Time-Limited and k-Limited polling systems: A Matrix Analytic Solution

Ahmad Al Hanbali; Roland de Haan; Richard J. Boucherie; Jan Kees van Ommeren

doi:10.4108/ICST.VALUETOOLS2008.4378

Time-Limited and k-Limited polling systems: A Matrix Analytic Solution

Ahmad Al Hanbali, Roland de Haan, Richard J. Boucherie, Jan Kees van Ommeren

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length 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. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.

Original language	English
Title of host publication	VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools
Publisher	ICST
ISBN (Print)	9789639799318
DOIs	https://doi.org/10.4108/ICST.VALUETOOLS2008.4378
State	Published - 2008
Externally published	Yes

Publication series

Name	VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools
Volume	2008-October

Bibliographical note

Publisher Copyright:
© 2008 ICST.

Keywords

Absorbing Markov chains
Autonomous-server discipline
Iterative scheme
Matrix analytic solution
Performance analysis
Polling system
Time-limited discipline
k-limited discipline

ASJC Scopus subject areas

Instrumentation

Access to Document

10.4108/ICST.VALUETOOLS2008.4378

Cite this

Al Hanbali, A., de Haan, R., Boucherie, R. J., & van Ommeren, J. K. (2008). Time-Limited and k-Limited polling systems: A Matrix Analytic Solution. In VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools; Vol. 2008-October). ICST. https://doi.org/10.4108/ICST.VALUETOOLS2008.4378

@inproceedings{44dd323695c64fa08a0458a239a39bad,

title = "Time-Limited and k-Limited polling systems: A Matrix Analytic Solution",

abstract = "In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length 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. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.",

keywords = "Absorbing Markov chains, Autonomous-server discipline, Iterative scheme, Matrix analytic solution, Performance analysis, Polling system, Time-limited discipline, k-limited discipline",

author = "{Al Hanbali}, Ahmad and {de Haan}, Roland and Boucherie, {Richard J.} and {van Ommeren}, {Jan Kees}",

note = "Publisher Copyright: {\textcopyright} 2008 ICST.",

year = "2008",

doi = "10.4108/ICST.VALUETOOLS2008.4378",

language = "English",

isbn = "9789639799318",

series = "VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools",

publisher = "ICST",

booktitle = "VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools",

}

Al Hanbali, A, de Haan, R, Boucherie, RJ & van Ommeren, JK 2008, Time-Limited and k-Limited polling systems: A Matrix Analytic Solution. in VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools. VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools, vol. 2008-October, ICST. https://doi.org/10.4108/ICST.VALUETOOLS2008.4378

Time-Limited and k-Limited polling systems: A Matrix Analytic Solution. / Al Hanbali, Ahmad; de Haan, Roland; Boucherie, Richard J. et al.
VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools. ICST, 2008. (VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools; Vol. 2008-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Time-Limited and k-Limited polling systems

T2 - A Matrix Analytic Solution

AU - Al Hanbali, Ahmad

AU - de Haan, Roland

AU - Boucherie, Richard J.

AU - van Ommeren, Jan Kees

PY - 2008

Y1 - 2008

N2 - In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length 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. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.

AB - In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length 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. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.

KW - Absorbing Markov chains

KW - Autonomous-server discipline

KW - Iterative scheme

KW - Matrix analytic solution

KW - Performance analysis

KW - Polling system

KW - Time-limited discipline

KW - k-limited discipline

UR - http://www.scopus.com/inward/record.url?scp=85084182164&partnerID=8YFLogxK

U2 - 10.4108/ICST.VALUETOOLS2008.4378

DO - 10.4108/ICST.VALUETOOLS2008.4378

M3 - Conference contribution

AN - SCOPUS:85084182164

SN - 9789639799318

T3 - VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools

BT - VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools

PB - ICST

ER -

Al Hanbali A, de Haan R, Boucherie RJ, van Ommeren JK. Time-Limited and k-Limited polling systems: A Matrix Analytic Solution. In VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools. ICST. 2008. (VALUETOOLS 2008 - 3rd International Conference on Performance Evaluation Methodologies and Tools). doi: 10.4108/ICST.VALUETOOLS2008.4378

Time-Limited and k-Limited polling systems: A Matrix Analytic Solution

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this