메모리 ARQ를 갖는 ALOHA 기반 랜덤 억세스 시스템을 위한 일반화된 분석 방법
Generalized Analytical Framework for ALOHA based Random Access System with Memory ARQ
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초록
본 논문에서는 메모리 ARQ을 사용하는 ALOHA 기반 랜덤 억세스 시스템의 평형상태(equilibrium) 성능을 분석 하기 위한 일반화된 방법을 제안한다. 제안된 분석 방법은 코드/패킷 결합 방법에서와 같이 메모리 ARQ을 사용하는 slotted 혹은 unslotted ALOHA 시스템을 위한 일반화된 분석 방법을 제공하는데 Kleinrock의 독립가정(Kleinlock independence assumption)과 Jackson의 정리를 이용하여 다차원 Markov 체인 모델을 푸는 복잡한 문제를 간단하 게 두 단계로 분리한다. 첫 번째 단계에서는 매 전송마다 평균 패킷 성공률 혹은 그 바운드를 찾는다. 두 번째 단계에 서는 첫 번째 단계에서 얻은 평균 패킷 성공률을 이용하여 확장된 대기 행렬 모델의 평형 조건을 만족하는 해를 구하고 이로부터 throughput 및 지연 성능을 구한다. 시뮬레이션을 통해 분석 방식의 타당성을 검증하였으며 또한 패킷 결합 방식의 HARQ가 CDMA ALOHA 시스템에서 분산제어 형태의 확산 인자(spreading factor) 적응을 제공한다는 것 을 보인다.
Abstract
In this paper, we establish a generalized framework to analyze the equilibrium behavior of ALOHA based random access system with memory Automatic Repeat reQuest (ARQ). It is resulted from the author's previous works, which employ the expanded queuing network models. In this paper, those analytical procedures is generalized to a unified approach for ALOHA systems, either slotted or unslotted, that employ ARQ with memory, such as code/packet combining schemes. Using Kleinrock independence, the approach employs Jackson's theorem to divide one complicated problem of solving multi-dimensional Markov chain model into two rather simple steps. First step is to find the average probability of packet success, or its bound, at each transmission attempt. In the second step, we solve for given average probability of packet success obtained from the first step the set of equations that gives the equilibrium condition of the expanded queuing models and find the throughput and delay performance. The effectiveness of the approach is verified with simulation, which also shows that packet combining provides a means of decentralized spreading factor adaptation in CDMA ALOHA systems.
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