Abstract
In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.
| Original language | English |
|---|---|
| Pages (from-to) | 57-82 |
| Number of pages | 26 |
| Journal | Annals of operations research |
| Volume | 198 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Sep 2012 |
Keywords
- EWI-21585
- Autonomous server discipline
- Time limited discipline
- Matrix analytic solution
- Absorbing Markov chains
- Phase-type service times
- Poisson batch arrivals
- Polling system
- Performance analysis
- Iterative scheme
- METIS-275145
- IR-76967
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Cite this
Al Hanbali, A., de Haan, R., Boucherie, R. J., & van Ommeren, J. C. W. (2012). Time-limited polling systems with batch arrivals and phase-type service times. Annals of operations research, 198(1), 57-82. https://doi.org/10.1007/s10479-011-0846-y