Abstract
A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a "usual" system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the "usual" system. Finally, the renewal theory is used to derive the general result. Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given.
| Original language | English |
|---|---|
| Pages (from-to) | 126-141 |
| Number of pages | 16 |
| Journal | Kybernetika |
| Volume | 50 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2014 |
Keywords
- Batch Poisson arrivals
- Queue-size distribution
- Renewal theory
- Single vacation
- Transient state
ASJC Scopus subject areas
- Software
- Control and Systems Engineering
- Theoretical Computer Science
- Information Systems
- Artificial Intelligence
- Electrical and Electronic Engineering
Fingerprint
Dive into the research topics of 'On transient queue-size distribution in the batch-arrivals system with a single vacation policy'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver