end-to-end latency analysis method for Mobile Cyber-Physical Systems. This method can be extended to systems with multiple intra-system processing units where flow conservation is not enforced. Attached Figure Description

[0080] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations do not constitute a limitation on the embodiments, and unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0081] Figure 1 A flowchart illustrating an end-to-end delay analysis method for a mobile cyber-physical system provided in an embodiment of this application;

[0082] Figure 2 A flowchart illustrating an end-to-end latency analysis method for an edge computing-assisted mobile cyber-physical system provided in an embodiment of this application;

[0083] Figure 3 A schematic diagram of end-to-end delay from a sensing device to an actuator is provided as an embodiment of this application;

[0084] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0085] As can be seen from the background technology, there is a problem that existing local delay analysis methods for mobile cyber-physical systems cannot be directly extended to mobile cyber-physical systems.

[0086] The purpose of network calculus is to perform performance analysis on networks with non-probabilistic traffic distributions. The basic idea of ​​network calculus is to describe the maximum burstiness of traffic, control and quantify these bursts, and ensure that these bursts can be transmitted losslessly within the system, so as to calculate a deterministic upper bound on the end-to-end delay in the network based on the maximum burstiness. As a network performance analysis tool, network calculus can generally be divided into deterministic network calculus and stochastic network calculus. Deterministic network calculus is relatively simple, aiming to obtain the worst-case boundary of network performance. Currently, the theory and research of deterministic network calculus are mature, but its analytical capabilities are limited. Stochastic network calculus aims to provide random quality of service guarantees for the network. It needs to consider the random burstiness and self-recognition characteristics of network data flows, as well as factors such as network channel access congestion and physical channel fading. Therefore, its application is relatively more complex, and related technologies have employed different mathematical methods and expressions to extend stochastic network calculus.

[0087] Specifically, some related technologies have studied the modeling and analysis of mobile edge computing (MEC) vehicular ad hoc networks with local latency based on stochastic geometry, deriving closed-form analytical models for both uplink and downlink local latency. Other technologies combine stochastic geometry and queuing theory to analyze the latency performance of MEC networks with multi-core edge servers. Still other technologies consider MEC systems with finite computation buffers at the edge servers, where the latency characteristics of a discrete-time two-stage cascaded queuing system are derived using matrix geometry. The results of these related technologies cannot be directly extended to mobile cyber-physical systems (M-CPS). This is because these analyses are based on the law of flow conservation, which is violated in M-CPS with edge computing; for example, traffic leaving the edge computing node is only a small fraction of traffic arriving at that node. On the other hand, another related technology addresses this challenge by extending the arrival and service flow, but considers latency bound to only two hops. In M-CPS with edge computing, it involves three wireless channels, one edge computing node, and one remote controller, making it more complex.

[0088] In summary, the shortcomings of these related technologies are as follows: First, latency performance analysis cannot address traffic non-conservation models. While these technologies, combining stochastic geometry and queuing theory, can effectively analyze latency in some edge computing networks, they are all based on the law of traffic conservation. Typically, stochastic network calculus is built upon this law. In mobile cyber-physical systems with edge computing, data flow changes after passing through edge computing nodes and remote controller nodes, implying traffic non-conservation. Therefore, traditional stochastic network calculus is unsuitable for mobile cyber-physical systems with edge computing, rendering these related technologies inapplicable to traffic non-conservation cyber-physical systems.

[0089] Secondly, it is impossible to perform delay analysis on networks that have both wireless channels and serving nodes. Related methods are only applicable to two-hop networks or multi-hop networks with multiple identical nodes exhibiting independent and identical distribution properties. However, in real-world cyber-physical systems, a complete closed-loop system often consists of wireless channels, edge computing processing units, sensors, remote controllers, and actuators, typically requiring separate random network calculus for each node.

[0090] Furthermore, a mobile cyber-physical system with edge computing is a multi-node network consisting of wireless channels, edge computing nodes, and remote control nodes. Currently, there are no technologies available for latency performance analysis of multi-node networks with illegal traffic conservation. As a control system, a mobile cyber-physical system also requires a stable, perceived latency limit, and there are no technologies available for obtaining this stable, perceived latency limit.

[0091] To address the aforementioned technical problems, this application provides an end-to-end delay analysis method for mobile cyber-physical systems (CPS), comprising: defining an arrival process and a service process respectively, obtaining an arrival accumulation and a cumulative service amount; the cumulative service amount includes edge computing cumulative service amount, wireless channel cumulative service amount, and remote control cumulative service amount; scaling the arrival accumulation and cumulative service amount respectively; projecting the scaled arrival accumulation and cumulative service amount into the signal-to-noise ratio (SNR) domain, and performing network calculations in the SNR domain to obtain calculation results; simplifying the calculation results to obtain a simplified formula; obtaining an inequality based on a lemma; and obtaining a stable-aware end-to-end delay limit based on the simplified formula and the inequality. The end-to-end delay analysis method for CPS provided in this application not only solves the problem of network calculations being impossible due to CPS violations of the flow conservation law, but also solves the problem of calculating the delay limit of multi-hop networks, and further provides a stable-aware delay limit.

[0092] The embodiments of this application will now be described in detail with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the embodiments of this application to facilitate a better understanding of the application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments.

[0093] See Figure 1 This application provides an end-to-end latency analysis method for a mobile cyber-physical system, comprising the following steps:

[0094] Step S1: Define the arrival process and the service process respectively to obtain the arrival accumulation and the cumulative service amount; the cumulative service amount includes the edge computing cumulative service amount, the wireless channel cumulative service amount and the remote control cumulative service amount.

[0095] Step S2: Scaling is performed on the cumulative arrival amount and the cumulative service amount, respectively.

[0096] Step S3: Project the scaled cumulative arrivals and cumulative service volume into the signal-to-noise ratio domain, and perform network calculations in the signal-to-noise ratio domain to obtain the calculation results.

[0097] Step S4: Simplify the calculation results to obtain the simplified formula.

[0098] Step S5: Based on the lemma, the inequality is obtained; and based on the simplified form and the inequality, the end-to-end delay bound of stable sensing is obtained.

[0099] The network calculus is divided into five steps: Step S1: Define the arrival process and the service process, obtaining the arrival accumulation and the cumulative service volume. The upper bound of the arrival accumulation is described using a linear function. The service process includes the wireless channel part, the edge computing part, and the remote control part. The upper bound of the service accumulation of the wireless channel is described as the sum of the channel capacities; the edge computing and remote control are described by the product of the service rate and the service time. Step S2: Scale the arrival accumulation and the cumulative service volume obtained in Step S1 to address the energy non-conservation problem of each service node. Next, Step S3: Project the scaled arrival accumulation and the cumulative service volume into the signal-to-noise ratio (SNR) domain, and perform network calculus in the SNR domain to obtain the calculation result. Project the scaled arrival accumulation and service accumulation obtained in Step S2 into the SNR domain so that (min, ×) network calculus can be used in this domain. Step S4: Simplify the calculation result to obtain a simplified formula. Specifically, simplification can be achieved by performing a Mellin transform on the result of step S3, using the Mellin transform to simplify the tedious calculations. Step S5: Based on the lemma, inequalities are obtained; and based on the simplified equation and the inequalities, the stable-aware end-to-end delay bound is obtained. Based on the relevant lemma, the arrival process and various service processes are linked together to analyze the delay of the entire system, and the stable-aware delay bound is given. Figure 2 This diagram illustrates an end-to-end latency analysis method for a mobile cyber-physical system assisted by edge computing. It can also be understood as... Figure 2 A flowchart illustrating the network calculation of an embodiment of this application is provided.

[0100] In some embodiments, step S1 defines the arrival process and the service process respectively to obtain the arrival accumulation and the cumulative service amount, including: defining the end-to-end delay respectively to obtain the limit of the cumulative arrival process; obtaining the wireless channel cumulative service amount based on the limit of the cumulative arrival process and the service rate in the time slot; obtaining the edge computing cumulative service amount based on the waiting time and the output rate of the edge computing processing delay; and obtaining the remote control cumulative service amount based on the indicator function and the output rate of the processing delay in the remote controller.

[0101] In some embodiments, the end-to-end delay is defined to obtain the boundary of the cumulative arrival process, including: defining the transmission delay of the wireless channel from the sensing device to the edge computing device, the processing delay of the edge computing, the transmission delay of the wireless channel from the edge computing device to the remote controller, the processing delay in the remote controller, and the transmission delay of the wireless channel from the remote controller to the actuator, respectively, and denoted as the first service node, the second service node, the third service node, the fourth service node, and the fifth service node, and represented by S1, S2, S3, S4, and S5 respectively.

[0102] Figure 3 A schematic diagram of the end-to-end delay from the sensing device to the actuator is shown. The end-to-end delay is the delay from the sensing device to the actuator, including the transmission delay of the wireless channel S1 from the sensing device to the edge computing device, the processing delay of the edge computing S2, the transmission delay of the wireless channel S3 from the edge computing device to the remote controller, the processing delay in the remote controller S4, and the transmission delay in the wireless channel S5 from the remote controller to the actuator. (A...) i (τ, t) and S i (τ, t) represents the cumulative arrival and service process of node i during the interval [τ, t), where i = {1, 2, 3, 4, 5}. This process is as follows: Figure 3 As shown. Wherein, each departure of service node i from A i It is directly fed to the next service node i+1.

[0103] Assuming the sensing device periodically generates raw data at a rate of b frames / timeslot, with each frame containing L bits, the boundary of the cumulative arrival process is obtained as shown in the following formula:

[0104]

[0105] Where A1(τ, t) represents the cumulative arrival and service process of the first service node during the interval [τ, t).

[0106] In the expression for the limit of the cumulative arrival process, It is the smallest integer greater than 1. It should be noted that the input and output data types and frame sizes of S2 and S4 are different, meaning that the flow conservation law no longer applies. This application addresses this issue by introducing a scaling factor and using network calculus to analyze end-to-end latency performance.

[0107] This application embodiment considers the system to be time-slotted, with each time slot denoted by t∈{0,1,…} and a time slot duration of Δt. Let the wireless channel coefficient in time slot t be h(t). It is assumed that h(t) remains constant within each time slot, but may change at the time slot boundaries. Furthermore, h(t) is independent and identically distributed across time slot t. Therefore, the wireless channel provides a time-varying service rate.

[0108] The service rate in time slot t is shown in the following formula:

[0109]

[0110] The cumulative service volume of the wireless channel is shown in the following formula:

[0111]

[0112] Where S1(τ,t) represents the cumulative service volume of the wireless channel; t represents the time slot; h(t) represents the wireless channel coefficient in time slot t; it is assumed that h(t) remains constant in each time slot t; B represents the channel bandwidth; N0 represents the power density of Gaussian white noise; p represents the transmit power from the transmitter to the receiver.

[0113] In some embodiments, the waiting time T w As shown in the following formula:

[0114]

[0115] Among them, T w This represents the waiting time; assuming each frame of raw data contains L bits, processing only occurs after the entire frame has completely entered the edge computing device, resulting in the waiting time T. w .

[0116] When the edge computing device receives a complete frame, it takes T seconds. p The time required to obtain device status information; assuming each frame of device status information contains bits, and the output rate of edge computing processing latency is frames / second, the cumulative service volume of edge computing is obtained as shown in the following formula:

[0117]

[0118] Where S2(τ, t) represents the cumulative service volume of edge computing; η represents the number of bits per frame representing device status information. d T is a constant representing the output rate of edge computing processing latency, measured in frames per second; d =T w +T p Tp is a constant, T w It is a random variable related to the time-varying wireless channel capacity, and T is obtained. d Distribution function:

[0119]

[0120] According to the central limit theorem, T d The distribution function follows a Gaussian distribution.

[0121] Assuming the control signal contains per frame Bit, the output rate of S4 is η r Frames per second. Similar to the edge computing process, the cumulative service volume for remote control is:

[0122]

[0123] Where S4(τ, t) represents the cumulative service volume of remote control; Indicates the number of bits contained in each frame of the control signal; η r The output rate represents the processing latency in the remote controller, in frames per second; Tr represents the waiting time before processing, and Tr is a constant.

[0124] In some embodiments, step S2 involves scaling the arrival accumulation and the accumulation service volume, including:

[0125] Based on the first scaling factor, the initial incoming traffic is reduced to obtain the reduced incoming traffic; and the cumulative service volume of the first service node and the cumulative service volume of the second service node are scaled respectively to obtain the first scaled cumulative service volume and the second scaled cumulative service volume.

[0126] Based on the second scaling factor, the incoming traffic is reduced, and scaling processing is applied to the first scaled cumulative service volume, the second scaled cumulative service volume, the third service node's cumulative service volume, and the fourth service node's cumulative service volume.

[0127] Before the second service node S2, data flows through the network at a size of L bits / frame, but after the second service node S2 provides service, the frame size is... This means that flow is not conserved in cyber-physical systems. On the other hand, to obtain the upper limit of latency, stochastic network calculus based on the law of flow conservation is usually used.

[0128] To address this issue, this application introduces a first scaling factor to facilitate calculation.

[0129] The first scaling factor is:

[0130]

[0131] make We reduce the initial incoming flow A1(τ, t); in addition, to eliminate its impact on the delay boundary calculation, we also need to scale the service accumulation S1 and S2.

[0132] make The cumulative service volume of the first service node S1 and the cumulative service volume of the second service node S2 are scaled to obtain the first scaled cumulative service volume and the second scaled cumulative service volume.

[0133] The second proportional factor is:

[0134]

[0135] The following formula reduces the incoming flow. First Scaling Cumulative Service Volume Second scaling cumulative service volume The cumulative service volume of the third service node S3 and the cumulative service volume of the fourth service node S4 are scaled.

[0136]

[0137]

[0138]

[0139]

[0140] in,

[0141] Then, the arrival and service processes, scaled according to a certain ratio, are mapped to the signal-to-noise ratio (SNR) domain. In the SNR domain, the arrival process... Service process Each by and Provided.

[0142] Therefore, after scaling with flow conservation, in the SNR domain, Figure 3 The arrival process Service process It is represented as follows:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] Where g1(γ)=(1+γ) μB , g5(γ)=(1+γ) B as well as

[0150] In some embodiments, the calculation results are simplified by Merlin transform to obtain a simplified formula;

[0151] make The calculation results are simplified as shown in the following formula:

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] in, And [ι] + =max{0, ι};

[0159] for Figure 3 The system consists of a topology with five service nodes connected in series. The service curve of the system is as follows:

[0160]

[0161] Among them, the operator It is a (min, ×) convolution, defined as:

[0162]

[0163] To illustrate how network calculus can be used to calculate the end-to-end delay from the sensor to the actuator, such as... Figure 3 As shown, this application introduces the following two lemmas.

[0164] Lemma 1: Let x1(τ, t) and x2(τ, t) be two independent nonnegative stochastic processes. For s < 1 The Mellin transform satisfies the inequality:

[0165]

[0166] Second Lemma: Define a system where the arrival process and the service process are represented as A(τ, t) and S(τ, t), respectively, and the corresponding signal-to-noise ratio (SNR) domain projection processes are respectively... and The delay probability satisfies the inequality Pr(D(t)>ω) ε )≤ε;,

[0167] Where, ω ε Is ω satisfied? The minimum value yields the second lemma:

[0168]

[0169] Based on the first and second lemmas, we obtain the inequality:

[0170]

[0171]

[0172] The probability of violating the marginal delay boundary is shown in the following formula:

[0173]

[0174] The end-to-end delay bound for stable sensing is calculated using the delay violation probability; the bound for the E2E delay violation probability is expressed as:

[0175]

[0176] The above formula obtains the end-to-end delay limit of stable sensing in a numerical manner.

[0177] The end-to-end delay analysis method for mobile cyber-physical systems provided in this application is mainly applicable to network calculus methods for end-to-end delay analysis of cyber-physical systems that do not conserve traffic and consider wireless fading channels, edge computing, and remote controllers.

[0178] Compared with existing technologies, the end-to-end latency analysis method for mobile cyber-physical systems provided in this application has the advantage of expanding the applicability of network calculus. In cyber-physical systems with edge computing, the extraction or transformation of information during edge computing and remote controller processing can lead to a non-conservation of input and output traffic. However, traditional network calculus, whether deterministic or stochastic, is based on the flow conservation theorem.

[0179] The method in this application introduces a scaling factor to scale part of the arrival and service processes to achieve mathematically conserved traffic. Therefore, network calculus can be used for end-to-end latency analysis even for networks with non-conserved traffic. Furthermore, a cyber-physical system with edge computing is a collection of wireless channels, edge computing units, sensors, remote controllers, and actuators, not a simple series connection of identical and independent processing units.

[0180] The method in this application fully considers various processes when designing network computation, including arrival processes, wireless channel service processes, edge computing service processes, and remote control service processes. It simplifies traditionally cumbersome network computation through SNR domain mapping and Mellin transform, and finally provides a stable-aware end-to-end delay limit. This method can also be extended to systems with non-conservative flow and multiple intra-system processing units.

[0181] Another embodiment of this application relates to an electronic device, such as... Figure 4 As shown, it includes at least one processor 101; and a memory 102 communicatively connected to at least one processor 101; wherein the memory 102 stores instructions executable by at least one processor 101, the instructions being executed by at least one processor 101 to enable at least one processor 101 to perform any of the above method embodiments.

[0182] The memory 102 and processor 101 are connected via a bus, which may include any number of interconnecting buses and bridges. The bus connects various circuits of one or more processors 101 and memory 102 together. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. A bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by processor 101 is transmitted over a wireless medium via an antenna, which further receives data and transmits it to processor 101.

[0183] Processor 101 is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory 102 can be used to store data used by processor 101 during operation.

[0184] Another embodiment of this application relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0185] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0186] Based on the above technical solutions, this application addresses the problem that existing local delay analysis methods for mobile cyber-physical systems cannot be directly extended to mobile cyber-physical systems. This application provides an end-to-end delay analysis method, device, and medium for mobile cyber-physical systems. The method includes the following steps: defining the arrival process and the service process respectively to obtain the arrival accumulation and the cumulative service amount; scaling the arrival accumulation and the cumulative service amount respectively; projecting the scaled arrival accumulation and the cumulative service amount into the signal-to-noise ratio domain, and performing network calculations in the signal-to-noise ratio domain to obtain the calculation results; simplifying the calculation results to obtain a simplified formula; obtaining an inequality based on the lemma; and obtaining a stable-aware end-to-end delay limit based on the simplified formula and the inequality.

[0187] This application provides an end-to-end latency analysis method for mobile cyber-physical systems (Mobile Cyber-Physical Systems). On one hand, it addresses the problem of network computation being impossible due to Mobile Cyber-Physical Systems violating the law of flow conservation. On the other hand, Mobile Cyber-Physical Systems with edge computing are multi-node networks containing wireless channels, edge computing nodes, and remote control nodes; this application solves the problem of calculating latency limits in multi-hop networks. Furthermore, as a control system, Mobile Cyber-Physical Systems require a stable, perceived latency limit; this application provides a stable, perceived latency limit through an end-to-end latency analysis method for Mobile Cyber-Physical Systems. This method can be extended to systems with multiple intra-system processing units where flow conservation is not enforced.

[0188] Those skilled in the art will understand that the above-described embodiments are specific examples of implementing this application, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of this application. Any person skilled in the art can make their own modifications and alterations without departing from the spirit and scope of this application; therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. An end-to-end delay analysis method for a mobile cyber-physical system, characterized in that, include: The arrival process and service process are defined separately to obtain the arrival accumulation and the cumulative service volume; the cumulative service volume includes the edge computing cumulative service volume, the wireless channel cumulative service volume, and the remote control cumulative service volume. The cumulative arrival amount and the cumulative service amount are scaled respectively. The scaled arrival accumulation and cumulative service volume are projected onto the signal-to-noise ratio domain, and network calculations are performed in the signal-to-noise ratio domain to obtain the calculation results. The calculation results are simplified to obtain a simplified formula; Based on the lemma, the inequality is obtained; Based on the simplification and the inequality, the end-to-end delay bound of stable sensing is obtained.

2. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 1, characterized in that, The definition of the arrival process and service process, and the resulting cumulative arrival volume and cumulative service volume, include: By defining the end-to-end delay separately, the limits of the cumulative arrival process are obtained; Based on the limits of the cumulative arrival process and the service rate in the time slot, the cumulative service volume of the wireless channel is obtained. The cumulative service volume of edge computing is obtained based on the output rate of waiting time and edge computing processing latency. The cumulative service volume of remote control is obtained based on the indicator function and the output rate of the processing delay in the remote controller.

3. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 2, characterized in that, The definition of end-to-end delays to obtain the limits of the cumulative arrival process includes: The transmission delay of the wireless channel from the sensing device to the edge computing device, the processing delay of the edge computing, the transmission delay of the wireless channel from the edge computing device to the remote controller, the processing delay in the remote controller, and the transmission delay of the wireless channel from the remote controller to the actuator are defined and denoted as the first service node, the second service node, the third service node, the fourth service node, and the fifth service node, respectively, and represented by S1, S2, S3, S4, and S5. Assuming the sensing device periodically generates raw data at a rate of b frames / timeslot, with each frame containing L bits, the boundary of the cumulative arrival process is obtained as shown in the following formula: Where A1(τ, t) represents the cumulative arrival process of the first service node during the interval [τ, t); The service rate in the time slot is shown in the following formula: The cumulative service volume of the wireless channel is shown in the following formula: Where S1(τ,t) represents the cumulative service volume of the wireless channel; t represents the time slot; h(t) represents the wireless channel coefficient in time slot t; it is assumed that h(t) remains constant in each time slot t; B represents the channel bandwidth; N0 represents the power density of Gaussian white noise; p represents the transmit power from the transmitter to the receiver.

4. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 3, characterized in that, The waiting time is shown in the following formula: Among them, T w This represents the waiting time; assuming each frame of raw data contains L bits, and processing is only performed after the entire frame has completely entered the edge computing device, the waiting time is obtained. When the edge computing device receives a complete frame, it takes T seconds. p The time is used to obtain device status information; assuming that each frame of device status information has bits, the cumulative service volume of edge computing is obtained as shown in the following formula: Where S2(τ,t) represents the cumulative service volume of edge computing; η represents the number of bits per frame representing device status information. d I(t-τ≥T) is a constant representing the output rate of edge computing processing latency, measured in frames per second; d ) is an indicator function; T d =T w +T p T p T is a constant. w It is a random variable related to the time-varying wireless channel capacity, and T is obtained. d Distribution function: Among them, T d The distribution function follows a Gaussian distribution; The cumulative service volume for remote control is: Where S4(τ,t) represents the cumulative service volume of remote control; Indicates the number of bits contained in each frame of the control signal; η r The output rate representing the processing latency in the remote controller, in frames per second; T r T represents the waiting time before processing. r It is a constant; I(t-τ≥T) r ) is an indicator function.

5. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 4, characterized in that, The scaling processing of the accumulated arrivals and the accumulated service volume includes: Based on the first scaling factor, the initial incoming traffic is reduced to obtain the reduced incoming traffic; and the cumulative service volume of the first service node and the cumulative service volume of the second service node are scaled respectively to obtain the first scaled cumulative service volume and the second scaled cumulative service volume. Based on the second scaling factor, the reduced incoming traffic is reduced, and scaling processing is applied to the first scaled cumulative service volume, the second scaled cumulative service volume, the cumulative service volume of the third service node, and the cumulative service volume of the fourth service node. Before the second service node S2, data flows through the network at a size of L bits / frame, but after the second service node S2 provides service, the frame size is... The first scaling factor is: make Reduce the initial incoming flow A1(τ,t); make The cumulative service volume of the first service node and the cumulative service volume of the second service node are scaled to obtain the first scaled cumulative service volume and the second scaled cumulative service volume. The second scaling factor is: The following formula is used to scale the reduced incoming traffic, the first scaled cumulative service volume, the second scaled cumulative service volume, the cumulative service volume of the third service node, and the cumulative service volume of the fourth service node. in, 6. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 5, characterized in that, In the signal-to-noise ratio domain, the arrival and service processes of each service node are as follows: Where, g1(γ)=(1+γ) μB , g5(γ)=(1+y) B as well as 7. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 6, characterized in that, The calculation results are simplified by Merlin transform to obtain a simplified formula; make The calculation results are simplified as shown in the following formula: in, And [ι] + =max{0, ι}; By connecting all service nodes in series, the system's service curve is as follows: Among them, the operator It is a (min, ×) convolution, defined as:

8. The end-to-end delay analysis method for mobile cyber-physical systems according to claim 7, characterized in that, The lemma includes the first lemma and the second lemma.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform an end-to-end latency analysis method for a mobile cyber-physical system as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the end-to-end delay analysis method for the mobile cyber-physical system according to any one of claims 1 to 8.

Images