Optimal server assignment in multi-server parallel queueing systems with random connectivities and random service failures
Bibliographic record
Abstract
The problem of assignment of K identical servers to a set of N symmetric parallel queues is investigated in this paper. The parallel queueing system is considered to be time slotted and the connectivity of each queue to each server is varying randomly over time and following Bernoulli distribution with a given parameter. Each server is capable of serving at most one packet per time slot (if it is connected and assigned to a queue). At any time slot, each server can serve at most one queue and each queue can be served by at most one server. We assume that the service of a scheduled packet by a connected server fails randomly with a certain probability. The packet arrival processes to the queues are assumed to be i.i.d. and follow Bernoulli distribution with a fixed parameter. For such a symmetric system, i.e., with the same arrival, connectivity and service failure parameters for all the queues, we show that Maximum Weighted Matching (MWM) server assignment policy is delay optimal. More specifically, using stochastic ordering and dynamic coupling techniques we prove that MWM minimizes, in stochastic ordering sense, a broad range of stochastic cost functions of the queue lengths including total queue occupancy (or equivalently average queueing delay).
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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 | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".