The analysis of batch sojourn-times in polling systems
| Autor: | René B. Koster, Ivo Adan, Jelmer P. van der Gaast |
|---|---|
| Přispěvatelé: | Department of Technology and Operations Management, Operations Planning Acc. & Control |
| Rok vydání: | 2017 |
| Předmět: |
Polling models
Mathematical optimization Computer science Real-time computing 0211 other engineering and technologies 02 engineering and technology Management Science and Operations Research 01 natural sciences 010104 statistics & probability FOS: Mathematics 0101 mathematics Queue Service (business) 021103 operations research Supply chain management Epoch (reference date) Probability (math.PR) Mean value analysis Computer Science Applications System characteristics Computational Theory and Mathematics Polling system Queueing models Polling Mathematics - Probability |
| Zdroj: | Queueing Systems, 85, 313-335. Springer Netherlands Queueing Systems: Theory and Applications, 85(3-4), 313-335. Springer |
| ISSN: | 1572-9443 0257-0130 |
| DOI: | 10.1007/s11134-016-9513-y |
| Popis: | We consider a cyclic polling system with general service times, general switch-over times, and simultaneous batch arrivals. This means that at an arrival epoch, a batch of customers may arrive simultaneously at the different queues of the system. For the exhaustive service discipline, we study the batch sojourn-time, which is defined as the time from an arrival epoch until service completion of the last customer in the batch. We obtain exact expressions for the Laplace–Stieltjes transform of the steady-state batch sojourn-time distribution, which can be used to determine the moments of the batch sojourn-time and, in particular, its mean. However, we also provide an alternative, more efficient way to determine the mean batch sojourn-time, using mean value analysis. We briefly show how our framework can be applied to other service disciplines: locally gated and globally gated. Finally, we compare the batch sojourn-times for different service disciplines in several numerical examples. Our results show that the best performing service discipline, in terms of minimizing the batch sojourn-time, depends on system characteristics. |
| Databáze: | OpenAIRE |
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