Optimal Multi-Server Allocation to Parallel Queues With Independent\n Random Queue-Server Connectivity
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Bibliographic record
Abstract
We investigate an optimal scheduling problem in a discrete-time system of L\nparallel queues that are served by K identical, randomly connected servers.\nEach queue may be connected to a subset of the K servers during any given time\nslot. This model has been widely used in studies of emerging 3G/4G wireless\nsystems. We introduce the class of Most Balancing (MB) policies and provide\ntheir mathematical characterization. We prove that MB policies are optimal; we\ndefine optimality as minimization, in stochastic ordering sense, of a range of\ncost functions of the queue lengths, including the process of total number of\npackets in the system. We use stochastic coupling arguments for our proof. We\nintroduce the Least Connected Server First/Longest Connected Queue (LCSF/LCQ)\npolicy as an easy-to-implement approximation of MB policies. We conduct a\nsimulation study to compare the performance of several policies. The simulation\nresults show that: (a) in all cases, LCSF/LCQ approximations to the MB policies\noutperform the other policies, (b) randomized policies perform fairly close to\nthe optimal one, and, (c) the performance advantage of the optimal policy over\nthe other simulated policies increases as the channel connectivity probability\ndecreases and as the number of servers in the system increases.\n
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it