KR101405841B1 - Method and system for allocating resources using transformation-based low complexity algorithm for nash bargaining solutions in dynamic networks - Google Patents

Abstract

According to embodiments of the present invention, a method for allocating resources of a dynamic network using a Nash bargaining solution comprises the steps of obtaining a linear transformation matrix which can map an effective utility set of a current time slot to the effective utility set of a next time slot; determining a transformation coordinate which is obtained by converting Nash bargaining solution of the current time slot by the linear transformation matrix; determining the effectiveness of the transformation coordinate with respect to the effective utility set of the next time slot; calculating the Nash bargaining solution of the next time slot based on a sub-feasible utility set of the effective utility set which regards a valid transformation coordinate as a concurrence failure point; and calculating the Nash bargaining solution of the next time slot based on a navigation area consisting of Pareto optimal points relative to a non-effective transformation coordinate.

Description

TECHNICAL FIELD The present invention relates to a network resource allocation method and system using a linear transformation based low complexity algorithm of a Nash negotiation solution in a dynamic network,

The present invention relates to a resource allocation technique, and more particularly, to a resource allocation technique using an Nash negotiation solution.

Research on resource allocation in computer systems and networks is one of the ongoing issues. There is a continuing effort to efficiently allocate limited resources within a system.

Some solutions using game theory-based bargaining solutions for multimedia resource allocation problems (H. Park and M. van der Schaar, "Bargaining strategies for networked multimedia resource management," IEEE Trans. Signal Processing , vol. 55, no. 7, pp. 3496-3511, July 2007.) has been proposed.

In particular, Nash bargaining solution (NBS) and Kalai-Smorodinsky bargaining solution (KSBS) have been proposed. This negotiation solution has been proposed as an efficient resource allocation method that guarantees the quality of service (QoS) in a limited network environment. However, there is a problem that the solution using the negotiation solution has a high computational complexity. As the amount of resources and the number of users using them increases, the computational complexity for computing the negotiation solution increases exponentially.

Accordingly, an approach of repeatedly performing low-complexity computations has been proposed in order to reduce computational complexity and computational complexity. Although this method greatly reduces the complexity of the computation for finding a solution in a given situation, it is still efficient because the feasible utility set is also variable in a dynamically changing environment such as a time-varying channel I can not.

SUMMARY OF THE INVENTION It is an object of the present invention to provide an efficient resource allocation method and system for deriving a Nash negotiation solution with low complexity in a dynamic network.

A dynamic network resource allocation method using an Nash negotiation solution according to an aspect of the present invention includes:

를 얻는 단계;A linear transformation matrix capable of mapping the effective utility set of the current time slot t to the utility set of the next time slot t +

;

를 상기 선형 변환 행렬

에 의해 변환한 변환 좌표

를 구하는 단계;Nash negotiation solution of current time slot t

To the linear transformation matrix

The transformed coordinates converted by

;

에 관하여 상기 변환 좌표

의 유효성 여부를 판정하는 단계;The effective utility set of the next time slot t + 1

The transformation coordinates

Determining whether the validity is valid;

를 합의 실패점으로 하는 유효 효용 집합

의 부 유효 효용 집합(sub feasible utility set)을 기초로, 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산하는 단계; 및Valid transform coordinates

A set of effective utility with a consensus failure point

Based on the sub feasible utility set, the Nash negotiation solution of the next time slot t + 1

; And

를 기준으로 유효 효용 집합의 파레토 최적점들로 구성된 탐색 영역을 기초로, 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산하는 단계를 포함할 수 있다.Invalid conversion coordinates

Based on the search area constituted by the Pareto optimal points of the effective utility set, the Nash negotiation solution of the next time slot t + 1

And a step of calculating

는 According to one embodiment, the linear transformation matrix

The

Diagonal matrix with one set of the effective utility of the current time slot t in accordance with the scale ratio of the effectiveness of the set of the next time slot t +1 sets the effective utility of the current time slot t may be mapped to the next available set of utility timeslot t +1 .

는 n 명의 사용자들 각자의 최대 달성 가능 효용비들을 대각선 성분으로 가지는 대각 행렬일 수 있다.According to one embodiment, the linear transformation matrix

May be a diagonal matrix with diagonal elements of the maximum achievable utility ratios of n users.

는 다음의 수학식According to one embodiment, the linear transformation matrix

Is expressed by the following equation

는 시간 슬롯 t에서 i 번째 사용자(이때, i는 1≤i≤n인 정수)가 자원 R(t)를 모두 독점하는 경우의 효용이며,

는 시간 슬롯 t+1에서 i 번째 사용자가 자원 R(t+1)를 모두 독점하는 경우의 효용일 수 있다.≪ / RTI >

Is a utility in the case where the i- th user ( i is an integer satisfying 1? I ? N ) in the time slot t monopolizes the resource R (t)

May be a utility when the i- th user monopolizes the resource R (t + 1) in the time slot t + 1 .

가 유효한 경우에 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산하는 단계는,According to one embodiment,

The Nash negotiation solution of the next time slot t + 1

Wherein:

를 유효 효용 집합

의 새로운 합의 실패점

로 설정하는 단계;Transformation coordinates

The effective utility set

New consensus failure point of

;

와 변환 좌표

에 의해 탐색 영역을 정의하는 단계; 및The new consensus failure point

And transform coordinates

Defining a search area by the search area; And

를 연산하는 단계를 포함할 수 있다.The NBS operation is performed in the search area defined above and the Nash negotiation solution of the next time slot t +

May be computed.

가 비유효한 경우에 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산하는 단계는,According to one embodiment,

Nash negotiation solution of the next time slot t +

Wherein:

중에서

를 기준으로 유효 효용 집합의 파레토 최적점들을 구하는 단계;Effective utility set

Between

Obtaining the Pareto optimal points of the effective utility set based on the Pareto optimal points;

Designating a search area made up of the Pareto optimal points; And

를 연산하는 단계를 포함할 수 있다.By performing validation in the search area, the Nash negotiation solution of the next time slot t +

May be computed.

According to one embodiment, a dynamic network resource allocation method using the Nash negotiation solution comprises:

및 각 사용자 i마다 할당되는 자원

에 관하여 최대 달성 가능 효용 함수

를 기초로 내쉬 협상 해법

를 연산하는 단계를 더 포함할 수 있다.At least in the first time slot t ₀ the effective utility set of the dynamic network

And resources allocated to each user i

Maximum achievable utility function

Nash negotiation solution based on

And a step of calculating the number of pixels.

A dynamic network resource allocation system using an Nash negotiation solution according to another aspect of the present invention includes:

An effective utility set generation unit for generating an effective utility set based on data on the network total resources, users' resource allocation requirements, and resource distribution status by examining a dynamic network environment;

A linear transformation matrix that is approximately mapped between the effective utility set of the current time slot and the effective utility set of the next time slot is obtained and the Nash negotiation solution NBS computed in the current time slot using the linear transformation matrix is used as the effective value of the next time slot An effective utility set mapping unit for obtaining transformed NBS coordinates mapped to the set;

A first Nash negotiation solution calculation unit for calculating an Nash negotiation solution for a next time slot based on an effective utility set of a next time slot provided by the effective utility set generation unit and transformed NBS coordinates provided by the effective utility set mapping unit; And

And a network resource allocation setting unit for allocating network resources for each user according to the computed NBS solution.

According to one embodiment, the linear transformation matrix < RTI ID = 0.0 >

The effective utility set of the current time slot and the effective utility set of the next time slot may be mapped to the effective utility set of the next time slot according to the scale ratio of the effective utility set of the next time slot.

According to one embodiment, the linear transformation matrix may be a diagonal matrix with diagonal components of the maximum achievable utility ratios of n users.

According to one embodiment, the linear transformation matrix is expressed by the following equation

는 시간 슬롯 t에서 i 번째 사용자(이때, i는 1≤i≤n인 정수)가 자원 R(t)를 모두 독점하는 경우의 효용이며,

는 시간 슬롯 t+1에서 i 번째 사용자가 자원 R(t+1)를 모두 독점하는 경우의 효용일 수 있다.≪ / RTI >

Is a utility in the case where the i- th user ( i is an integer satisfying 1? I ? N ) in the time slot t monopolizes the resource R (t)

May be a utility when the i- th user monopolizes the resource R (t + 1) in the time slot t + 1 .

According to one embodiment,

The first Nash negotiation solution operation unit may perform an NBS operation within a sub-effectiveness set defined by setting the transformed NBS coordinates as a new sum failure point if the transformed NBS coordinates are valid based on the validity set of the next time slot . ≪ / RTI >

According to one embodiment, the first Nash negotiation solution operation unit may be configured so that, if the transformed NBS coordinates are ineffective based on the effective set of the next time slot, the Pareto optimal points of the effective utility set In a search area consisting of < RTI ID = 0.0 > a < / RTI >

According to one embodiment, a dynamic network resource allocation system using the Nash negotiation solution comprises:

And a second Nash negotiation solution calculation unit for calculating an Nash negotiation solution at least in the first time slot based on the first set of the effective benefits according to the resource allocation request and the given network total resources at least in the initial time slot.

According to the resource allocation method and system using the linear conversion-based low complexity algorithm of the Nash negotiation solution of the present invention, the Nash negotiation solution can be quickly obtained by excluding the resource distribution pair that does not affect the negotiation solution from the calculation.

According to the resource allocation method and system using the linear transformation-based low complexity algorithm of the Nash negotiation solution of the present invention, it is possible to provide a resource distribution scheme in a variable environment of a dynamic network by using a fast operation speed.

1 is a conceptual diagram illustrating a resource allocation method using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention.
FIG. 2 is a conceptual diagram illustrating a time-dependent change of effective utility sets in a dynamic network and a change of NBS according to the linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention.
FIG. 3 is a flowchart illustrating a resource allocation method using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention.
4 is a flowchart illustrating an Nash negotiation solution calculation procedure in a case where transformed coordinates are determined to be valid among resource allocation methods using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention.
FIG. 5 is a flowchart illustrating a Nash negotiation solution calculation procedure in a case where transformed coordinates are determined to be ineffective among resource allocation methods using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention.
6 is a block diagram illustrating a resource allocation system using a linear transform based low complexity algorithm of the Nash negotiation solution in accordance with an embodiment of the present invention.
7 and 8 are graphs illustrating a method of allocating resources in a dynamic network according to an embodiment of the present invention in order to compare the performance of an existing methodology with a resource allocation methodology using a linear transformation-based low complexity algorithm according to an embodiment of the present invention. These are graphs comparing the number of operations required to derive and the error rate.

For the embodiments of the invention disclosed herein, specific structural and functional descriptions are set forth for the purpose of describing an embodiment of the invention only, and it is to be understood that the embodiments of the invention may be practiced in various forms, The present invention should not be construed as limited to the embodiments described in Figs.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The same reference numerals are used for the same constituent elements in the drawings and redundant explanations for the same constituent elements are omitted.

The present invention relates to a research project entitled " Robust real-time multimedia transmission strategy in various network environment "(assignment number 20120002917) of Ewha Womans University, and a research project sponsored by the Ministry of Knowledge Economy (National Project No. NIPA-2012-H-0301-12-1008) of the "Development of Next Generation Digital TV Broadcasting System (realistic / mobile / bi-directional) core technology" Research Project of U-OFFICE Service based on High Speed Wireless Network "project (NIPA-2012-H-0301-12-4004) under the support project of university IT research center managed by the Information and Communication Industry Promotion Agency under Ministry of Knowledge Economy Based on the results of research conducted with the support of

1 is a conceptual diagram illustrating a resource allocation method using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention.

Referring to FIG. 1, a method for finding a solution of a resource allocation problem in a dynamic network using a Nash negotiation solution, and a Nash negotiation solution using a low complexity algorithm based on a linear transformation matrix is illustrated .

The dynamic network resource allocation problem with multiple users can be formulated as follows.

를 가진다. 효용 함수

는 달성 품질을 나타낸다. 사용자들이 어떤 시간 t에 네트워크에서 공유하는 총자원은 R(t)이고, 사용자 i에게 할당되는 자원은

라고 표현된다.There are n users who want to use multimedia in a dynamic network, and each user i ( i is an integer with 1? I ? N ) has its own utility function,

. Utility function

Indicates the achieved quality. The total resources that users share in the network at any time t is R (t), and the resources allocated to user i are

.

이다.For the sake of optimal resource allocation and computation, assuming that there is no packet error in this network as an ideal case, it can be said that the total available resource R (t) is evenly distributed among n users. In other words

to be.

로써 달성할 수 있는 효용은

라고 표현된다.When user i assigns resources assigned to him

The utility that can be achieved with

.

가 형성될 수 있는데, 이 집합

는 비어있지 않고(non-empty), 볼록하며(convex), 닫혀(closed) 있다.Thus, a joint feasible utility set

May be formed,

Are non-empty, convex, and closed.

에서, 각 사용자의 최소 효용 집합(set of minimum utilities)은 합의 실패점(disagreement point)

라고 표시된다.set

, The set of minimum utilities for each user is the disagreement point,

Is displayed.

Normally, the Nash negotiation solution can be found through exhaustive search for all potential utility pairs, which often requires very high computational complexity, and thus this approach is inefficient in reality.

However, as suggested in the resource allocation method using the linear transformation-based low complexity algorithm of the present invention, if considering the linearity transformation between adjacent effective utility sets or between them, the complexity required for the search in the time- Can be greatly reduced.

Referring now to FIG. 2 for a moment, and with reference to FIG. 2, with respect to aspects over time of validity aggregates and NBS in a time-varying environment, FIG. 2 illustrates a linear transformation based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention , A conceptual diagram illustrating a change over time of effective utility sets in a dynamic network and a corresponding change in NBS.

은 비어있지 않고 볼록하며 닫힌 2차원 그래프의 안쪽 영역에 존재하는 유효 효용 쌍들의 집합으로 나타난다.2, the entire user for convenience of explanation, the case is to be limited to two people (n = 2), the effective utility set in the time slot t

Is represented as a set of validity pairs that exist in the inner region of a non-empty, convex, closed 2D graph.

의 유효 효용들 중에 두 사용자들에게 최대 효용을 주는 해는

이다.The effective utility set in the time slot t

Of the usefulness of the two utilities, the solution that gives the maximum utility to

to be.

은

에 비해 더 확장되며, 나아가 두 사용자들에게 최대 효용을 주는 해는

이다. In the next time slot t +1, when the available network total resources are increased,

silver

, And further, the solution that gives the maximum utility to both users

to be.

은

에 비해 크게 축소되며, 나아가 두 사용자들에게 최대 효용을 주는 해는

이다.Then, in the next time slot t + 2, the available network resources are reduced,

silver

, And the year that gives the maximum utility to both users

to be.

,

및

를 관찰하면서, NBS 점들의 변동은 유효 효용 집합들의 형태의 변동에 영향을 받는다는 점에 주목하였다.The inventors of the present application have found that in an environment where the total network resources fluctuate with time

,

And

, It is noted that the variation of the NBS points is influenced by the variation of the form of the effective utility sets.

내의

의 좌표를 총자원의 크기가 커진 다음 시간 슬롯 t+1의 유효 효용 집합

으로 매핑하여

과 비교하면,

의 매핑된 좌표는

의 유효한 공간 내에 있지만 파레토 최적(Pareto Optimal) 점은 아니다. 파레토 최적과 관련하여,

의 매핑된 좌표를 기준으로 우상의 사분영역만

의 매핑된 좌표보다 더 큰 효용을 가지며, 나머지 영역들에 대해서는 효용을 따질 필요가 없다는 점은 분명하다. 따라서

은

의 매핑된 좌표를 새로운 합의 실패점

로 삼아 NBS 연산될 수 있다. NBS(t)를

에 매핑한 좌표는

에 상당히 가까울 것으로 기대되므로, NBS 연산은 매우 빠르게 완료될 수 있다.Referring again to Figure 1, for example, the effective utility set of the current time slot t

undergarment

The effective utility set of the next time slot t + 1 after the increase of the total resource size

To

In comparison with the above,

The mapped coordinates of

But it is not a Pareto Optimal point. Regarding Pareto optimization,

Based on the mapped coordinates of the upper right quadrant

It is evident that there is no need to look at utility for the remaining regions. therefore

silver

The mapped coordinates of the new consensus point

And NBS can be calculated. NBS (t)

The coordinates mapped to

It is expected that the NBS operation can be completed very quickly.

의

의 좌표를 총자원의 크기가 작아진 다음 시간 슬롯 t+1의 유효 효용 집합

로 매핑하여

와 비교하면,

의 매핑된 좌표는

의 유효한 공간 밖에 있다. 이 경우에도 파레토 최적과 관련하여,

의 매핑된 좌표를 이상적 목표로 정하면, 유효 효용 집합

의 파레토 최적점들은

의 매핑된 좌표를 기준으로 좌하의 사분영역 내에서 찾을 수 있다. 또한

는

에 속하는 효용들 중에서 가장 효용이 높은 효용 쌍에 존재한다. 따라서,

는 유효 효용 공간

의 경계를 이루는 효용들 중에 존재하고, 이러한 유효 효용 공간

의 경계를 이루는 효용들만 탐색하면서 NBS 연산함으로써 매우 빠르게 획득될 수 있다.On the other hand, the current time slot t

of

The effective utility set of the next time slot t + 1 after the total resource size is reduced

To

In comparison,

The mapped coordinates of

Is outside the valid space of In this case, too, with respect to Pareto optimal,

Is set as an ideal target, the effective utility set

Pareto optimal points of

Can be found in the lower-left quadrant based on the mapped coordinates of the lower left corner. Also

The

Of the utilities belonging to the highest utility. therefore,

The effective space

, And the effective utility space

Can be obtained very quickly by performing the NBS operation while searching only the utilities constituting the boundary of " NBS ".

At this time, depending on the embodiment, the coordinates of the NBS of the previous time slot may be directly mapped to the validity set of the next time slot, among the validity sets of two consecutive time slots. In this case, however, the fluctuating scale differences of the utility sets will not be considered.

In another embodiment, the NBS of the current time slot may be mapped into the validity set of the next time slot according to the scale ratio between the validity set of the current time slot and the validity set of the next time slot.

Specifically, the NBS of the current time slot may be mapped to the effective consumption set of the next time slot according to the ratio between the maximum utility in the current time slot and the maximum utility in the next time slot.

와

는 다음 수학식 1과 같이 표현될 수 있다.First, the effective utility set of n users distributing the total resources R (t) and R (t + 1) available at time t and t +1

Wow

Can be expressed by the following equation (1).

와

은 각각 시간 t 및 t+1에서 사용자 i에게 할당된 자원들을 가리킨다. 또한 상응하는 효용은

및

로 각각 표현된다.here,

Wow

Quot; refers to resources allocated to user i at times t and t + 1, respectively. The corresponding utility

And

Respectively.

On the other hand, the validity interface of the effective utility set is a convex and closed subspace with vertices at points where the effective utility set meets the orthogonal axis of the space whose origin is the point of failure, Each vertex implies an achievable utility, i. E. Maximum achievable efficiency, when a user i monopolizes all network resources R (t) .

Thus, if each user utilizes the utility of monopolizing the resource in the current time slot t and the ratio of the achievable utility in monopolizing the resource in the next time slot t + 1, The NBS can be appropriately mapped to the effective set of timeslots of the next time slot with different scales.

In particular, linear transformation by "independence of positive linear transformations", one of the axioms of the Nash negotiation solution, does not affect the results.

는 다음의 수학식 2와 같이 각 사용자의 최대 달성 가능 효용비(ratio of the maximum achievable utility)에 기초하여 정의될 수 있다.Thus, the nxn linear transformation matrix

Can be defined based on the ratio of the maximum achievable utility of each user as: < EMI ID = 2.0 >

는 원점, 즉

으로 가정할 수 있다. 다만, 합의 실패점

가 원점이 아닌

인 경우에는, 합산되는 항만 고려해주면 된다.Here, for convenience of explanation,

Is the origin

. However,

Is not the origin

, Only the ports to be added are considered.

는 현재 시간 슬롯 t의

를 다음 시간 슬롯 t+1의 유효 효용 집합 공간 내에 정확하게 매핑하지 않을 수 있지만 근사적으로 매핑할 수는 있다.Such a linear transformation matrix

Lt; RTI ID = 0.0 > t &

May not be precisely mapped into the validity aggregation space of the next time slot t + 1, but may be approximated.

를 적절하게 구한 경우에 다음 시간 슬롯 t+1에서 내쉬 협상 해법

를 빠르게 구하는 방법이라고 할 수 있다.Linear transformation it based on the resource allocation method using a low complexity algorithm of the invention is now Nash negotiation solution in time slot t

The Nash negotiation solution at the next time slot t + 1

Can be quickly obtained.

와 유효 효용 집합

에 관하여 내쉬 협상 해법

은 본 발명의 명세서에 기재되지는 않았지만 예를 들어 종래의 전수 탐색 기법 또는 본 발명자가 본 출원의 연구와 관련하여 출원한 한국특허출원 제10-2012-0027289 (2012년 3월 16일자 출원)에 개시된 바와 같은 부 유효 효용 집합들(sub-feasible utility sets)에 대한 반복적 연산을 통한 내쉬 협상 해법 탐색 기법을 이용하여 획득될 필요가 있다는 점을 의미한다.On the contrary, at least at the first time t ₀ ,

And the effective utility set

About Nash Negotiation Solutions

Is not described in the specification of the present invention but can be applied, for example, to a conventional full search technique or Korean Patent Application No. 10-2012-0027289 (filed on March 16, 2012) filed in connection with the present invention by the present inventor Means that it needs to be obtained using the Nash negotiation solution search method through iterative operations on the sub-feasible utility sets as disclosed.

가 결정되면, 본 발명의 본 발명의 선형 변환 기반 저복잡도 알고리즘을 이용하는 자원 할당 방법을 이용하여 다음 시간 슬롯 t+1에서

은 다음과 같은 방법론을 통해 빠르게 획득될 수 있다.Once in any time slot t including the initial time slot t ₀ , including the method of the present invention,

If it is determined that the linear transformation of the present invention of the present invention based on using a resource allocation method using a low complexity algorithm in the next time slot t +1

Can be quickly obtained through the following methodology.

에 n×n 선형 변환 행렬

를 곱한 변환 NBS를

라고 하면, 다음 수학식 3과 같이 표현될 수 있다.The nash negotiation hint of n users in the current time slot t

An n x n linear transformation matrix

The transformed NBS multiplied by

Can be expressed by the following equation (3).

는 시간 슬롯 t의

로부터 얻은 변환 NBS 좌표로서, 시간 슬롯 t+1에서의

을 찾는 데에 활용된다.here

Lt; RTI ID = 0.0 >

As the transformed NBS coordinates from time slot t + 1,

.

는 자원의 변화와 각 사용자별 효용 함수의 변화에 기초하며 시간 슬롯 t+1에서는 수학식 4와 같이 유효(feasible)할 수도 있고 비유효(infeasible)할 수도 있다.As described above,

Is based on a change in resources and a change in utility function for each user, and may be feasible or infeasible as shown in Equation (4) in a time slot t + 1.

가 시간 슬롯 t+1에서 유효하면서 또한 파레토 최적은 아닌 경우에, 유효 효용 집합

에서 NBS를 연산하기 위한 합의 실패점

는

로 설정된다. 또한 유효 효용 집합

중에서 새로운 합의 실패점

즉

를 기준으로 우상 사분면에 해당하는 영역에 대해서만 NBS 연산이 필요하다.First, if

≪ / RTI > is valid at time slot t + 1 and not Pareto optimal,

A consensus failure point for computing the NBS in

The

. Also,

New consensus failure point in

In other words

The NBS operation is required only for the region corresponding to the upper right quadrant.

가 시간 슬롯 t+1에서 유효하면서 또한 파레토 최적은 아닌 경우에, 유효 효용 집합

중에서

를 기준으로 우상 사분면에 해당하는 영역에 대해서만 NBS 연산을 수행한다.therefore,

≪ / RTI > is valid at time slot t + 1 and not Pareto optimal,

Between

The NBS calculation is performed only for the region corresponding to the right-top quadrant.

가 시간 슬롯 t+1에서 유효하면서 또한 파레토 최적인 경우가 되며, 이 경우는

은

와 동일하다.On the other hand, if both the network resources and the user environment do not change between two successive time slots

Is valid at time slot t + 1 and is also Pareto optimal, in which case

silver

.

가 시간 슬롯 t+1에서 비유효한 경우에는, 유효 효용 집합

의 파레토 최적점들을 먼저 찾고, 파레토 최적점들로 이루어진 탐색 영역을 형성하며, 이러한 탐색 영역에 대해서 유효성 검사(feasibility test)를 통해

연산을 수행할 수 있다.Next, if

Is invalid at time slot t + 1, the effective utility set

The search for the Pareto optimal points first, the search for the Pareto optimal points, and the feasibility test for this search area

Operation can be performed.

  The utility pairs inside the Pareto optimal points are not necessary for the NBS operation because they do not give maximum utility to each user.

In this manner, the resource allocation method using the linear transformation-based low complexity algorithm of the Nash negotiation solution of the present invention can obtain the NBS of the next time slot very quickly using the NBS of the previous time slot.

FIG. 3 is a flowchart illustrating a resource allocation method using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention.

및 각 사용자 i마다 할당되는 자원

에 관하여 최대 달성 가능 효용 함수

를 기초로 내쉬 협상 해법

를 연산하는 단계부터 시작한다.Referring to FIG. 3, a resource allocation method using a linear transformation-based low complexity algorithm of the Nash negotiation solution computes, at step S31, at least a first time slot t ₀ ,

And resources allocated to each user i

Maximum achievable utility function

Nash negotiation solution based on

. ≪ / RTI >

의 최초 초기값이 주어지거나, 또는 기존의 방법론들에 의해 최초의 내쉬 협상 해법

가 연산되어야 한다.The resource allocation method using the Nash negotiation solution of the present invention is a method of quickly calculating the Nash negotiation solution of the next time slot based on the Nash negotiation solution in the previous time slot,

Is given the initial initial value of the Nash negotiation solution, or by the existing methodologies,

Lt; / RTI >

이 획득된 이후에, 최초의 시간 슬롯 t ₀을 포함하는 현재 시간 슬롯 t의 내쉬 협상 해법

을 기초로 다음 시간 슬롯 t+1에서 네트워크 자원 분배에 적용할 내쉬 협상 해법

을 연산하는 단계를 매 시간 슬롯마다 반복적으로 수행할 수 있다.The first Nash negotiation solution

After the acquisition, Nash negotiation solution in the current time slot t including a first time slot t ₀

Nash negotiation solution to apply to network resource distribution in the next time slot t +1 based on

May be repeatedly performed for each time slot.

와 다음 시간 슬롯 t+1의 유효 효용 집합

의 모양이나 크기의 변동으로 나타날 수 있다. 이러한 변동은 현재 시간 슬롯 t의 유효 효용 집합 공간과 다음 시간 슬롯 t+1 유효 효용 집합 공간 사이의 선형 변환 행렬

로써 근사화할 수 있다.Dynamic changes in the network environment, such as fluctuation and each user of a change in the utility function can be achieved up to a total of the network resources are available utility sets the current time slot t

And the effective utility set of the next time slot t + 1

The shape and the size of the object can be changed. This variance is a linear transformation matrix between the effective utility set space of the current time slot t and the next time slot t + 1 effective utility set space

Can be approximated as.

를 얻는다.In step S32, a linear transformation matrix, which can map the set of validity of the current time slot t to the set of validity effects of the next time slot t +

.

는 n 명의 사용자들의 최대 달성 가능 효용비들을 대각선 성분으로 가지는 대각 행렬일 수 있다.According to an embodiment, a linear transformation matrix

May be a diagonal matrix with the maximum achievable utility ratios of n users as diagonal elements.

는 n 명의 사용자들의 현재 시간 슬롯의 최대 달성 가능 효용과 다음 시간 슬롯의 최대 달성 가능 효용의 비율들을 대각선 성분으로 가지는 대각 행렬일 수 있다.Specifically, a linear transformation matrix

May be a diagonal matrix with diagonal components of the maximum achievable utility of the current time slot of n users and the maximum achievable utility of the next time slot.

를 선형 변환 행렬

에 의해 변환한 변환 좌표

를 구한다.In step S33, the Nash negotiation solution of the current time slot t

To a linear transformation matrix

The transformed coordinates converted by

.

에 관하여 변환 좌표

의 유효성 여부를 판정한다.In step S34, the effective utility set of the next time slot t +

Conversion coordinates about

Is validated.

가 유효하면, 단계(S35)로 진행하고, 그렇지 않으면 단계(S36)로 진행한다.If the transformation coordinates

The process proceeds to step S35, and if not, the process proceeds to step S36.

를 새로운 합의 실패점

로 하는 유효 효용 집합

의 부 유효 효용 집합(sub feasible utility set)을 기초로 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산한다.In step S35, valid conversion coordinates

The new consensus failure point

The effective utility set to

Nash negotiation solution of the next time slot t +1 based on the sub feasible utility set

.

를 기준으로 하는 유효 효용 집합

의 파레토 최적점들로 구성되는 탐색 영역을 기초로 다음 시간 슬롯 t+1의 내쉬 협상 해법

을 연산한다.On the other hand, in step S36,

The effective utility set based on

The Nash negotiation solution of the next time slot t + 1 based on the search area consisting of the Pareto optimal points of < RTI ID = 0.0 >

.

4 is a flowchart illustrating an Nash negotiation solution calculation procedure in a case where transformed coordinates are determined to be valid among resource allocation methods using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention.

가 유효하여 단계(S35)로 진행할 경우에, 단계(S351)에서, 변환 좌표

를 유효 효용 집합

의 새로운 합의 실패점

로 설정한다.Referring to FIG. 4,

Is valid and the process proceeds to step S35, in step S351,

The effective utility set

New consensus failure point of

.

와 변환 좌표

에 의해 탐색 영역을 정의한다.Then, in step S352, a new consensus failure point

And transform coordinates

To define a search area.

를 연산한다.In step S353, the NBS operation is performed in the defined search area to determine the Nash negotiation solution of the next time slot t +

.

Meanwhile, FIG. 5 is a flowchart illustrating an Nash negotiation solution calculation procedure in a case where transformed coordinates are determined to be invalid among resource allocation methods using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an embodiment of the present invention.

가 유효하지 않아서 단계(S36)로 진행될 경우에는, 단계(S361)에서, 유효 효용 집합

중에서

를 기준으로 하는 파레토 최적점들을 구한다.Referring to FIG. 5, in step S34,

Is not valid and the process proceeds to step S36, in step S361,

Between

Of the Pareto optimal points.

의 경계선이다.The Pareto optimal points thus obtained are actually the effective utility set

.

In step S362, a search area consisting of Pareto optimal points is designated.

를 연산한다.In step S363, by performing validation in the search area, the Nash negotiation solution of the next time slot t +

.

6 is a block diagram illustrating a resource allocation system using a linear transform based low complexity algorithm of the Nash negotiation solution in accordance with an embodiment of the present invention.

6, the resource allocation system 60 includes a network resource examining unit 61, an effective utility set generating unit 62, an effective utility set mapping unit 63, a first Nash negotiation solving operation 64, Nash negotiation solution calculation unit 65 and a network resource allocation setting unit 66. [

The network resource inquiry unit 61 examines the dynamic network environment to collect data on the network total resources, the resource allocation requests of the users, and the resource distribution status, and the effective-efficiency-set generation unit 62 generates effective- Generate sets.

The second Nash negotiation solution operation unit 65 computes the Nash negotiation solution at least in the first time slot based on the first set of effective benefits according to the given network total resources and the resource allocation requirement at least in the initial time slot.

The second Nash negotiation solution calculation unit 65 can provide an initial value for the Nash negotiation solution calculation of the first Nash negotiation solution operation unit 64 although it is slower than the first Nash negotiation solution operation unit 64 have.

When the network total resource or the user's resource allocation request and distribution situation fluctuates with the passage of time, the changed situation is detected by the network resource investigation unit 61, and the effective-efficiency-set generation unit 62 Then, a new effective utility set of the next time slot is generated.

The effective utility set mapping unit 63 obtains a linear transformation matrix that is approximately mapped between the effective utility set of the current time slot and the effective utility set of the next time slot and uses the linear transformation matrix to perform Nash negotiation Solution Obtain the transformed NBS coordinates by mapping the NBS to the effective utility set of the next time slot.

The first Nash negotiation solution calculation unit 64 calculates the Nash negotiation solution of the next time slot based on the effective utility set of the next time slot provided by the effective utility set generation unit 62 and the converted NBS coordinates provided by the effective utility set mapping unit 63, And calculates a negotiation solution.

Specifically, the first Nash negotiation solution calculation unit 64, if the transformed NBS coordinates are valid based on the validity set of the next time slot, sets the transformed NBS coordinates as a new sum failure point Lt; / RTI >

In addition, the first Nash negotiation solution calculation unit 64 may convert the transformed NBS coordinates into the Pareto optimal points of the validity set of the next time slot if the transformed NBS coordinates are ineffective based on the validity set of the next time slot And performs NBS operations in the search area.

The network resource allocation setting unit 66 allocates network resources for each user according to the NBS solution derived by the first Nash negotiation solution calculation unit 64. [

The first Nash negotiation solution calculation unit 64 can derive the Nash negotiation solution even in a dynamic network environment because the NBS operation speed is very fast compared to the conventional method and thus the network resources can be efficiently distributed in the dynamic network environment .

FIG. 7 is a diagram illustrating a resource allocation methodology using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention and a method for deriving a resource allocation solution in a set dynamic network according to an embodiment of the present invention These are graphs comparing the number of operations required.

Referring to FIG. 7, the computational complexity according to the conventional NBS and the Inter NBS is represented by graphs represented by a rectangular pointer and a triangle pointer, and the resource allocation methodology of the present invention, Intra NBS) is shown as a graph displayed as circular pointers.

The number of users is three, the utility function is properly defined for each user, and the nominal value of total resources varies from one time slot to another.

Since the inventive resource allocation methodology (Intra NBS) in the first time slot computes the Nash negotiation solution using the iterative search methodology (Inter NBS), the inventive resource allocation methodology (Intra NBS) It has the same computational complexity as the iterative search methodology (Inter NBS) indicated by the triangle pointer.

However, since the time slot thereafter, it can be seen that the number of operations required by the present invention's resource allocation method (Intra NBS) is reduced from one hundredth of a million to one ten billionth of that of the conventional conventional NBS have.

Although the Inter NBS method is reduced by about one thousandth compared to the conventional NBS method, the resource allocation method of the present invention (Intra NBS) is less than the Inter NBS method (Inter NBS) The number of operations is reduced to one tenth of a millionth.

In FIG. 7, the resource allocation methodology (Intra NBS) of the present invention shows that the operation speed is very fast if the total amount of resources is small, and when the total amount of resources is rapidly changed, such as time slots 6, 11, 12, Although the operation speed is slow, it is faster than the conventional methodologies.

FIG. 8 is a diagram illustrating a resource allocation methodology using a linear transformation-based low complexity algorithm of the Nash negotiation solution according to an exemplary embodiment of the present invention. These are graphs comparing the frequency of errors.

Referring to FIG. 8, the difference between the NBS solution obtained by the resource allocation methodology (Intra NBS) of the present invention and the NBS solution obtained by the existing iterative operation methodology (Inter NBS) based on the NBS solution obtained by the conventional full- In the case of each error, the NBS solutions by the resource allocation methodology (Intra NBS) of the present invention indicated by the triangle pointers have an error rate of only 1 to 2%, but the NBS solutions by the NBS Solutions have an error rate of 3-7%.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, Modification is possible. Accordingly, the spirit of the present invention should be understood only in accordance with the following claims, and all of the equivalent or equivalent variations will fall within the scope of the present invention.

Further, the apparatus according to the present invention can be implemented as a computer-readable code on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of the recording medium include a ROM, a RAM, an optical disk, a magnetic tape, a floppy disk, a hard disk, a nonvolatile memory, and the like, and a carrier wave (for example, transmission via the Internet).

60 Resource Allocation System 61 Network Resource Investigation Department
62 Effective Efficiency Set Generation Unit 63 Efficiency Efficiency Set Mapping Unit
64 first Nash negotiation solution calculation part 65 second Nash negotiation solution calculation part
66 Network resource allocation setting unit

Claims (16)

A method of allocating resources in a dynamic network using a Nash negotiation solution,
A linear transformation matrix capable of mapping the effective utility set of the current time slot t to the utility set of the next time slot t +

;
Nash negotiation solution of current time slot t

To the linear transformation matrix

The transformed coordinates converted by

;
The effective utility set of the next time slot t + 1

The transformation coordinates

Determining whether the validity is valid;
Valid transform coordinates

A set of effective utility with a consensus failure point

Based on the sub feasible utility set, the Nash negotiation solution of the next time slot t + 1

; And
Invalid conversion coordinates

Based on the search area constituted by the Pareto optimal points of the effective utility set, the Nash negotiation solution of the next time slot t + 1

Wherein the Nash negotiation solution includes a step of calculating an Nash negotiation solution. The method of claim 1, wherein the linear transformation matrix

The
Is a diagonal matrix with the effective utility of the set of current time slot t in accordance with the scale ratio of the effectiveness of the set of the next time slot t +1 sets the effective utility of the current time slot t may be mapped to the next available set of utility timeslot t +1 Wherein the method comprises the steps of: The method of claim 1, wherein the linear transformation matrix

Is a diagonal matrix with diagonal elements of the maximum achievable utility ratios of n users. ≪ RTI ID = 0.0 > [ 10] < / RTI > 4. The method of claim 3,

Is expressed by the following equation

≪ / RTI >

Is a utility in the case where the i- th user ( i is an integer satisfying 1? I ? N ) in the time slot t monopolizes the resource R (t)

Is a utility in the case where the i- th user monopolizes the resource R (t + 1) in the time slot t + 1. The resource allocation method of claim 1, The method according to claim 1,

The Nash negotiation solution of the next time slot t + 1

Wherein:
Transformation coordinates

The effective utility set

New consensus failure point of

;
The new consensus failure point

And transform coordinates

Defining a search area by the search area; And
The NBS operation is performed in the search area defined above and the Nash negotiation solution of the next time slot t +

The method of claim 1, further comprising the steps of: The method according to claim 1,

Nash negotiation solution of the next time slot t +

Wherein:
Effective utility set

Between

Obtaining the Pareto optimal points of the effective utility set based on the Pareto optimal points;
Designating a search area made up of the Pareto optimal points; And
By performing validation in the search area, the Nash negotiation solution of the next time slot t +

The method of claim 1, further comprising the steps of: The method according to claim 1,
At least in the first time slot t ₀ the effective utility set of the dynamic network

And resources allocated to each user i

Maximum achievable utility function

Nash negotiation solution based on

The method comprising the steps of: (a) calculating an Nash negotiation solution; A computer-readable recording medium having stored thereon a program for implementing a resource allocation method of a dynamic network using a Nash negotiation solution according to any one of claims 1 to 7. An effective utility set generation unit for generating an effective utility set based on data on the network total resources, users' resource allocation requirements, and resource distribution status by examining a dynamic network environment;
A linear transformation matrix that is approximately mapped between the effective utility set of the current time slot and the effective utility set of the next time slot is obtained and the Nash negotiation solution NBS computed in the current time slot using the linear transformation matrix is used as the effective value of the next time slot An effective utility set mapping unit for obtaining transformed NBS coordinates mapped to the set;
A first Nash negotiation solution calculation unit for calculating an Nash negotiation solution for a next time slot based on an effective utility set of a next time slot provided by the effective utility set generation unit and transformed NBS coordinates provided by the effective utility set mapping unit; And
And a network resource allocation setting unit that allocates network resources for each user according to the computed NBS solution. The method of claim 9, wherein the linear transformation matrix
And a diagonal matrix capable of mapping an effective utility set of a current time slot to an effective utility set of a next time slot according to a scale ratio of an effective utility set of a current time slot and an effective utility set of a next time slot. A resource allocation system for a dynamic network to use. 11. The system of claim 9, wherein the linear transformation matrix is a diagonal matrix having n maximum users' maximum achievable utility ratios as diagonal elements. 12. The method of claim 11, wherein the linear transformation matrix is expressed by the following equation

≪ / RTI >

Is a utility in the case where the i- th user ( i is an integer satisfying 1? I ? N ) in the time slot t monopolizes the resource R (t)

Is a utility in the case where the i- th user monopolizes the resource R (t + 1) at time slot t + 1 . The method of claim 9,
The first Nash negotiation solution operation unit may perform an NBS operation within a sub-effectiveness set defined by setting the transformed NBS coordinates as a new sum failure point if the transformed NBS coordinates are valid based on the validity set of the next time slot Wherein the Nash negotiation solution is operative to perform the Nash negotiation solution. The method of claim 9,
The first Nash negotiation solution calculation unit may be configured to determine whether or not the converted NBS coordinates are in the search area composed of the Pareto optimal points of the effective utility set based on the transformed NBS coordinates when the transformed NBS coordinates are ineffective based on the effective- Wherein the NBS negotiation solution is operative to perform an NBS operation in the resource allocation system of the dynamic network. The method of claim 9,
Further comprising a second Nash negotiation solution operation unit for calculating at least an Nash negotiation solution in a first time slot based on a first set of effective benefits in accordance with a resource allocation request and a given total network resources at least in a first time slot A resource allocation system for dynamic networks using the Nash negotiation solution. 17. A computer-readable recording medium having stored thereon a program for operating a computer as a resource allocation system of a dynamic network using an Nash negotiation solution according to any one of claims 9 to 15.

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