**본 논문은 제가 따로 요약 하였기에 저작권법에 접촉되지 않습니다.


(IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 8, AUGUST 2006)



A Tutorial on Cross-Layer Optimization in Wireless Networks


Xiaojun Lin, Member, IEEE, Ness B. Shroff, Senior Member, IEEE, and R. Srikant, Fellow, IEEE


-Tutorial Paper-



Abstract-

 Tutorial paper 최근의 무선시스템에서의 자원배분 문제 최적화 기법에 대한 발전에 대해서 보여준다.

1)우리는 Cellular networks(single hop)  위한 ‘opportunistic (channel-aware) scheduling’ 영역의 중요한 결과들을 살펴봄으로써 시작했다왜냐하면, Cellular networks 성능 최적화가 많이 필요한 영역이기 때문이다.

우리는 배웠던 중요한 교훈들을 설명하고 2)multi-hop wireless networks에서의 일반적인 자원배분 문제들에 대한 주요한 문제점들에 대해서 이야기  것이다.

그리고 Tutorial 뒷부분에서는 3) loosely coupled” cross-layer solution 안에서의 깔끔하게 최적화문제로 풀어낸

Multi-hop resource allocation problem naturally results 보여  것이다.

 말의 의미는하나의 알고리즘으로써 서로 다른 Protocol stack Layer (예를 들면, MAC/ PHY) 대한 map 얻는 것이기도 하며송수신되는 정보 (왔다갔다하는) 통해서 결합되는 알고리즘을 의미한다.

 알고리즘은 바로매우 복잡한 MAC층에서의 최적화된 스케줄링 구성요소로 취급될 것이고분산되는 간단한

솔루션들이 필요하다그리고 우리는 어떻게 Cross Layer framework에서 불완전한 스케줄링을 사용할 것인지를 시연하고최근에 개발된 분산 알고리즘에 대해서도 알아  것이다그리고 마지막으로 우리는 a set of open research problems 토의함으로써 마칠 것이다.

 


다시 말해서  논문은 아래의 5가지 단계를 따른다.


1) 기회주의적 스케줄링을 살펴봄


2) 멀티  무선네트워크에서의 자원배분 문제를 알아봄


3) 위의 자원배분 문제를 Loosely-coupled  Cross Layer에서 다시 자원배분 문제를 접근함


4) 그리고 어떻게 불완전한 스케줄링 알고리즘을 사용했는지분산 알고리즘은 무엇인지 설명  것이다.


5) 마지막으로 이와 함께 고민할  있는 Open Problems 다룸으로 마친다.








Q. 논문의 이해를 위해서 고민해봐야 하는 내용들

 

-Cross-Layer 의미는?

OSI7 같은 Independent layers 독립적인 rule break 하는 것이다왜냐하면이를 통하여 비약적인 성능의 향상의 결과가 있기 때문이다방법론적으로다른 layers 간의 변수공유와 같은 방법이 존재한다디자인 형태는 6가지가 존재하며,  내부적인 feedback  상호작용은 3가지 형태로 요약이 가능하다.

 

 

분산 알고리즘이란? ‘Distributed Algorithm’

 

A distributed algorithm is an algorithm designed to run on computer hardware constructed from interconnected processors. Distributed algorithms are used in many varied application areas of distributed computing, such as telecommunications, scientific computing, distributed information processing, and real-time process control. Standard problems solved by distributed algorithms include leader election, consensus, distributed search, spanning tree generation, mutual exclusion, and resource allocation.[1]


 

I. INTRODUCTION

 

Optimization-based  접근법은 지금까지 통신 네트워크 영역에서 “Resource allocation problem” 해결을 위해서 광범위하게 연구 되어왔다예를 들면, Internet congestion control 시스템의 성능을 최대한으로 끌어내는 convex optimization problem 으로 distributed primal or dual solutions 자원배분문제를 어떻게 해결하는가  대한 모범적인 예로써 생각할 수가 있다이런 류의 접근법(실험법 TCP(transmission control protocol) 대한 깊은 이해와 향상된 혼잡제어(congestion control) 라는 솔루션을 보여준다.[1-6]

어쨌든 질문의 핵심은 앞서 말한 접근법이 통합된 multi-hop wireless networks에서 *a clean-slate design of the protocol stack으로 적용   있다는 점이다사실Internet setting 에서의 그러한 기술의 직접적인 어플리케이션을 허용하지 않는 무선통신의 맥락에서 있어서  특별한 도전들이 있다특히무선매체는 본질적으로 유저들의 데이터송신에 의한 간섭이 많이 일어나는 다중접속매체로써채널의 capacity time-varying  성격을 보인다이러한 이유로무선매체는 사용자와 네트워크 Layer간의 상호의존성을 띄기 때문에 기존의 유선과는 반대의 성격을 가진다하지만이런 어려움에도 불구하고최근에 통합  최적화된 형태로써의 Multiple layer들의 무선자원을 자유로이 공유하거나 넘나드는(Cross Layer개념진보된 결과들을 보여준다이와 관련된 흥미로운 내용은 섹션3에서 설명한다.

(The solution of such an optimization framework will itself exhibit a layered structure with only a limited degree of cross-layer coupling.)

 

 

*The notion of a clean-slate design becomes especially attractive for multi-hop wireless networks, where the burdens of legacy systems are far less than for the Internet.

*Protocol Stack : 서로 다른 기기들이 데이터 통신을 하는  필요한 통신 규약을 구현해 주는 소프트웨어 모듈들의 모임 기기 간에 통신을   해당 통신 규약을 구현해 주는 핵심 소프트웨어이며프로파일은 상호 접속성을 확보하기 위해 애플리케이션에서 사용해야  통신 규약을 규정한 것이다예를 들어노트북 컴퓨터와 휴대 전화가 통신하기 위해서는 통신 규약이 서로 맞아야 데이터를 교환할  있다통신 규약 스택은 각각의 하드웨어에 탑재되어 통신 규약을 맞추어 구현해 주는 역할을 담당한다대표적인 것으로 TCP/IP 스택이 있으며이는 윈도즈 운영 체계에 포함되어 있다.

 

 

우리는 use of such an optimization approach for two classes of cross-layer problem 분명히 보여  것이다 다시 말해서,

Cellular (or access-point-based single-hop networks)에서 기회주의적 스케줄링 문제점을 보고 시나리오를 발전시켜서 multi-hop wireless networks에서의 혼잡제어와 스케줄링 문제를 살펴볼 것이다.

그리고 optimization approach 해결하기 위한 중요한 도구로 사용되는 convex programming  대해서 알아볼 것이다.

 

특히, convex programming에서 Lagrange duality 복잡한 최적화 문제를 간단한 여러 가지 문제로써 분해하는 중요한 핵심 도구이다하지만우리는 종종 우리는 이것만으로 문제를 100% 해결하는 것에는 부족하단 것을 안다왜냐하면유선 네트워크와는 반대로많은 무선 네트워크에서의 Cross-layer control problems  not convex (볼록않기 때문이다.

예를 든다면무선 네트워크에서의 간섭문제들로 인하여각각의 시간에 대해서 활성화 되어야 하는 링크들의 부분집합들에 대한 선택에 있어서 정확히 선택해야 하는 정교한 스케줄링 mechanisms 요구하는  같은 것이다무선 네트워크에서 링크들의 capacity 신호와 간섭레벨에 의존적이고그러한 것들은 파워와 링크의 전송 스케줄에 의존적이다그래서 link capacity, power assignment, and the transmission schedule 에서의 관계들은 전형적으로 non-convex 하다.

그러므로스케줄링 요소는 어려운 non-convex problem 풀기 위해 필요하고이는 보통 전체 솔루션에서 병목현상을 뛴다.

무선 네트워크에서 이러한 문제들을 내재하는 non-convex 문제들을 해결하기 위해선, convex-programming 적인 진보된 테크닉의 사용이 요구된다.

 

 

 

 tutorial paper에선아래의 6가지 예시들을 집중적으로 살펴  것이다.

1)       Tools from convex programming,

2)       Combinatorial optimization

3)       Stochastic stability

4)       Graph theory

5)       Large deviations

6)       Heavy-traffic limits are used to obtain realistic and efficient solutions to the cross-layer control problem.

 

cross-layer optimization 는 최근 사이에 꽤 큰 이슈로 발전 되었고, 이를 위한 포괄적인 조사는 공간적인 (space constraints) 제한을 가진다. 따라서, 이 paper에선 모두를 다 조사하진 못했다. 오히려, 포커스는 주요한 이슈와 도전들, 그리고 테크닉과 open problem들에 대해서 독자들에게 알려주는 정보전달에 대해서 맞춰져 있다. [7]을 참조하길 바란다.

 

 

 논문의 구성은 아래와 같다.

Section II: cellular networks에서 scheduling 문제점에 대한 설명을 하면서스케줄링 선택에 있어서 물리계층 채널 정보를 결합시키는 점에 대해서 강조한다.

Section III:  we investigate the joint congestion-control and scheduling problem in multi-hop wireless networks.

섹션3 내용은 주로 the cross-layer problem  a congestion control component and a scheduling component 2가지로 깔끔하게 분해하며 접근한다하지만, non-convexity성격 때문에 실제 네트워크에서 스케줄링은 매우 어렵지만 cross-layer solution으로 심플하지만 불완전한 해결법으로 어느 정도 접근해본다.

Section IV: 당연히  부분은 앞으로  보완되고 다듬어져 가야 한다.

Section V: recent developments in obtaining imperfect distributed scheduling policies with provably achievable throughput bounds.

We then conclude with a set of open problems.

 

 

II. OPPORTUNISTIC SCHEDULING FOR CELLULAR WIRELESS NETWORKS

 

오랫동안 multiuser scheduling problem 산업과 학교에서 많은 조명을 받아왔다그리고 multiuser scheduling problem 무선 네트워크에서 독특한 특징으로써 많은 동기부여를 받아왔다. : 자원의 크기, mobile 유저의 간섭문제시변 채널의 조건들(이동성과 페이딩으로 인한)

 

좋은 스케줄링 방법이란높은 네트워크 성능을 만족시키는 채널 컨디션을 기회주의적 형태로 분석 활용하는 것을 의미한다.

예를 들면, N명이 이용자들과 베이스 컨디션으로 구성된 cellular networks 고려하는 것이다.

게다가가정해보자.  유저들의 base station 으로부터의 타임슬롯시스템과 다운링크 통신에 대해서 가정해보자.

base station 채널 조건을 기반으로 어느 유저가 전송이 가능한지 결정할 수가 있다 아이디어는 SINR기반의 채널컨디션에 따라서 수신 단으로의 전송을 베이스 스테이션이 주어진 BER 만족시키며 높은 속도로 전송을 허용하는 것을 의미한다이것은 Base Station  기회주의적 기법으로 높은 네트워크 성능유지를 위하여 채널의 조건을 이용한다는 의미이다.

이와는 달리 기존의 전통적인 방법에선채널의 가변성을 제거하는 것이 주된 관심사였다.

 (예를 들면, spread spectrum, repetitive coding, and power averaging)

 

Opportunistic scheduling  대한 설명~ (앞장참고)

 

우리의 초점은 Downlink에서의 base station 전송 시나리오로 한정하며/무한 backlogged cased 위한 Opportunistic scheduling solutions  것이다.

 




A. Infinite-Backlog Case

 

Infinite-Backlog Case 종종 통신시스템 분야에서 프로토콜의 성능평가와 최대의 성능 량을 보기 위하여 사용된다.

이는 매우 심플하고 중요한 이해를 제공하는 다루기 쉬운 평가방법이다 단락의 내용에서의 목적은 실행가능한 스케줄링 정책 Q 찾는것이다. Q 주어진 공정성과 QoS 요구조건을 만족하며전반적으로 시스템 성능이 최대화를 보여주는 스케줄링 정책을 의미한다.

: policy Q Vector. 의미한다.

 : The index of the user selected for transmission : 전송을 위한 선택되는 유저의 인덱스

 : The data rate transmitted to user ; 사용자에게 전송되는 통신속도

Ui : the utility function of user , ; 유저의 이용률 함수

: measures the value or benefit to user i of the receiving data rate xi. ; i번째 유저의 수신속도 xi 이익 또는 값의 측정값

(Note that xi is a function of the channel condition and the coding and modulation scheme used.)

 

There have been many scheduling schemes that address this problem [9]–[13].

그리고 흥미롭게도 이들의 심플하고 근시안적인 스케줄 정책들의 형태는 아래의 식으로 표현이  수가 있다.

 

 

 and  constants and can be viewed as Lagrange multipliers. For example, consider the following problem studied in [12], [13]:

*Lagrange Multipliers: 출력물 참조

 

 

 :  The set of all stationary scheduling policies,

 : The minimum fraction of time-slots assigned to user (i.e., fairness in time)

 

명백하게 이것은 비선형 최적화 문제를 나타낸다하지만이것을 위의 Q*식에서  = 0  적절한 값의 선택으로 최적화를 쉽게 보여준다.

Q*식의 최적화 법은 각각의 타임슬롯에서 실행되고 확률적인 근사적 알고리즘을 통하여 얻을 수가 있다. [13]

유사하게도, temporal fairness 대신에 우리는 아래와 같은 QoS form 고려할 수가 있다.

 

• Fairness in utility: Each user receives at least a fraction of the aggregate utility value [11], [13].

 

• Minimum data rate requirement: Each user receives a minimum data rate of bps [13].

 

• Proportional fairness: Here, the objective is to achieve a solution that is proportionally fair, i.e., increasing the mean throughput of one user from the optimal level by results in a cumulative percentage decrease by greater than of the mean throughput of other users [14]. It turns out that such a solution is achieved when the optimization problem is to maximize the sum of the logarithms of the expected rates (or the product of the expected rates), i.e.,

식을 통하여 도출되는 각각의 케이스는 Q* 식과 상응하는 동일한 최적화 솔루션을 보여준다. (=0 )

그러므로이런 결과는 우리에게 무선네트워크상에서 시스템 성능의 기회적인 향상으로 이용될  있는 심플하면서 근시안적인 지표의 스케줄링 정책이라고 말해준다.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B. Stability of Opportunistic Scheduling Schemes

 

이전에 A에서는 Infinite-Backlog Case  시스템으로 가정하여서 QoS/fairness constraints 조건하에 시스템의 Utility 평가하는 문제였다.

이제는, opportunistic scheduling 좀더 발전시켜서시스템의 QoS 제한성과 안정성을 위배하지 않는 범위 내에서 다루는 문제를  것이다.

먼저여기에 확률적인 안정성에서 유용성의 최대화로부터 이동한 문제가 있다 문제는 throughput-optimal scheduling 크게 관심 받아왔다. [15]

 것은 최대화의  가중치의 합의 비율이 바로최적의 처리량을 나타낸다는 스케줄링 법을 보여준다그리고 cellular networks에서 스케줄링 법은 아래의 형식을 따른다.

 : the queue length of user ,

xi : again the data rate transmitted to user

 

위의 스케줄링은 공정한 걸로 간주되며이것은 큐의 길이 정보가 최적화된 스케줄링 법에서 매우 중요한 것이라는 사실을 보여준다.

그래서이를 통하여많은 Idea들은 queue-length-based 처리량최적화와 안정성에 초점을 맞추어 opportunistic scheduling schemes 개발 되어왔다. [16]-[20]

(예를 들어), 논문 [16],[17]에서 아래의 form 따르는 간단한 index 스케줄링 법들은 최적의 처리량을 보여준다.

 

 : 상수,      the head-of-the-line packet delay at queue,      : the data rate of user.

그리고 delay-based 정책지표는 지수함수 가중치로 최적의 처리량을 보여준다.

최적의 처리량 스케줄링 법은 [21] 논문을 참고하길 바란다논문의 저자는 유저들이 시스템에 도달하는 임의의 부하의 양과 전송개시 하는 부하의 양을 모델링 했다그리고 최근에 논문[22], [23]에서의 저자는  traffic 제한성들과  편차로부터의 QoS 사용하는 기술과 안정성 기반의 다른 형태의 스케줄링을 특징짓고 구분하기를 시도하였다 핵심은 finite-Backlog Case에서 delay 제한성의 조건만 가질  QLB( 길이 기반 중요성이라는 결과로 이어진다.  QLB 정책의 네트워크 처리량은 그렇지 않는 스케줄링 법보다  높은 처리량을 보인다.

게다가시스템이 증가하는 경우와 초기에 증가하는  네트워크 처리량 정책안에서주어진 delay조건을 위반하며

 

 

Moreover, for a given delay violation constraint, when the number of users in the system increases, the total network throughput under policy (1) initially increases, and then eventually decreases to zero, but not so under the QLB policy. This should not be entirely surprising since index policies of the form (1) are agnostic to the delays incurred for different users and may not serve users whose queues are building up fast enough to remain within a delay violation probability.

 

 

 

또한 소정의 지연 제약 조건 위반으로 인해 시스템 증가하는 사용자 수가 정책 아래에서의  네트워크 처리량이 먼저 상승한 경우 다음 최종적으로  QLB 정책에 따라 제로가 아니다폼의 인덱스 정책이 다른 사용자 때문에 발생하는 지연에 사로 잡혀 있으면 지연 위반 확률에 체재하기 위하여 충분한 속도로 구축  사용자에게 서비스를 제공하지 않을지도 모르기 때문에 이것은 전혀 놀라운 일이 아니다.

 

또한주어진 지연 위반 제약 조건시스템 증가에 있는 사용자의 수가 정책에 따라 전체 네트워크 처리량이 처음 증가  그리고 결국 그렇게 QLB 정책 하에서 제로로 감소하지만폼의 인덱스 정책이 다른 사용자에 따른 지연 독립적이며해당 대기  지연 시간 위반 확률 내에 남아있는 만큼 빠르게 구축하는 사용자에게 서비스를 제공   없습니다 때문에 이것은 전혀 놀라운 일이  된다.










..작성중







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