Optimal Partition for a Multi-Type Queueing System
Bibliographic record
Abstract
We study an optimal server partition and customer assignment problem for an uncapacitated first-come-first-served queueing system with heterogeneous types of customers. Each type of customer is associated with a Poisson arrival, a certain service time distribution, and a unit waiting cost. The goal is to minimize the expected total waiting cost by partitioning the server into subqueues, each with a smaller service capacity, and routing customer types probabilistically. First, we show that by properly partitioning the queue, it is possible to reduce the expected waiting costs by an arbitrarily large ratio. Then, we show that for any given server partition, the optimal customer assignment admits a certain geometric structure, enabling an efficient algorithm to find the optimal assignment. Such an optimal structure also applies when minimizing the expected sojourn time. Finally, we consider the joint partition-assignment optimization problem. The customer assignment under the optimal server partition admits a stronger structure. Specifically, if the first two moments of the service time distributions satisfy certain properties, it is optimal to deterministically assign customer types with consecutive service rates to the same subqueue. This structure allows for more efficient algorithms. Overall, the common rule of thumb to partition customers into continuous segments ranked by service rates could be suboptimal, and our work is the first to comprehensively study the queue partition problem based on customer types. Funding: Financial support from the National Natural Science Foundation of China [Grants 72192830, 72192832, 71825003, 72394361, and 72425013] and the Guangdong Provincial Key Laboratory on Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2023.0035 .
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".