Analysis of Triggered Packet Streams: A Matrix-Analytic Method for Exponential Triggering Delays
Abstract
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 MT/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.
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BibTeX
@misc{rahnamania2026analysis,
title = {{Analysis of Triggered Packet Streams: A Matrix-Analytic Method for Exponential Triggering Delays}},
author = {Mehran Rahnamania and Michel Mandjes and Farid Ashtiani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02320},
eprint = {2609.02320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02320},
}
RIS
TY - UNPB
TI - Analysis of Triggered Packet Streams: A Matrix-Analytic Method for Exponential Triggering Delays
AU - Mehran Rahnamania
AU - Michel Mandjes
AU - Farid Ashtiani
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02320
UR - https://arxiv.org/abs/2609.02320
AB - 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 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.
ER -