CN114520992A - Method for optimizing time delay performance of fog access network based on cluster process - Google Patents

Method for optimizing time delay performance of fog access network based on cluster process Download PDF

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CN114520992A
CN114520992A CN202210152805.2A CN202210152805A CN114520992A CN 114520992 A CN114520992 A CN 114520992A CN 202210152805 A CN202210152805 A CN 202210152805A CN 114520992 A CN114520992 A CN 114520992A
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target user
user
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CN114520992B (en
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郑亚楠
胡昊南
殷波
姜言
张继良
张�杰
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Guangzhou Car Garment Technology Co ltd
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W40/00—Communication routing or communication path finding
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Abstract

The invention relates to the technical field of mobile communication, in particular to a method for optimizing time delay performance of a fog access network based on a cluster process, which comprises the steps of constructing a fog access network model based on a Poisson cluster process and initializing the model; defining a user positioned at the origin as a target user, calculating the signal-to-interference ratio of the target user, judging whether the value is greater than a set threshold value, if so, recording the value of the average local delay as 1, otherwise, calculating the value of the average local delay of successful unloading of the target user; judging whether the average local time delay is smaller than a set time delay threshold value or not, if so, retaining the current parameters and the average local time delay corresponding to the parameters, and selecting the parameters with the minimum average local time delay as the parameters of the Poisson cluster process-based fog access network model to unload the tasks; the invention achieves the improvement of the time delay performance of the whole system by limiting the computing resources and the average local time delay of the fog access point and jointly optimizing the sizes of the uplink power control compensation factor and the user activity factor.

Description

Method for optimizing time delay performance of fog access network based on cluster process
Technical Field
The invention relates to the technical field of mobile communication, in particular to a method for optimizing time delay performance of a fog access network based on a cluster process.
Background
With the development of mobile communication technology, new applications (such as virtual reality technology and augmented reality technology) such as a computational density type and a time delay sensitive type show a trend of explosive growth, and Gartner predicts that by 2020, the number of network terminals reaches 208 hundred million, and the composite growth rate is 34%. In accordance with the united states published reports on 2016-2045 new technology trends, over 1000 million devices were connected into the access network by 2045. With the proliferation of user accessible devices, massive data and network traffic are generated, with the attendant problems of significant end-to-end processing delay and a dramatic drop in user experience. To solve such problems, the delay performance becomes one of the key indicators for evaluating the quality of mobile communication. Meanwhile, in the future B5G network, the delay requirement is limited to be even 1ms, and in order to meet such delay requirement, a new network architecture is proposed: fog wireless access network architecture. The fog wireless access network makes full use of the computing power of users and edge equipment, and the deployment of the fog wireless access network architecture can effectively reduce the end-to-end time delay. Uplink transmission delay is the main component of end-to-end delay in a fog access network, and average local delay is the main component affecting transmission delay. However, the average local latency in a fog access network is affected by user and fog access point deployment strategies, power control, user liveness, and the like. It is unknown whether the average local time delay of the mist access network can be reduced by introducing cluster distribution during deployment of the user and the mist access node. Therefore, a new technology is urgently needed to analyze the time delay performance of the fog access network based on the cluster process, so that key factors influencing the time delay performance of the network are extracted, and operators are helped to deploy network architectures. The unique technology of random geometry is applied to wireless network research, can convert abstract problems into mathematical derivation problems, and effectively solves the problem that average local time delay cannot be calculated. However, the delay obtained by the research still cannot meet the requirement of the future network on the delay, how to further reduce the delay becomes a bottleneck for improving the network performance, and the delay is widely regarded by research institutions, equipment manufacturers, mobile communication operators and the like.
In conclusion, the invention designs a time delay performance analysis optimization model of the fog access network based on the clustering process. Under this model, the locations of the users and the fog access points are modeled as a model that is closer to the actual distribution. In addition, the scheme provides a new method for calculating the average local time delay according to the fog access network model based on the cluster process, and provides reasonable approximation, aiming at solving the problem that the average local time delay is difficult to calculate. Based on the theoretical analysis result of the average local time delay, factors influencing the time delay performance of the fog access network are analyzed, and the network performance is improved through the combined optimization of user activity factors, uplink power control compensation factors and the like.
Disclosure of Invention
In order to optimize the mist access network delay and improve user experience and network performance, the invention provides a method for optimizing the mist access network delay performance based on a cluster process, as shown in fig. 2, which specifically comprises the following steps:
step 101: constructing a Poisson cluster process-based fog access network model, initializing an algorithm, setting parameter values, enabling a signal-to-interference ratio threshold value theta to be 0dB, enabling an uplink transmission power control compensation factor epsilon to be 0, enabling epsilon to be [0,1], enabling a path loss index alpha to be 3 and enabling alpha to be {3,4 };
Step 102: defining a user positioned at an original point as a target user, and calculating the signal-to-interference ratio of the target user and recording the signal-to-interference ratio as SIR;
step 103: judging whether the SIR of the target user is larger than a signal-to-interference ratio threshold theta, if so, indicating that the target user can successfully unload, and assuming that the average local time delay is recorded as D, and making D equal to 1;
step 104: if the SIR of the target user is smaller than the signal to interference ratio threshold value theta, the target user fails to unload in the time slot, and the target user continues to try to unload in the next time slot;
step 105: calculating the value of an average local delay log (MLD) of successful unloading of a target user;
step 106: judging whether the average local time delay MLD is smaller than a set time delay threshold tau, if so, reserving the epsilon value and the corresponding MLD value;
step 107: if yes, abandoning the epsilon value, readjusting epsilon by the step size delta epsilon, and executing the step 103 to the step 106 again;
step 108: selecting an MLD value with the minimum MLD value and the corresponding epsilon value from all the obtained epsilon values and the corresponding MLD values as the optimal MLD value and epsilon value when the road loss index alpha is 3;
step 109: step 203-step 208 are executed again by letting α be 4, and an optimal MLD value and an optimal epsilon value when α is 4 are obtained;
Step 110: and judging whether the MLD value when the alpha is 3 is smaller than that when the alpha is 4, if so, making the alpha be 4 and taking the corresponding MLD value and the epsilon value, otherwise, making the alpha be 4 and taking the corresponding MLD value and the epsilon value as unloading parameters.
Further, the fog access network model based on the poisson cluster process at least comprises a terminal layer and an access layer, wherein the terminal layer is composed of a plurality of user devices; the access layer is composed of a plurality of fog access points, and the number of user equipment covered by each fog access point is different and known.
Further, the process of constructing the poisson cluster process-based mist access network model comprises the following steps:
determining the coverage range of a Poisson cluster process-based fog access network model, and generating N in the coverage rangefFog access points, each obeying a density of λfThe poisson point process of (a);
using a fog access point as the center of a circle and the radius as
Figure BDA0003511112950000031
In the range of (1) to generate NuAnd (4) users.
Further, the SIR of the target user is expressed as:
Figure BDA0003511112950000032
wherein, YoThe distance between the target fog access point and the target user is obtained; h isoThe power gain between the target fog access point and the target user is obtained; y isnAs interferenceThe distance between the user and the target fog access point; rnTo interfere with the distance between the user and the fog access point to which it is connected; h is nTo interfere with the power gain between the user and his connected fog access point; phi (phi) ofnIs a set of interfering users; ε represents an uplink transmission power control compensation factor; a is anRepresenting the probability of interfering with the upload of the user; l (| r |) r-αR represents a distance, and α is a road loss index.
Further, the signal-to-interference ratio threshold θ is expressed as:
Figure BDA0003511112950000033
wherein, R is the uplink transmission rate; b is the total bandwidth of the wireless channel transmission.
Further, calculating the value of the average local delay log MLD of the successful offloading of the target user, that is, based on the knowledge of random geometric theory, calculating the probability that the SIR received by the target user is greater than a certain threshold θ, and recording the probability as ps(θ); p is to bes(θ) as a random variable, count psB-order moment M of (theta)bBy substituting b-1 into MbThe MLD value is recorded as the average local delay.
Further, the probability p that the target user receives an SIR greater than the threshold value thetas(θ) is expressed as:
Figure BDA0003511112950000041
the user activity interference method comprises the following steps that p is interference user activity, the value range of p is 0-1, and a user can set the interference user activity according to needs, wherein the interference user activity is the sum of the interference user activity and the user activity as an implementation mode; rnTo interfere with the distance between the user and the fog access point to which it is connected; alpha is a path loss index; ε represents an uplink transmission power control compensation factor; y is oThe distance between the target fog access point and the target user is obtained; the target user in real life transmits data packet to the fog access point through uplink, and then the service target usesThe fog access point of the user is the target fog access point, and the distance between the target user and the fog access point serving the target user is the distance Y between the target user and the target fog access pointoOther users active in the same time slot will interfere with the transmission of the target user, and the distance between the other users and the access point of the fog serving these users is denoted Rn。
Further, when the average local delay MLD value of successful unloading of the target user is set as that when the target user unloads the task to the fog access point, the target user tries to send the data packet to the fog access point in each time slot, and the time slot number of the data packet which is tried to be sent by the target user when the target user successfully sends the data packet for the first time is cut off.
The invention provides a cluster process-based time delay analysis optimization scheme for a fog access network, which jointly optimizes the sizes of uplink power control compensation factors and path loss indexes by limiting parameters related to communication resource allocation, such as the number of users in the same cluster and the bandwidth obtained by each user, so as to improve the time delay performance of the whole system.
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FIG. 1 is a network model of a fog access network based on a clustering process according to the present invention;
FIG. 2 is a flow chart of an algorithm for analyzing and optimizing the delay performance of the fog access network based on the clustering process in the embodiment of the invention;
fig. 3 is a graph of the uplink power control factor versus the average local delay after the optimization algorithm is performed.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method for optimizing time delay performance of a fog access network based on a clustering process, which specifically comprises the following steps:
step 101: constructing a Poisson cluster process-based fog access network model, initializing an algorithm, setting parameter values, enabling a signal-to-interference ratio threshold value theta to be 0dB, enabling an uplink transmission power control compensation factor epsilon to be 0 epsilon, and epsilon to be [0,1], enabling a path loss index alpha to be 3 and enabling alpha to be {3,4 };
Step 102: defining a user positioned at an origin point as a target user, and calculating the signal-to-interference ratio of the target user and recording the signal-to-interference ratio as SIR;
step 103: judging whether the SIR of the target user is larger than a signal-to-interference ratio threshold theta, if so, indicating that the target user can successfully unload, and assuming that the average local time delay is recorded as D, and making D equal to 1;
step 104: if the SIR of the target user is smaller than the signal-to-interference ratio threshold value theta, the unloading failure of the target user in the time slot is indicated, and the target user can continuously try to unload in the next time slot;
step 105: calculating the value of an average local delay log (MLD) of successful unloading of a target user;
step 106: judging whether the average local time delay MLD is smaller than a set time delay threshold tau, if so, reserving the epsilon value and the corresponding MLD value;
step 107: if yes, abandoning the epsilon value, readjusting epsilon by the step size delta epsilon, and executing the step 103 to the step 106 again;
step 108: selecting an MLD value with the minimum MLD value and the corresponding epsilon value from all the obtained epsilon values and the corresponding MLD values as the optimal MLD value and epsilon value when the road loss index alpha is 3;
step 109: step 203-step 208 are executed again by letting α be 4, and an optimal MLD value and an optimal epsilon value when α is 4 are obtained;
Step 110: and judging whether the MLD value when the alpha is 3 is smaller than that when the alpha is 4, if so, making the alpha be 4 and taking the corresponding MLD value and the epsilon value, otherwise, making the alpha be 4 and taking the corresponding MLD value and the epsilon value as unloading parameters.
Example 1
The network model provided by the invention comprises two layers: the first layer is an equipment layer (front end) which comprises a smart phone, a tablet computer, wearable intelligent equipment and the like; the second layer is the access layer (near end) including fog access points, etc.
The location distribution of the user equipment at the front end and the location distribution of the near-end fog access points have correlation, generally, the fog access points are deployed in places with relatively dense user distribution, and a fog access point deployment strategy must be researched, namely whether the fog access nodes can reduce uplink transmission delay in the fog access network or not according to a certain rule during deployment.
The near-end fog access node has the calculation and cache capacity and can support most of the service flow in the network. Thus, the fog access point provides high quality, low latency communication services to users of an increasing number of latency sensitive applications. In actual life, the positions of the users and the fog access points are related, for example, the users are often distributed at positions close to the fog access points, so that the users are considered to be uniformly distributed around the fog access points with the radius of the fog access points as the center of a circle
Figure BDA0003511112950000061
Where c ═ pi λ, λ is the density of the mist access points.
The position of the mist access point is generated according to the poisson point process, denoted Xk，k∈Nf，NfThe number of the fog access points in the range with the radius r; the user location connected to the target fog access point is denoted as Yn,k，n∈Nk，NkRepresenting the number of users in the coverage area of the kth fog access point. Assuming that the path loss between the user and the fog access point is small-scale fading, the log-distance model between the user and the fog access point is expressed as:
l(|r|)＝r-α
where r is the distance between the user and the fog access point and α is the road loss index.
Defining that a transmission link from a user n to a fog access point k experiences Rayleigh fading (Rayleigh fading) in small-scale fading, the power gain h of the link isn,kObeying an exponential distribution with mean μ, expressed as:
hn,k～exp(μ)；
in order to express the SIR expression received by a target user, a target fog access point is placed into an origin point, a user connected to the fog access point positioned at the origin point is a target user, and the distance between the target fog access point and the target user is expressed as Y under the condition that only one interference user exists in other cellsoThe power gain between the two is denoted as hoThe distance between the interfering user and the target fog access point is denoted as Y nThe distance between the interfering user and the fog access point to which it is connected is denoted RnThe power gain between the two is denoted as hnThen the SIR received by the fog access point at the origin can be expressed as:
Figure BDA0003511112950000071
wherein phi isnDenoted as interfering users,. epsilon.denotes the uplink transmission power control compensation factor, anRepresents the probability of interfering with the upload of the user, and an-bernoulli (p), i.e. anAccording to the Bernoulli distribution.
The invention is based on a fog access point deployment model of cluster distribution, and the probability that SIR received by a target user is larger than a certain threshold value theta is expressed as ps(θ)，psThe b-order matrix of (theta) is denoted as MbThe average local delay is denoted as L, which means the number of times of attempts in the process of first successful reception of a data packet sent by a sending end by a receiving end in a wireless link. Assuming that the distance between the transmitting end and the receiving end is a random variable R, the average local delay can be represented as E L]. Since the transmission power and the fading process are subject to the independent same distribution model, the probability that the SIR of the receiving end is greater than the threshold value theta is also subject to the independent same distribution. The average local delay can therefore be expressed as:
Figure BDA0003511112950000072
substituting b-1 into M based on SIR expression given in example 1bIn (b), the following relationship is obtained Is represented by the following formula:
Figure BDA0003511112950000073
example 2
The model in fig. 1 considers a cluster distribution based deployment model of fog access points, combining the network model and basic knowledge in example 1, ps(θ) can be expressed as:
Figure BDA0003511112950000081
in addition to this, to obtain MbThe invention proposes the following theorem:
the fog access point is simulated into a poisson point process with the density of c/pi, and users are uniformly distributed around the fog access point with the circle center and the radius of the fog access point
Figure BDA0003511112950000082
In the range of (1), | Yo|2Uniformly distributed in the range of 0-1/c, | Rn|2Uniformly distributed in the range of 0-1/c, uniformly distributed in the range of 0-2 pi, and Rn 2＝u、Yo 2＝v、
Figure BDA0003511112950000083
Then the closed-form solution of the average local delay, i.e. MbCan be expressed as:
Figure BDA0003511112950000084
wherein eta is represented by
Figure BDA0003511112950000085
b represents an order, the value of which is a positive integer; x is the square of the distance between other interfering users and the target user; θ is the SIR threshold.
However, the theoretical expression includes quadruple integration, and in order to save calculation time and reduce calculation complexity, the invention provides the following approximate method:
distance Y between target fog access point and interference usernApproximating the distance between the target fog access point and the fog access point to which the interfering user is connected, then the approximation result
Figure BDA0003511112950000086
The closed-form solution of (c) can be expressed as:
Figure BDA0003511112950000091
wherein the content of the first and second substances,
Figure BDA0003511112950000092
Figure BDA0003511112950000093
is coefficient of quadratic term, expressed as
Figure BDA0003511112950000094
Γ (x) represents a gamma function.
Concept pair introducing meta distribution
Figure BDA0003511112950000095
And (6) carrying out verification. The meta distribution represents the proportion of the part of the target fog access point in a network model, which receives the signal-to-interference ratio larger than the threshold value theta, to all the fog access points, namely ps(θ) is expressed as:
F(θ,x)＝P！t(ps(θ)＞x),x∈[0,1]；
wherein, P！tThe reduced Palm probability is expressed, i.e. the probability of an event assuming that the point process of the transmitter contains one point at a certain location. The expression of meta distribution is relatively abstract, and the distribution characteristic is difficult to be seen by naked eyesThe method comprises the following steps:
assuming that the random variable X obeys a mean value μ beta distribution, its Probability generating function (PDF) can be expressed as:
Figure BDA0003511112950000096
the meta distribution can be expressed as:
Figure BDA0003511112950000101
wherein the content of the first and second substances,
Figure BDA0003511112950000102
representing a beta function, wherein j is an imaginary number unit, and t is an integral variable; mjtTo replace b in Mb with jt; f (θ, x) is a Meta distribution representing the coverage probability, that is, an approximation of the Meta distribution. If order
Figure BDA0003511112950000103
In combination with the above formula psThe mean of (θ) can be expressed as:
Figure BDA0003511112950000104
psThe variance of (θ) is expressed as:
Figure BDA0003511112950000105
binding of psThe mean and variance, β, of (θ) can be expressed as:
Figure BDA0003511112950000106
after the meta distribution is subjected to the beta approximation, the approximation of the meta distribution can be expressed as:
Figure BDA0003511112950000107
wherein, IX(a,b)＝∫ta-1(1-t)b-1dt, which represents a regular incomplete beta function.
Verification by Monte Carlo simulation
Figure BDA0003511112950000108
After correctness, average local delay M-1The closed-form solution of (c) can be expressed as:
Figure BDA0003511112950000109
wherein the content of the first and second substances,
Figure BDA0003511112950000111
p represents an interference activity factor.
Example 3
The invention provides a method for analyzing and optimizing time delay performance of a fog access network based on a cluster process. The optimization aim is to optimize the average local time delay of an uplink in the fog access network under the condition of meeting the limit conditions of computing resources and time delay. Thus, the optimization problem can be modeled as:
Figure BDA0003511112950000112
constraint conditions are as follows:
0＜p＜1；
α＝{3，4}
0≤ε≤1；
Rn＝20M；
B＝20M
the constraint condition C1 indicates that the road loss index takes the value of an integer 3 or 4; constraint C2 indicates that the uplink power control compensation factor is between 0 and 1 and increases in steps of 0.1; the constraint condition C3 represents that the coverage probability of the receiving end is not less than 0.4; the constraint condition C4 represents that the threshold range of the signal-to-interference ratio SIR of the receiving end is-15 dB-15 dB; the constraint C5 indicates that the coverage probability variance at the receiving end is between 0-0.08.
The present embodiment provides the system flow of the present invention, which is an optional embodiment of the method for analyzing and optimizing the time delay performance of the fog access network based on the cluster process, and the specific steps are as follows:
Step 201: initializing an algorithm;
step 202: setting parameter values, p ═ 0.8, λf＝20/km2θ is 0dB and ε is [0,1 ]]；
Step 203: defining a user positioned at an origin point as a target user, and calculating the signal-to-interference ratio of the target user and recording the signal-to-interference ratio as SIR;
step 204: judging whether the SIR of the target user is larger than a signal-to-interference ratio threshold value theta, if so, indicating that the target user can successfully unload, and assuming that the average local time delay is marked as D, wherein D is 1;
step 205: if the time slot number is less than the preset time slot number, the unloading of the target user in the time slot is failed, and the target user continues to try unloading in the next time slot;
step 206: until the target user successfully unloads for the first time, setting the number of the time slots spent by the target user as D, and then setting MLD as D;
step 207: judging whether the average local time delay MLD is smaller than a time delay threshold tau or not, if so, reserving the epsilon value and the MLD value corresponding to the epsilon value;
step 208: if yes, abandoning the epsilon value, readjusting epsilon, increasing by step size of 0.1, and executing the step 203-step 207 again when the maximum value is 1;
step 209: comparing MLD corresponding to each epsilon, reserving epsilon when MLD is minimum, and obtaining optimal epsilon when alpha is 31And MLD1；
Step 210: changing alpha to 4, re-executing step 203-step 207, and obtaining the optimal epsilon when alpha is 4 2And MLD2；
Step 211: judging MLD1Whether or not it is less than MLD2If less than, the output optimum value is alpha 4, epsilon2And MLD2；
Step 212: if the output value is larger than the preset value, the output optimal value is alpha-3, epsilon1And MLD1；
Step 213: the algorithm ends.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (8)

1. A method for optimizing the time delay performance of a fog access network based on a cluster process is characterized by comprising the following steps:
step 101: constructing a Poisson cluster process-based fog access network model, initializing an algorithm, setting parameter values, enabling a signal-to-interference ratio threshold value theta to be 0dB, enabling an uplink transmission power control compensation factor epsilon to be 0 and epsilon to be [0,1], enabling a path loss index alpha to be 3 and enabling alpha to be {3,4 };
step 102: defining a user positioned at an origin point as a target user, and calculating the signal-to-interference ratio of the target user and recording the signal-to-interference ratio as SIR;
step 103: judging whether the SIR of the target user is greater than a signal-to-interference ratio threshold theta, if so, indicating that the target user can successfully unload, recording the average local time delay value as D, and making D equal to 1;
Step 104: if the SIR of the target user is smaller than the signal to interference ratio threshold value theta, the target user fails to unload in the time slot, and the target user continues to try to unload in the next time slot;
step 105: calculating the value of the average local time delay MLD of successful unloading of the target user;
step 106: judging whether the average local time delay MLD is smaller than a set time delay threshold tau, if so, reserving the epsilon value and the corresponding MLD value;
step 107: if yes, abandoning the epsilon value, readjusting epsilon by the step size delta epsilon, and executing the step 103 to the step 106 again;
step 108: selecting an MLD value with the minimum MLD value and the corresponding epsilon value from all the obtained epsilon values and the corresponding MLD values as the optimal MLD value and epsilon value when the road loss index alpha is 3;
step 109: step 203-step 208 are executed again by letting α be 4, and an optimal MLD value and an optimal epsilon value when α is 4 are obtained;
step 110: and judging whether the MLD value when the alpha is 3 is smaller than that when the alpha is 4, if so, making the alpha be 4 and taking the corresponding MLD value and the epsilon value, otherwise, making the alpha be 4 and taking the corresponding MLD value and the epsilon value as unloading parameters.
2. The method according to claim 1, wherein the cloud access network model based on the poisson cluster process at least includes a terminal layer and an access layer, and the terminal layer is composed of a plurality of user equipments; the access stratum is composed of a plurality of fog access points, each of which covers a different and known number of user equipments.
3. The method for optimizing the delay performance of the fog access network based on the cluster process as claimed in claim 2, wherein the process of constructing the fog access network model based on the poisson cluster process comprises:
determining the coverage range of a Poisson cluster process-based fog access network model, and generating N in the coverage rangefEach fog access point is obeyed by a density of lambdafPoisson's point process of (a);
using a fog access point as the center of a circle and the radius as
Figure FDA0003511112940000021
In the range of (1) to generate NuAnd (4) users.
4. The method of claim 1, wherein the SIR of the target user is expressed as follows:
Figure FDA0003511112940000022
wherein, YoThe distance between the target fog access point and the target user is obtained; h isoThe power gain between the target fog access point and the target user is obtained; y isnThe distance between the interfering user and the target fog access point; rnTo interfere with the distance between the user and the fog access point to which it is connected; h isnPower gain for interfering users to their connected fog access points; phinIs a set of interfering users; ε represents an uplink transmission power control compensation factor; a isnRepresenting the probability of interfering with the upload of the user; l (| r |) ═ r-αR represents a distance, and α is a road loss index.
5. The method for optimizing the delay performance of the fog access network based on the cluster process as claimed in claim 1, wherein the signal-to-interference ratio threshold θ is expressed as:
Figure FDA0003511112940000023
wherein, R is the uplink transmission rate; b is the total bandwidth of the wireless channel transmission.
6. The method as claimed in claim 1, wherein the method for optimizing the delay performance of the fog access network based on the cluster process is characterized in that the value of the average local delay score MLD for successful offloading of the target user is calculated, that is, based on the random geometric theory knowledge, the probability that the SIR received by the target user is greater than a certain threshold θ is calculated and recorded as ps(θ); p is to bes(θ) as a random variable, count psB-order moment M of (theta)bBy substituting b-1 into MbThe MLD value is recorded as the average local delay.
7. The method as claimed in claim 6, wherein the probability p that the target user receives SIR greater than the threshold θ is defined as the probability p that the target user receives SIR greater than the threshold θs(θ) is expressed as:
Figure FDA0003511112940000031
wherein, p is the activity of the interference user; rnTo interfere with the distance between the user and the fog access point to which it is connected; alpha is a path loss index; ε represents an uplink transmission power control compensation factor; y isoThe distance between the target fog access point and the target user.
8. The method as claimed in claim 1, wherein the average local delay count MLD for successful offloading of the target user is set to be a value of when the target user offloads the task to the mist access point, and each time slot of the target user attempts to send the data packet to the mist access point, and the number of time slots for which the target user attempts to send the data packet when the target user successfully sends the data packet for the first time is cut off.
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