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- Title
The analysis of batch sojourn-times in polling systems.
- Authors
Gaast, Jelmer; Adan, Ivo; Koster, René
- Abstract
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.
- Subjects
QUEUEING networks; DIRECTION of arrival estimation; LAPLACE transformation; MEAN value theorems; COMPUTER algorithms
- Publication
Queueing Systems, 2017, Vol 85, Issue 3/4, p313
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-016-9513-y