Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks
Bibliographic record
Abstract
We study a double-sided queue with batch arrivals and abandonment. There are two types of customers, patient ones who queue but may later abandon, and impatient ones who depart immediately if their order is not filled. The system matches units from opposite sides of the queue based on a first-come first-served policy. The model is particularly applicable to a class of alternative trading systems called crossing networks that are increasingly important in the operation of modern financial markets. We characterize, in closed form, the steady-state queue length distribution and the system-level average system time and fill rate. These appear to be the first closed-form results for a double-sided queuing model with batch arrivals and abandonment. For a customer who arrives to the system in steady state, we derive formulae for the expected fill rate and system time as a function of her order size and deadline. We compare these system- and customer-level results for our model that captures abandonment in aggregate, to simulation results for a system in which customers abandon after some random deadline. We find close correspondence between the predicted performance based on our analytical results and the performance observed in the simulation. Our model is particularly accurate in approximating the performance in systems with low fill rates, which are representative of crossing networks.
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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) | 0.001 | 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 | 0.002 |
| Open science | 0.002 | 0.001 |
| 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".