基于可选休假和优先权Geo/G/1重试排队的P2P网络分析

摘要/Abstract

摘要：

该文旨在根据 P2P 网络中节点状态的动态变化, 构建一个排队模型, 以精确模拟节点在系统中的动态趋势. 基于这一模型框架, 建立了一个带二次可选休假、优先权和不耐烦请求节点的 Geo/G/1 重试排队系统. 利用嵌入 Markov 链的方法, 构造相应维数的 Markov 链, 分析网络系统中各个节点状态的一步转移概率; 利用补充变量法推导系统满足的平衡方程组, 通过求解平衡方程组得到网络系统中各类节点的性能指标. 通过调整不同参数, 验证系统的性能指标随参数的变化趋势.

关键词: 离散时间重试排队, P2P 网络, 二次可选休假策略, 嵌入 Markov 链, 不耐烦请求节点

Abstract:

This article aims to construct a queuing model based on the dynamic changes in node states within a P2P network, enabling an accurate simulation of the dynamic trends of nodes within the system. Based on this model framework, a Geo/G/1 retrial queuing system was established with second optional vacation, priority, and impatient customers. To analyze the one-step state transition probabilities of each node within the network, the embedded Markov chain method was utilized and a Markov chain of the corresponding dimension was constructed. This paper used the supplementary variable method to derive the system of equilibrium equations satisfied by the system and obtained the performance indexes of various types of nodes within the network by solving the system of equations. The trend of the system's performance indexes with different parameters is also verified.

Key words: discrete-time retrial queue, P2P networks, second optional vacation strategy, embedded Markov chain, impatient requesting nodes

中图分类号:

O226

马占友, 秦国丽, 姜子姝, 沈颖. 基于可选休假和优先权Geo/G/1重试排队的P2P网络分析[J]. 数学物理学报, 2025, 45(1): 295-304.

Zhanyou Ma, Guoli Qin, Zishu Jiang, Ying Shen. Analysis of P2P Networks Based on Geo/G/1 Retrial Queue with Optional Vacation and Priority[J]. Acta mathematica scientia,Series A, 2025, 45(1): 295-304.

图/表 5

图1

${{\pi }_{0,0,0}}$ 与 $\eta$ 和 $p$ 的关系图"

图1

图2

${{\pi }_{0,0,0}}$ 与 $\alpha$ 和 ${{a}_{0}}$ 的关系图"

图2

图3

${{\varphi }_{1}}\left( 1,1 \right)$ 与 $q$ 和 $p$ 的关系图"

图3

图4

${{\varphi }_{2}}\left( 1,1 \right)$ 与 $\alpha$ 和 ${{a}_{0}}$ 的关系图"

图4

图5

${{U }_{L}}$ 与 $\eta$ 和 $p$ 的关系图"

图5

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