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June 6, 2026Theory of Probability and Mathematical Statistics

Scaling limits for some Mittag-Leffler queues

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Authors

GAGiacomo AscioneLCLuigia Caputo

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Overview

Examines scaling limits in heavy-tailed queue models using Mittag-Leffler distributions, indicating new insights into queue behavior.

Key Points

  • This research explores the scaling limits of five models of heavy-tailed queues that incorporate Mittag-Leffler distributions.
  • Considered five modified queueing models based on Mittag-Leffler distributions.
  • Provided distributions for inter-arrival and service times in both original and modified models.
  • Analyzed scaling limits to characterize traffic regimes of the proposed queues.
  • Identified characteristic behaviors of limiting processes in heavy-tailed queues.
  • Demonstrated that classical M/M/1 queue can be recovered from modified models with specific parameters.
  • Established a relationship between limiting processes and queue traffic regimes.

Cite This Study

Ascione et al. (2026) studied this question.

synapsesocial.com/papers/6a23ba6871a5da9775e760c2https://doi.org/10.1090/tpms/1251
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