Modeling and Analysis of Discrete-Time Multiserver Queues with Batch Arrivals: GI<sup>X</sup>/Geom/m
Bibliographic record
Abstract
Multiserver queues are often encountered in telecommunication systems and have special importance in the design of ATM networks. This paper analyzes a discrete-time multiserver queueing system with batch arrivals in which the interbatch and service times are, respectively, arbitrarily and geometrically distributed. Using supplementary-variable and embedded-Markov-chain techniques, the queue is analyzed only for the early arrival system. Since the late arrival system can be discussed similarly, it is not considered here. In addition to developing relations among state probabilities at prearrival, arbitrary, and outside observer's observation epochs, the numerical evaluation of state probabilities is also discussed. It is also shown that, in the limiting case, the relations developed here tend to continuous-time counterparts. Further, the waiting-time distribution of a random customer of a batch is obtained. Finally, in some cases simulation experiments have been performed to validate our results.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".