CN104918134A - Data packet scheduling method of interactive multi-viewpoint video based on Nash bargaining - Google Patents

Abstract

The invention discloses a data packet scheduling method of interactive multi-viewpoint video based on Nash bargaining. According to the method, various users determine viewpoint video data packet requests in a user side firstly, and the video data packet requests are fed back to a server; the server receives the various users' viewpoint video data packet requests then, and interactive multi-viewpoint video data packet scheduling is modeled into a Nash bargaining model in an optimized manner; afterwards, a server side lists an optimal condition (KKT condition) by utilizing Lagrange dual and constraint conditions to solve the optimized model, and the probability of video data packets, which are sent, of the various viewpoints of the server side is determined; and, finally, the server side updates the probability of video data packets, which are sent, of the various viewpoints. According to the method, on the condition of a limited network bandwidth resource, the server can schedule viewpoint video data packages to all users according to the viewpoint video data package requests periodically fed back by the users and achieve performance balance between network transmission efficiency and user fairness.

Description

A kind of based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price

Technical field

The present invention relates to a kind of based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, belonging to Multimedia Data Transmission technical field.

Background technology

Along with the fast development of network multimedia related-art technology and the continuous upgrading of Video service, people have been not content with traditional single viewpoint video, so multi-view point video technology is arisen at the historic moment and become one of most important development trend of current video research field.The most outstanding feature of multi-view point video is exactly interactivity, and how embodying this feature becomes the problem that multi-view point video application needs to solve.Interactive video in multiple viewpoints transfer of data is the video data transmitting corresponding viewpoint according to the demand of user, can reduce the data volume of transmission and meet the requirement of user to video quality.

Current interactive multi-view video system server end can provide the video data of multiple viewpoint, the user of user side according to self preference, can select the viewpoint of server end, in viewing process, arbitrarily can switch the viewpoint of demand, achieve the mutual of user side and server end.

The video data of multiple viewpoint due to Server Side Include, compared to the data of traditional single viewpoint video, the data volume of multi-view point video is larger.Under limited network bandwidth resources, when network congestion occurs, the data packet dispatching method of existing interactive video in multiple viewpoints, in the video data packet scheduling of viewpoint, if with the viewpoint demand meeting user side most users for target, preferential transmission by the video packets of data of the viewpoint of most users demand, and ignores the fairness between all users, can cause the greatest differences of each user video quality; If with the fairness between all users for target, dispatch the video packets of data of all viewpoints coequally, and do not consider the different demands of user to viewpoint, then network transmission efficiency can be caused to reduce.

Summary of the invention

The object of the present invention is to provide a kind of based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, in order to ensure higher network transmission efficiency, take into account the fairness between user simultaneously, the method can when network bandwidth resources be limited, server, according to the video packets of data request of the viewpoint of user's periodic feedback, to the video packets of data of all user scheduling viewpoints, realizes the performance balance between network transmission efficiency and user fairness.

In order to achieve the above object, design of the present invention is:

First, at user side, each user determines the video packets of data request of the viewpoint of self, and feeds back to server;

Then, server receives the video packets of data request of the viewpoint of each user, and becomes to receive assorted model of bargain by the data packet dispatching optimization modeling of interactive video in multiple viewpoints;

Then, server end utilizes Lagrange duality and constraints to list optimal condition (KKT, Karush-Kuhn-Tucker condition) solving-optimizing model, determines the probability that the video packets of data of each viewpoint of server end is sent out;

Finally, server end is according to the change of the video packets of data request of user's viewpoint, and the probability that the video packets of data upgrading all viewpoints is sent out, realizes Internet Transmission optimization,

According to foregoing invention design, the present invention adopts following technical proposals:

Based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, its concrete steps are as follows:

Step 1. determines the video data demand packet of user n own view m

(1). the preference of the video packets of data of definition viewpoint

At user side, definition user n, to the preference of the video packets of data of viewpoint m, is designated as its expression formula is:

n＝1,2,...,N，m＝1,2,...,M

Wherein, be in server end viewpoint m towards, M is number of views, be user n head towards, N is the number of users in user side, be in server end viewpoint m towards with the head of user n towards between angle;

(2). user is to the preference function u of the video packets of data of viewpoint in definition _n,m, its expression formula is:

$u_{n,m}=\left\{\begin{array}{cc}1,& {\mathrm{\&xi;}}_m^n\&GreaterEqual;E;\\ 0,& {\mathrm{\&xi;}}_m^n<E.\end{array}\right.$

Wherein, Ε is for judging that whether user n sends the threshold value of the video packets of data of viewpoint m to server request; If u _n,mbe 1, then user n sends the video packets of data of viewpoint m to server request, otherwise user n does not send the video packets of data of viewpoint m to server request;

Step 2. sets up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain

(1). the utility function u of definition viewpoint m _m, its expression formula is:

$u_m=x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}$

Wherein, x _mit is the probability that the serviced device of video packets of data of viewpoint m sends;

(2). the minimum utility function of definition viewpoint m its expression formula is:

Wherein, ε is a normal number;

(3). set up objective optimisation problems

According to utility function and the minimum utility function of described viewpoint m, set up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain, specific as follows:

Target problem: $\max \underset{m=1}{\overset{M}{\mathrm{\&Pi;}}}(x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

Constraints:

①.0≤x _m≤1,m＝1,...,M,

②. ${\mathrm{\&Sigma;}}_{m=1}^M{x}_m=1,$

③. $x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}\&GreaterEqual;u_m^{\min },m=1,...,M.$

Optimization aim: while having higher network transmission efficiency, takes into account the fairness between all users;

Constraints:

1.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be between 0 and 1;

2.. the serviced device of video packets of data of all viewpoints sends to the probability sum of user to be 1;

3.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be greater than minimum probability;

The sending probability of all viewpoint video packets determined by step 3. solving-optimizing model

(1). logarithm process is carried out to former target problem:

$\max {\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

(2). definition Lagrange duality:

$L(X,\mathrm{\&lambda;},\mathrm{\&alpha;},\mathrm{\&beta;})={\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })+\mathrm{\&lambda;}({\mathrm{\&Sigma;}}_{m=1}^M{x}_m-1)+{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&alpha;}}_m{x}_m-{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&beta;}}_m(x_m-1)$

Wherein, λ, α _mand β _mrepresent Lagrange multiplier, this logarithm problem has convex target function, and constraints is convex set;

(3). utilize KKT condition to solve: to list optimal condition (KKT condition) according to Lagrange duality and constraints, as follows:

$\frac{\&PartialD;L}{{\&PartialD;x}_m}=\frac{{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}}{x_m\&CenterDot;{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-u_m^{\min }}+\mathrm{\&lambda;}+{\mathrm{\&alpha;}}_m-{\mathrm{\&beta;}}_m=0;$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m=1,\mathrm{\&lambda;}\&NotEqual;0;{\mathrm{\&alpha;}}_m{x}_m=0,{\mathrm{\&alpha;}}_m\&GreaterEqual;0;{\mathrm{\&beta;}}_m(x_m-1)=0,{\mathrm{\&beta;}}_m\&GreaterEqual;0;$

0≤x _m≤1；

The optimum probability that the serviced device of video packets of data calculating viewpoint m sends, its calculating formula is:

$x_m^{*}=\frac{1}{M}+\mathrm{\&epsiv;}\&CenterDot;({\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-\frac{1}{M}\&CenterDot;\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m})m=1,...,M$

Step 4. upgrades the sending probability of the video packets of data of all viewpoints

Adapt to user's head towards change, display device periodically follow the trail of upgrade user head towards, the each user of user side repeats step 1 and sends the video packets of data request of new viewpoint to server, server end repeats step 2 to 3, the probability that the video packets of data upgrading all viewpoints is sent out, realizes Internet Transmission optimization.

This method has the following advantages compared with the prior art:

Of the present invention a kind of based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, the method introduces that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain, server is according to the viewpoint video data packet request of user's periodic feedback, with the video packets of data of optimum probability to all user scheduling viewpoints, while having higher network transmission efficiency, take into account the fairness between all users.

Accompanying drawing explanation

Fig. 1 is the general flow chart of the inventive method;

Fig. 2 is the video packets of data sending probability fairness schematic diagram of each viewpoint;

Fig. 3 is each user satisfaction schematic diagram;

Fig. 4 is average user satisfaction schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are described in further detail: a kind of based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, it is characterized in that, the method first, at user side, each user determines the video packets of data request of the viewpoint of self, and feeds back to server; Then, server receives the video packets of data request of the viewpoint of each user, and becomes to receive assorted model of bargain by the data packet dispatching optimization modeling of interactive video in multiple viewpoints; Then, server end utilizes Lagrange duality and constraints to list optimal condition (KKT, Karush-Kuhn-Tucker condition) solving-optimizing model, determines the probability that the video packets of data of each viewpoint of server end is sent out; Finally, server end is according to the change of the video packets of data request of user's viewpoint, and the probability that the video packets of data upgrading all viewpoints is sent out, realizes Internet Transmission optimization.

The present embodiment is tested under premised on technical solution of the present invention, as shown in Figure 1, give detailed execution mode and concrete operating process, mainly comprise the video data demand packet determining user n own view m, the video data packet scheduling setting up viewpoint optimized receive assorted model of bargain, solving-optimizing model determine all viewpoint video packets sending probability, upgrade all sending probabilities of viewpoint video packet and the performance evaluation of the inventive method.

1. determine the video data demand packet of user n own view m

(1). the video packets of data preference of definition viewpoint

The video sequence that the present invention chooses 8 viewpoints carries out instance analysis, each view sequence comprises 96 frames, adopt H.264/AVC standard to each viewpoint absolute coding, after coding, resolution is 640 × 480, each gop size is 8, quantization parameter is chosen for 28, and 8 viewpoints are evenly distributed between 20 ° and 160 ° with identical differential seat angle.At user side, the head that display device periodically obtains user towards, the head of first kind user towards being evenly distributed between 45 ° to 135 °, the head of Equations of The Second Kind user towards being evenly distributed between 0 ° to 45 ° or 135 ° to 180 °, be in server end viewpoint m towards, 8 is number of views, be user n head towards, N is the number of users in user side, then user n to the preference of the video packets of data of viewpoint m is:

n＝1,2,...,N，m＝1,2,...,8

Wherein be in server end viewpoint m towards with the head of user n towards between angle;

(2). user is to the preference function u of the video packets of data of viewpoint in definition _n,m, its expression formula is:

$u_{n,m}=\left\{\begin{array}{cc}1,& {\mathrm{\&xi;}}_m^n\&GreaterEqual;E;\\ 0,& {\mathrm{\&xi;}}_m^n<E.\end{array}\right.$

Wherein, Ε is for judging that whether user n sends the threshold value of the video packets of data of viewpoint m to server request; If u _n,mbe 1, then user n sends the video packets of data of viewpoint m to server request, otherwise user n does not send the video packets of data of viewpoint m to server request;

2. set up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain

(1). the utility function u of definition viewpoint m _m, its expression formula is:

$u_m=x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}$

Wherein, x _mit is the probability that the serviced device of video packets of data of viewpoint m sends;

(2). the minimum utility function of definition viewpoint m its expression formula is:

Wherein, ε is a normal number;

(3). set up objective optimisation problems

According to utility function and the minimum utility function of described viewpoint m, set up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain, specific as follows:

Target problem: $\max \underset{m=1}{\overset{M}{\mathrm{\&Pi;}}}(x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

Constraints:

①.0≤x _m≤1,m＝1,...,M,

②. ${\mathrm{\&Sigma;}}_{m=1}^M{x}_m=1,$

③. $x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}\&GreaterEqual;u_m^{\min },m=1,...,M.$

Optimization aim: while having higher network transmission efficiency, takes into account the fairness between all users;

Constraints:

1.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be between 0 and 1;

2.. the serviced device of video packets of data of all viewpoints sends to the probability sum of user to be 1;

3.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be greater than minimum probability;

3. the sending probability of all viewpoint video packets determined by solving-optimizing model

(1). logarithm process is carried out to former target problem:

$\max {\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

(2). definition Lagrange duality:

$L(X,\mathrm{\&lambda;},\mathrm{\&alpha;},\mathrm{\&beta;})={\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })+\mathrm{\&lambda;}({\mathrm{\&Sigma;}}_{m=1}^M{x}_m-1)+{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&alpha;}}_m{x}_m-{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&beta;}}_m(x_m-1)$

Wherein, λ, α _mand β _mrepresent Lagrange multiplier, this logarithm problem has convex target function, and constraints is convex set;

(3). utilize KKT condition to solve: to list optimal condition (KKT condition) according to Lagrange duality and constraints, as follows:

$\frac{\&PartialD;L}{{\&PartialD;x}_m}=\frac{{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}}{x_m\&CenterDot;{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-u_m^{\min }}+\mathrm{\&lambda;}+{\mathrm{\&alpha;}}_m-{\mathrm{\&beta;}}_m=0;$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m=1,\mathrm{\&lambda;}\&NotEqual;0;{\mathrm{\&alpha;}}_m{x}_m=0,{\mathrm{\&alpha;}}_m\&GreaterEqual;0;{\mathrm{\&beta;}}_m(x_m-1)=0,{\mathrm{\&beta;}}_m\&GreaterEqual;0;$

0≤x _m≤1；

The optimum probability that the serviced device of video packets of data calculating viewpoint m sends, its calculating formula is:

$x_m^{*}=\frac{1}{M}+\mathrm{\&epsiv;}\&CenterDot;({\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-\frac{1}{M}\&CenterDot;\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m})m=1,...,M$

4. upgrade the sending probability of the video packets of data of all viewpoints

Adapt to user's head towards change, display device periodically follow the trail of upgrade user head towards, the each user of user side repeats step 1 and sends the video packets of data request of new viewpoint to server, server end repeats step 2 to 3, the probability that the video packets of data upgrading all viewpoints is sent out, realizes Internet Transmission optimization;

5. carry out performance evaluation after adopting the inventive method, realize the optimization of each viewpoint data packet dispatching

In order to analyze the performance of the inventive method, compare with the data packet dispatching method of following two kinds of existing interactive video in multiple viewpoints:

Ratio is dispatched: to meet the viewpoint demand of user side most users for target, preferentially send by the video packets of data of the viewpoint of most users demand;

Equity dispatching: with the fairness between all users for target, dispatches the video packets of data of all viewpoints coequally;

(1). the fairness of each viewpoint video Packet Generation probability

When Fig. 2 compared for the data packet dispatching method of employing three kinds of interactive video in multiple viewpoints each viewpoint video Packet Generation probability fairness between difference, during equity dispatching, the fairness perseverance of each viewpoint video Packet Generation probability is 1 thus not draw in the drawings; As shown in the figure, the fairness of the inventive method each viewpoint video Packet Generation probability is better than ratio scheduling, and when Equations of The Second Kind user people measure ratio lower time, the fairness of the inventive method each viewpoint video Packet Generation probability is obviously better than ratio dispatches; Difference between two kinds of dispatching methods reduces along with the increase of Equations of The Second Kind user number ratio, and when the first kind is identical with Equations of The Second Kind user number, the fairness of two kinds of dispatching method each viewpoint video Packet Generation probability closely;

(2). the satisfaction of each user

The satisfaction contrast of each user when Fig. 3 reflects the data packet dispatching method of employing three kinds of interactive video in multiple viewpoints, now total number of users amount is 50, and first kind user number accounts for 80%; As can be seen from the figure equity dispatching has the curve of relative smooth, and between ratio scheduling different user, the difference of satisfaction is maximum, and each user satisfaction difference of the inventive method is then between the two;

(3). average user satisfaction

Fig. 4 reflects the impact of average user satisfaction by amount of bandwidth change of the data packet dispatching method of employing three kinds of interactive video in multiple viewpoints; As shown in the figure, the average user satisfaction of three kinds of dispatching methods all presents ascendant trend, because more bandwidth means can send more data along with bandwidth increase; When adoption rate is dispatched, first kind user satisfaction is the highest by contrast, and Equations of The Second Kind user satisfaction is minimum on the contrary; Equity dispatching has contrary result compared to ratio scheduling; And the inventive method can average out between.

Claims (1)

1., based on receiving the data packet dispatching method of interactive video in multiple viewpoints of assorted agreed-upon price, it is characterized in that, first, at user side, each user determines the video packets of data request of the viewpoint of self to the method, and feeds back to server; Then, server receives the video packets of data request of the viewpoint of each user, and becomes to receive assorted model of bargain by the data packet dispatching optimization modeling of interactive video in multiple viewpoints; Then, server end utilizes Lagrange duality and constraints to list optimal condition (KKT condition) solving-optimizing model, determines the probability that the video packets of data of each viewpoint of server end is sent out; Finally, server end changes according to the video packets of data request of user's viewpoint, and the probability that the video packets of data upgrading all viewpoints is sent out realizes Internet Transmission optimization, and its concrete steps are as follows:

Step 1. determines the video data demand packet of user n own view m

(1). the preference of the video packets of data of definition viewpoint

At user side, definition user n, to the preference of the video packets of data of viewpoint m, is designated as its expression formula is:

Wherein, be in server end viewpoint m towards, M is number of views, be user n head towards, N is the number of users in user side, be in server end viewpoint m towards with the head of user n towards between angle;

(2). user is to the preference function u of the video packets of data of viewpoint in definition _n,m, its expression formula is:

$u_{n,m}=\left\{\begin{array}{cc}1,& {\mathrm{\&xi;}}_m^n\&GreaterEqual;E;\\ 0,& {\mathrm{\&xi;}}_m^n<E.\end{array}\right.$

Wherein, Ε is for judging that whether user n sends the threshold value of the video packets of data of viewpoint m to server request; If u _n,mbe 1, then user n sends the video packets of data of viewpoint m to server request, otherwise user n does not send the video packets of data of viewpoint m to server request;

Step 2. sets up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain

(1). the utility function u of definition viewpoint m _m, its expression formula is:

$u_m=x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}$

Wherein, x _mit is the probability that the serviced device of video packets of data of viewpoint m sends;

(2). the minimum utility function of definition viewpoint m its expression formula is:

Wherein, ε is a normal number;

(3). set up objective optimisation problems

According to utility function and the minimum utility function of described viewpoint m, set up that the video data packet scheduling of viewpoint is optimized receives assorted model of bargain, specific as follows:

Target problem: $\max \underset{m=1}{\overset{M}{\mathrm{\&Pi;}}}(x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

Constraints:

①.0≤x _m≤1,m＝1,...,M,

②. ${\mathrm{\&Sigma;}}_{m=1}^M{x}_m=1,$

③. $x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}\&GreaterEqual;u_m^{\min },m=1,...,M.$

Optimization aim: while having higher network transmission efficiency, takes into account the fairness between all users;

Constraints:

1.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be between 0 and 1;

2.. the serviced device of video packets of data of all viewpoints sends to the probability sum of user to be 1;

3.. the serviced device of video packets of data of each viewpoint sends to the probability of user to be greater than minimum probability;

The sending probability of all viewpoint video packets determined by step 3. solving-optimizing model

(1). logarithm process is carried out to former target problem:

$\max {\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })$

(2). definition Lagrange duality:

$L(X,\mathrm{\&lambda;},\mathrm{\&alpha;},\mathrm{\&beta;})={\mathrm{\&Sigma;}}_{m=1}^M\ln (x_m\&CenterDot;\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m}-u_m^{\min })+\mathrm{\&lambda;}({\mathrm{\&Sigma;}}_{m=1}^M{x}_m-1)+{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&alpha;}}_m{x}_m-{\mathrm{\&Sigma;}}_{m=1}^M{\mathrm{\&beta;}}_m(x_m-1)$

Wherein, λ, α _mand β _mrepresent Lagrange multiplier, this logarithm problem has convex target function, and constraints is convex set;

(3). utilize KKT condition to solve: to list optimal condition (KKT condition) according to Lagrange duality and constraints, as follows:

$\frac{\&PartialD;L}{\&PartialD;x_m}=\frac{{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}}{x_m\&CenterDot;{\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-u_m^{\min }}+\mathrm{\&lambda;}+{\mathrm{\&alpha;}}_m-{\mathrm{\&beta;}}_m=0;$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m=1,\mathrm{\&lambda;}\&NotEqual;0;{\mathrm{\&alpha;}}_m{x}_m=0,{\mathrm{\&alpha;}}_m\&GreaterEqual;0;{\mathrm{\&beta;}}_m(x_m-1)=0,{\mathrm{\&beta;}}_m\&GreaterEqual;0;$

0≤x _m≤1；

The optimum probability that the serviced device of video packets of data calculating viewpoint m sends, its calculating formula is:

$x_m^{*}=\frac{1}{M}+\mathrm{\&epsiv;}\&CenterDot;({\mathrm{\&Sigma;}}_{n=1}^N{u}_{n,m}-\frac{1}{M}\&CenterDot;\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{u}_{n,m})m=1,...,M$

Step 4. upgrades the sending probability of the video packets of data of all viewpoints

Adapt to user's head towards change, display device periodically follow the trail of upgrade user head towards, the each user of user side repeats step 1, send the video packets of data request of new viewpoint to server, server end repeats step 2 to 3, the probability that the video packets of data upgrading all viewpoints is sent out, realizes Internet Transmission optimization.