Computational Procedures for a Class of GI/D/<i>k</i> Systems in Discrete Time
Bibliographic record
Abstract
A class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first‐in first‐out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi‐birth‐death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 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".