Abstract
| 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 |
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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
Cite this
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Time-limited polling systems with batch arrivals and phase-type service times. / Al Hanbali, Ahmad; de Haan, Roland; Boucherie, Richardus J.; van Ommeren, Jan C.W.
In: Annals of operations research, Vol. 198, No. 1, 09.2012, p. 57-82.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Time-limited polling systems with batch arrivals and phase-type service times
AU - Al Hanbali, Ahmad
AU - de Haan, Roland
AU - Boucherie, Richardus J.
AU - van Ommeren, Jan C.W.
PY - 2012/9
Y1 - 2012/9
N2 - 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.
AB - 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.
KW - EWI-21585
KW - Autonomous server discipline
KW - Time limited discipline
KW - Matrix analytic solution
KW - Absorbing Markov chains
KW - Phase-type service times
KW - Poisson batch arrivals
KW - Polling system
KW - Performance analysis
KW - Iterative scheme
KW - METIS-275145
KW - IR-76967
U2 - 10.1007/s10479-011-0846-y
DO - 10.1007/s10479-011-0846-y
M3 - Article
VL - 198
SP - 57
EP - 82
JO - Annals of operations research
JF - Annals of operations research
SN - 0254-5330
IS - 1
ER -