﻿ 基于二维Markov链和中继聚合方法的多跳ARQ系统吞吐量的分析 Throughput Analysis of Multi-Hop ARQ System Based on Two-Dimensional Markov Chain and Relay Aggregation

Statistics and Application
Vol.06 No.02(2017), Article ID:21219,7 pages
10.12677/SA.2017.62026

Throughput Analysis of Multi-Hop ARQ System Based on Two-Dimensional Markov Chain and Relay Aggregation

Boyi He, Suoping Li, Zufang Dou

School of Science, Lanzhou University of Technology, Lanzhou Gansu

Received: Jun. 11th, 2017; accepted: Jun. 26th, 2017; published: Jun. 30th, 2017

ABSTRACT

In this paper, we analyzed the throughput of multi-hop ARQ system based on the method of relay aggregation. Firstly, we defined the node-state of two-hop ARQ system which consisted of a pair of transceivers and one relay node, and obtained the four-state transition matrix by establishing a two-dimensional Markov chain, then obtained the state transition probability of relay nodes in two hop ARQ system. Secondly, in the N + 1-hop ARQ system composed of a pair of transceivers and N relay nodes, we used relay aggregation to merge N relay nodes into a super relay and made the N+1-hop system equivalent to the two-hop system in principle, then obtained the state transition probability of relay nodes in N + 1-hop ARQ system. Finally, we defined the state of the multi-hop ARQ system as “G” and “B”, and got eight-state of state transfer processes of multi-hop ARQ system by combining with the state of the super relay and direct channel, and obtained the analytical solution for the throughput of multi-hop ARQ systems based on the steady-state equation. In fact, it was shown that there was a unified method to study the throughput performance of multi-relay and multi-hop ARQ system.

Keywords:Relay Aggregation, ARQ, Markov Chain, Direct Channel, Throughput

1. 引言

2. 基于中继聚合的多跳ARQ协议

2.1. 两跳ARQ系统的节点状态模型

(1)

(2)

;. (3)

Figure 1. Multi-hop ARQ system

Figure 2. Two-hop ARQ model

Figure 3. State transition of two dimensional vector

.

2.2. 多跳ARQ系统的节点状态模型

(4)

(5)

(6)

Figure 4. State transition of two dimensional vector

Table 1. State transition of

3. 多跳ARQ系统的吞吐量模型

(7)

(8)

(9)

Throughput Analysis of Multi-Hop ARQ System Based on Two-Dimensional Markov Chain and Relay Aggregation[J]. 统计学与应用, 2017, 06(02): 231-237. http://dx.doi.org/10.12677/SA.2017.62026

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