触发分组流分析：指数触发延迟的矩阵分析方法

中文摘要 AI 辅助

在许多通信网络中，分组的传输可能会在一段（可能是随机的）延迟后自动触发来自同一源的后续分组的传输，而无需确认或反馈。这种行为出现在多阶段状态更新、主动协议以及其他用户生成因果依赖分组流的应用中。为分析这些系统，本文引入了$\boldsymbol{\rm M^T/G/1}$排队模型。在该模型中，主顾客按照泊松过程到达，每个主顾客会在一段独立延迟后触发一个次顾客加入队列。这种到达机制超出了具有更新到达过程的经典排队模型的范围。当触发延迟服从指数分布时，我们利用无记忆特性建立了易于处理的马尔可夫描述。通过截断待处理次顾客的数量，我们在拉普拉斯-斯蒂尔杰斯变换域中推导出一个有限的线性代数方程组，并使用矩阵分析方法求解。基于得到的工作量分布，我们使用PASTA（泊松到达见时间平均）方法处理主顾客，使用Palm条件法处理次顾客，计算了分类型性能指标。最后，我们通过数值实验验证了该截断方法的准确性。

英文摘要

In many communication networks, the transmission of a packet may automatically trigger the transmission of a subsequent packet from the same source after a (possibly random) delay, without requiring acknowledgment or feedback. Such behavior arises in multi-stage status updating, proactive protocols, and other applications where users generate causally dependent packet streams. In this paper, in order to analyze these systems, we introduce the $\mathrm{M^T/G/1}$ queue. In this model, primary customers arrive according to a Poisson process, and each primary customer triggers a secondary customer to join the queue after an independent delay. This arrival mechanism falls outside the scope of classical queueing models with renewal arrival processes. When the triggering delays follow an exponential distribution, we exploit the memoryless property to set up a tractable Markov description. By truncating the number of pending secondary customers, we derive a finite system of linear algebraic equations in the Laplace--Stieltjes transform domain and solve them using matrix-analytic methods. Based on the resulting workload distribution, we compute class-specific performance metrics using PASTA for primary customers and Palm conditioning for secondary customers. Finally, we validate the accuracy of this truncation through numerical experiments.

发表机构

• Sharif University of Technology（谢里夫理工大学）
• Leiden University（莱顿大学）
• University of Amsterdam（阿姆斯特丹大学）

机构由 AI 辅助整理，请以论文原文为准。