Analysis of a multi-item queueing inventory system operating with an exchange facility
Bibliographic record
Abstract
This paper explores a stochastic queuing-inventory system designed to efficiently manage both new and returned items, offering practical solutions for diverse customer needs. The system differentiates services for various customer classes through dedicated channels, encompassing the sale of new and returned items, as well as the purchase of used items from customers. This model incorporates four parallel queues for distinct customer classes, each serviced by a dedicated server. Customer arrivals are modeled using a Markovian Arrival Process (MMAP), with service times being exponentially distributed and independent. An $(s, S)$ policy is implemented for replenishing fresh items. The primary objective is to enhance service accessibility for various customer types within a single facility, promoting operational efficiency and customer satisfaction. Additionally, the system's ability to purchase used items underscores its role in fostering sustainability in an evolving society. By applying the Neuts matrix geometric technique, the paper analyzes the system to derive the long-term probability distribution and significant performance metrics. Numerical methods are utilized to investigate key system parameters and performance measures, and a cost function is introduced and optimized concerning the reorder level. This comprehensive analysis offers valuable insights for optimizing inventory and queuing systems in practical, real-world applications.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".