Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis
Bibliographic record
Abstract
Internet traffic flows have often been characterized as having power-tailed (long-tailed, fat-tailed, heavy-tailed) packet interarrival times or service requirements. In this work, we focus on the development of complete and computationally efficient steady-state solutions of queues with power-tailed interarrival times when the service times are assumed exponential. The classical method for obtaining the steady-state probabilities and delay-time distributions for the G/M/1 (G/M/c) queue requires solving a root-finding problem involving the Laplace-Stieltjes transform of the interarrival-time distribution function. Then the exponential service assumption is combined with the derived geometric arrival-point probabilities to get both the limiting general-time state and delay distributions. However, in situations where there is a power tail, the interarrival transform is typically quite complicated and never analytically tractable. In addition, it is possible that there is only a degenerate steady-state system-size probability distribution. Thus, an alternative approach to obtaining a steady-state solution is typically needed when power-tailed interarrivals are present. We exploit the exponentiality of the steady-state delay distributions for the G/M/1 and G/M/c queues, using level-crossings and a transform approximation method, to develop an alternative root-finding problem when there are power-tailed interarrival times. Extensive computational results are given.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".