CN108737507B - D2D wireless caching method - Google Patents

D2D wireless caching method Download PDF

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CN108737507B
CN108737507B CN201810394414.5A CN201810394414A CN108737507B CN 108737507 B CN108737507 B CN 108737507B CN 201810394414 A CN201810394414 A CN 201810394414A CN 108737507 B CN108737507 B CN 108737507B
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任品毅
刘景�
杜清河
孙黎
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Xian Jiaotong University
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Abstract

The invention discloses a D2D wireless caching method, which obtains the popularity distribution of files through the request of a user for the current popular files. And designing a wireless caching scheme according to the popularity distribution of the files. According to the scheme, on the premise of reducing the operation complexity, the cache hit probability of the D2D wireless cache is effectively improved at the cost of less performance loss. Compared with the traditional wireless cache technology, the method can effectively reduce the redundancy of the cache, improve the cache hit probability, and has wider application scenes.

Description

D2D wireless caching method
Technical Field
The invention belongs to the technical field of D2D communication, and particularly relates to a D2D wireless caching method.
Background
In recent years, due to the rapid popularization of intelligent terminals, the number of users accessing the mobile internet by using wireless communication is increasing, and the service demand of the users is also increasing. In the peak time of the communication service, the base station needs to serve a large number of terminal users, so that the problems of delay, terminals and the like are easy to occur, and the user experience is reduced. The existing scheme aims to improve the system capacity by increasing available spectrum resources and improving the spectrum utilization efficiency, solves the existing problems and does not pay attention to the characteristics of data traffic.
As mentioned in cisco for future global mobile data traffic prediction, by 2021 mobile video traffic will account for 78% of the total mobile traffic. A large amount of communication resources are used for video traffic transmission. Video files themselves have one important characteristic: content reusability, i.e., a few hot videos may be viewed many times by a large number of users over a period of time. In addition, the popularity of the hot spot files changes relatively slowly within a certain time limit. In addition, with the advancement of storage technologies, the storage capacity of hard disks has been rapidly increasing. Now, the capacity of the ordinary mechanical hard disk reaches the TB order of magnitude, and the price is only a few hundred yuan. The storage capacity of the hard disk is larger and larger, the read-write performance is better and better, and the cost performance is higher and higher. This provides a good opportunity for the development of video caching technology.
In addition, the D2D communication technology has been proposed to make the D2D terminal caching technology attract attention. The D2D terminal caching technology means that the base station caches popular files in advance in the memory of the user terminal. When a user requests file transmission, the user can firstly search the file in the memory of the user. If the requested file is cached in the memory in advance, the user can directly use the file; if the file is not cached in local storage, but is cached in terminal storage in the surrounding vicinity, the user requests the end user storing the file to transfer the file via D2D communication technology; if the file is not stored in both the local storage and the terminal storage in the vicinity of the user, the user issues a file transfer request to the base station or the server.
The existing D2D wireless caching strategy mainly has the problems of high implementation complexity, low cache hit rate, excessive redundancy of file caches, limitation to specific scenes and the like. Meanwhile, the possibility that the opposite side is unwilling to provide service when the terminal requests the opposite side to transmit the file is not considered.
Disclosure of Invention
The invention aims to provide a D2D wireless caching method to solve the problems.
In order to achieve the purpose, the invention adopts the following technical scheme:
a D2D wireless caching method comprises the following steps:
step 1: acquiring a content popularity distribution expression:
suppose that a user requests a file from a repository M of M fileslib(ii) a Each user independently requests files from the file library according to Zipf distribution; the higher the probability that the top ranked file is requested;wherein the probability that a file ranked at position i is requested is
Figure GDA0002433526410000021
Wherein γ represents the prevalence constant of the Zipf distribution;
step 2: obtaining an optimization model
Each user can freely select a cellular communication mode and a D2D communication mode for communication, and when the users communicate in the D2D communication mode, the maximum communication radius of the users is RD2D(ii) a K adjacent users exist in the range of the maximum D2D communication radius, and K obeys the Poisson point process with the density of lambda; the user is centered on himself with radius RD2DHas a probability of k users in the range of
Figure GDA0002433526410000022
Suppose that each user can cache MdFiles, without loss of generality, assume that each file is 1 in size; at RD2DThe D2D communication technology is used for file transmission among users in the range, and files cached by the users are called virtual caches; user intention RD2DThe probability that other users in the range share the self cache file is rho; the probability that a user can obtain a file from the virtual cache is called cache hit probability and is marked as Pi Hit；
With qiRepresenting the probability that the user caches the file ranked at the ith bit, then
Figure GDA0002433526410000031
The probability that a user requests a file ranked at the ith bit and acquires the file is expressed as
Figure GDA0002433526410000032
Substituting the formulas (1) and (2) into the formula (4) to obtain
Figure GDA0002433526410000033
The positions of all users are randomly distributed, so that the cache hit probability of all users is the same on average; the probability that the user finds the requested file in the virtual cache is
Figure GDA0002433526410000034
By determining the caching probability q of the filei＝[q1,q2,...,qM]Maximizing the average cache hit rate; the optimization model is therefore represented as:
Figure GDA0002433526410000035
and step 3: proposing an optimization algorithm
File library MlibThe file in (1) is divided into two parts: partial files with high popularity and partial files with relatively low popularity. Under a cache strategy of Zipf distribution, files with high popularity are cached redundantly, so that the cache probability of the part is reduced in proportion; the less popular file cache hit probability is low, so we scale up this partial cache probability.
Namely, it is
Figure GDA0002433526410000041
In the formula:
α indicates a high popularity multiplier of file caching probability
β denotes a low popularity multiplier of file caching probability
M' — the last file with high popularity corresponds to the rank
Wherein α and β satisfy the conditions of 0- α -1, β -1, and
Figure GDA0002433526410000042
substituting formula (8) into formula (7)
At this point, the original optimization model is transformed into
Figure GDA0002433526410000043
And 4, step 4: solve for the optimal value
By observing the formula (9), the following results can be found
Figure GDA0002433526410000044
Obtaining an optimal solution by a formula (9);
is represented by the formula (10)
Figure GDA0002433526410000051
Substituting (11) into equation (9) yields the equivalence problem:
Figure GDA0002433526410000052
firstly, keeping M 'unchanged, obtaining α the optimum value when M' is, and then obtaining the optimum value of M 'by traversing M' from 1 to M.
Further, the specific steps of obtaining the optimal M' value in step 4 are as follows:
order to
Figure GDA0002433526410000053
By solving equations
Figure GDA0002433526410000054
To obtain a solution α of the equationM'；
Then, through traversing M 'from 1 to M, the optimal α value α' is obtained;
at the same time, the optimum β value β' is obtained from equation (11).
Further, in step 1, when γ is larger, the request of the user is more concentrated on the hot spot file with the top rank.
Compared with the prior art, the invention has the following technical effects:
compared with the optimal cache strategy, the cache hit probability of the D2D communication wireless cache method provided by the invention has about 3% of performance loss, but the optimal cache strategy needs a plurality of iterative computation processes, and the method can obtain a result only by traversing the file library once, and the operation complexity of the method is lower than that of the optimal cache strategy; compared with the common equal-probability random cache strategy, the most popular file cache strategy and the Zipf distributed cache strategy, the cache hit probability of the method is higher than that of the above strategies, and the performance is better than that of the above centralized strategies. Therefore, the method has more application scenes.
Drawings
FIG. 1 is a cumulative distribution function of a Zipf distribution with prevalence constants γ of 0.6, 1, and 1.4, respectively, for the Zipf distribution;
FIG. 2 is a diagram of a D2D wireless cache network model;
fig. 3 shows the neighboring user sharing probability ρ of 0.5, MdWhen the number is 3, improving a theoretical performance curve and an actual simulation performance curve graph of a cache strategy of Zipf distribution;
fig. 4 shows that when the neighboring user sharing probability ρ is 0.5, MdWhen the number is 3, the performance graphs of the optimal caching strategy and the caching strategy for improving Zipf distribution;
fig. 5 shows that when the neighboring user sharing probability ρ is 0.5, MdWhen the number is 3, performance graphs of an equiprobable random cache strategy, a most popular file cache strategy, a cache strategy of Zipf distribution and a cache strategy of improving Zipf distribution are obtained;
Detailed Description
The invention is further described below with reference to the accompanying drawings:
referring to fig. 1-5, the present invention provides a D2D wireless caching strategy. We first studied the distribution of popularity of hot files. And in combination with the popularity of the hot spot file, the hit probability of the file cached by the D2D is modeled under the conditions that the users in the cell obey the Poisson Point process and the caching space of the user terminal is limited. A suboptimal caching algorithm with low complexity is provided. Simulation shows that the algorithm can achieve performance close to the optimal caching strategy.
Step 1: obtaining content popularity distribution expression
When researchers have studied the distribution of recent web page requests and video browsing, it has been found that these distributions can be approximated by Zipf distributions. Therefore, in the related algorithm design and simulation, we assume that the request distribution of the user follows the Zipf distribution. Suppose that a user requests a file from a repository M of M fileslib. Each user independently requests files from the file repository according to the Zipf distribution. The higher the probability that the top ranked file is requested. Wherein the probability that a file ranked at position i is requested is
Figure GDA0002433526410000071
Where γ represents the prevalence constant of the Zipf distribution. When γ is larger, the user's request is more focused on the top ranked hotspot video file.
Step 2: obtaining an optimization model
Let us consider that in a cell, there is one Base Station (BS) and N end users, and users are evenly distributed around the Base Station with radius RBSWithin the range of (1). Each user can communicate in cellular communication mode and D2D communication mode, and when the users communicate in D2D communication mode, the maximum communication radius of the users is RD2D. And there are K adjacent users within the range of the maximum D2D communication radius, K following the poisson point process with density λ. The user is centered on himself with radius RD2DHas a probability of k users in the range of
Figure GDA0002433526410000072
Suppose that each userHomoenergetic buffers MdFor each file, without loss of generality, assume that each file is 1 in size. At RD2DFiles can be transmitted between users in a range by using the D2D communication technology, and files cached by the users are called virtual caches. User intention RD2DThe probability that other users in the range share the self cache file is rho. We call the probability that a user can obtain a file from the virtual cache as the cache hit probability, denoted as Pi Hit。
We use qiRepresenting the probability that the user caches the file ranked at the ith bit, then
Figure GDA0002433526410000073
The probability that a user requests a file ranked at the ith bit and retrieves the file (i.e., the cache hit probability) may be expressed as
Figure GDA0002433526410000074
Substituting the formulas (1) and (2) into the formula (4) to obtain
Figure GDA0002433526410000075
The positions of all users are randomly distributed, so that the cache hit probability of each user is the same on average. The probability that a user can find a requested file in the "virtual cache" is
Figure GDA0002433526410000081
We want to determine the caching probability q of a filei＝[q1,q2,…,qM]The average cache hit rate is maximized. The optimization problem can be expressed as:
Figure GDA0002433526410000082
this is a condition-limited non-linear convex optimization problem. The optimization problem has high complexity and is difficult to apply in an actual system.
And step 3: proposing an optimization algorithm
We propose a caching strategy that improves the Zipf distribution. The basic idea of this strategy is: first, a document library MlibThe file in (1) is divided into two parts: partial files with high popularity and partial files with relatively low popularity. If the cache probability of the file with high popularity can be properly reduced and the cache probability of the file with low popularity is improved, the cache hit probability better than that of a cache strategy of Zipf distribution can be realized.
Namely, it is
Figure GDA0002433526410000083
Wherein α and β satisfy the conditions of 0- α -1, β -1, and
Figure GDA0002433526410000091
substituting formula (8) into formula (7)
At this point, the original optimization problem turns into
Figure GDA0002433526410000092
And 4, step 4: solve for the optimal value
To obtain the optimal solution of equation (9), a condition is satisfied, i.e.
Figure GDA0002433526410000093
This condition is a necessary condition for obtaining an optimal solution.
Is represented by the formula (10)
Figure GDA0002433526410000094
Substituting (11) into equation (9) yields the equivalence problem:
Figure GDA0002433526410000095
firstly, keeping M 'unchanged, solving α the optimal value when M', and then, solving the optimal M 'value by traversing M' between 1 and M.
The method comprises the following specific steps:
order to
Figure GDA0002433526410000101
By solving equations
Figure GDA0002433526410000102
To obtain a solution α of the equationM'°
And traversing M 'from 1 to M to obtain an optimal α value α'.
At the same time, the optimum β value β' is obtained from equation (11).
As can be seen from fig. 1, the popularity constant γ of the Zipf distribution is different, and the cumulative distribution function of the corresponding Zipf distribution is also different. When gamma is smaller, the popularity difference of the files with different ranks is smaller; when γ is large, the popularity difference of the files with different ranks becomes larger and larger, and the requests of the user for the files are gradually concentrated on the top several files.
As can be seen from fig. 2, within a cell, neighboring terminals may form a "virtual cache" through the D2D communication mode. The user can acquire files required by the user from the virtual cache with a certain probability.
As can be seen from fig. 3, the theoretical performance of the cache strategy for improving the Zipf distribution is consistent with the actual simulation performance.
As can be seen from fig. 4, the performance under the optimal caching strategy is better than that of the caching strategy improving the Zipf distribution, but the performance difference between the two is not very large. The performance of the cache strategy for improving the Zipf distribution is about 3% lower than that of the optimal cache strategy.
As can be seen from fig. 5, comparing the equal-probability random caching strategy, the most popular file caching strategy, and the cache strategy of the Zipf distribution, the cache strategy for improving the Zipf distribution proposed by the present solution has the best performance. Under the equal probability random cache strategy, the cache hit probability is always kept at a lower level. The most popular file caching strategy has the worst performance when the popularity constant gamma of the file is small, the performance is obviously improved when the gamma is increased, and the most popular file caching strategy performance is close to that of a Zipf distributed caching strategy when the gamma value is large. When the gamma value is smaller, the performance difference between the Zipf distributed cache strategy and the Zipf distributed improved cache strategy is not obvious, when the gamma value is larger, the performance difference between the Zipf distributed cache strategy and the Zipf distributed improved cache strategy is larger, and the final performance difference is about 5%.
Therefore, in summary, the D2D communication wireless cache method provided by the invention can effectively improve the cache hit probability of the D2D wireless cache at the cost of less performance loss on the premise of reducing the operation complexity.
While the invention has been described in further detail with reference to specific preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A D2D wireless caching method is characterized by comprising the following steps:
step 1: acquiring a content popularity distribution expression:
suppose that a user requests a file from a repository M of M fileslib(ii) a Each user independently requests files from the file library according to Zipf distribution; the higher the probability that the top ranked file is requested; wherein the probability that a file ranked at position i is requested is
Figure FDA0002433526400000011
Wherein γ represents the prevalence constant of the Zipf distribution;
step 2: obtaining an optimization model
Each user can freely select a cellular communication mode and a D2D communication mode for communication, and when the users communicate in the D2D communication mode, the maximum communication radius of the users is RD2D(ii) a K adjacent users exist in the range of the maximum D2D communication radius, and K obeys the Poisson point process with the density of lambda; the user is centered on himself with radius RD2DHas a probability of k users in the range of
Figure FDA0002433526400000012
Suppose that each user can cache MdA file, each file size is assumed to be 1; at RD2DThe D2D communication technology is used for file transmission among users in the range, and files cached by the users are called virtual caches; user intention RD2DThe probability that other users in the range share the self cache file is rho; the probability that a user can obtain a file from the virtual cache is called cache hit probability and is marked as Pi Hit；
With qiRepresenting the probability that the user caches the file ranked at the ith bit, then
Figure FDA0002433526400000013
Cache hit probability Pi HitThe probability of requesting a file ranked at the ith bit and retrieving the file for the user is expressed as
Figure FDA0002433526400000014
Substituting the formulas (1) and (2) into the formula (4) to obtain
Figure FDA0002433526400000021
The positions of all users are randomly distributed, so that the cache hit probability of all users is the same on average; the probability that the user finds the requested file in the virtual cache is
Figure FDA0002433526400000022
By determining the caching probability q of the filei＝[q1,q2,…,qM]Maximizing the average cache hit rate; the optimization model is therefore represented as:
Figure FDA0002433526400000023
and step 3: proposing an optimization algorithm
File library MlibThe file in (1) is divided into two parts: partial files with high popularity and partial files with low popularity; under a cache strategy of Zipf distribution, files with high popularity are cached redundantly, so that the cache probability of the part is reduced in proportion; the file cache with low popularity has low hit probability, so the cache probability of the part is enlarged proportionally;
namely, it is
Figure FDA0002433526400000024
In the formula:
α indicates a high popularity multiplier of file caching probability
β denotes a low popularity multiplier of file caching probability
M' — the last file with high popularity corresponds to the rank
Wherein α and β satisfy the conditions of 0- α -1, β -1, and
Figure FDA0002433526400000031
1≤M'≤M；
substituting formula (8) into formula (7)
At this point, the original optimization model is transformed into
Figure FDA0002433526400000032
And 4, step 4: solve for the optimal value
By observing the formula (9), the following results can be found
Figure FDA0002433526400000033
Obtaining an optimal solution by a formula (9);
is represented by the formula (10)
Figure FDA0002433526400000034
Substituting (11) into equation (9) yields the equivalence problem:
Figure FDA0002433526400000041
firstly, keeping M 'unchanged, obtaining α the optimum value when M' is, and then obtaining the optimum value of M 'by traversing M' from 1 to M.
2. The D2D wireless caching method according to claim 1, wherein the specific steps of finding the optimal M' value in step 4 are as follows:
order to
Figure FDA0002433526400000042
By solving equations
Figure FDA0002433526400000043
To obtain a solution α of the equationM'；
Then, through traversing M 'from 1 to M, the optimal α value α' is obtained;
at the same time, the optimum β value β' is obtained from equation (11).
3. The D2D wireless caching method according to claim 1, wherein in step 1, when γ is larger, the user's request is more concentrated on the top-ranked hotspot file.
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