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Analysis of Triggered Packet Streams: Stochastic Bounds on System Time under General Triggering Delays — arXiv:2610.40865

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40865
License (as archived): CC0-1.0
Archived: 2026-11-02T04:47:09.365Z
SHA-256 of the archived text: b59430ba946ac5a31b2b8f9d6e51974992ed142b147b79fad517d0cf370c752e
Stable URL of this page: https://metraipolis.com/documento/dc_7ecdbec599cb

How to cite

Analysis of Triggered Packet Streams: Stochastic Bounds on System Time under General Triggering Delays — arXiv:2610.40865 — arXiv (en), https://arxiv.org/abs/2610.40865 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7ecdbec599cb (Metraipolis archive dc_7ecdbec599cb, sha256 b59430ba946ac5a31b2b8f9d6e51974992ed142b147b79fad517d0cf370c752e)

BibTeX

@misc{dc7ecdbec599cb,
  title = {Analysis of Triggered Packet Streams: Stochastic Bounds on System Time under General Triggering Delays — arXiv:2610.40865},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40865},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7ecdbec599cb; sha256 b59430ba946ac5a31b2b8f9d6e51974992ed142b147b79fad517d0cf370c752e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40865. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many emerging communication systems increasingly involve devices that transmit packets in multiple causally dependent stages as part of an internal workflow, rather than waiting for receiver feedback. To analyze such systems, we recently introduced the $\mathrm{M^T/G/1}$ queue, in which primary customers arrive according to an exogenous Poisson process, and each triggers a secondary customer to join the queue after an independent random delay, called the \textit{triggering delay}. Our prior heuristic approximations assume identical exponential service times, and our matrix-analytic framework assumes exponential triggering delays. However, no exact analysis is available when both distributions are general. In this paper, we derive stochastic bounds, in the usual stochastic order, on the system-time distribution of each customer class under general triggering-delay and service-time distributions. The service times within each primary--secondary pair may be generally dependent. Using sample-path coupling and level-crossing arguments, we show that the stationary workload is stochastically sandwiched between those of two classical queues: a two-class $\mathrm{M/G/1}$ queue with independent Poisson arrivals (lower bound), and a batch-arrival $\mathrm{M^{[2]}/G/1}$ queue where each primary--secondary pair arrives simultaneously (upper bound). Notably, these bounds do not depend on the triggering-delay distribution, and they are asymptotically tight in the sense that the stationary workload converges in distribution to that of the lower- and upper-bound queues as the triggering delays diverge to infinity and converge to zero in probability, respectively. We translate these workload bounds into system-time bounds for each customer class. Simulation experiments support these bounds.

Tema degli esploratori: calcolo e infrastrutture (elenco arXiv cs.PF, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Performance (cs.PF).
Pagina del lavoro: https://arxiv.org/abs/2610.40865 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T04:43:11.648Z dalla pagina https://arxiv.org/list/cs.PF/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).