Time-limited and k-limited polling systems: a matrix analytic solution

Ahmad Al Hanbali; Roland de Haan; Richardus J. Boucherie; Jan C.W. 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
, Richardus J. Boucherie
, Jan C.W. van Ommeren

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

2 Citations (Scopus)

175 Downloads (Pure)

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	Undefined
Title of host publication	The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools)
Place of Publication	Gent, Belgium
Publisher	ICST
Pages	-
Number of pages	10
ISBN (Print)	978-963-9799-31-8
DOIs	https://doi.org/10.4108/ICST.VALUETOOLS2008.4378
Publication status	Published - 2008
Event	3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008 - Athens, Greece Duration: 20 Oct 2008 → 24 Oct 2008

Publication series

Name
Publisher	Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering (ICST)
Number	CFP08545-D

Workshop

Workshop	3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008
Period	20/10/08 → 24/10/08
Other	20-24 October 2008

Access to Document

10.4108/ICST.VALUETOOLS2008.4378

2008-XHanbaliHaanBoucherieOmmeren_Time_LtdFinal published version, 461 KB

Time-Limited and k-Limited Polling Systems: A Matrix Analytic Solution
Hanbali, A. A., de Haan, R., Boucherie, R. J. & van Ommeren, J.-K., 5 Oct 2009.
Research output: Working paper › Preprint › Academic

Open Access
File
11 Downloads (Pure)

Cite this

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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.",

author = "\{Al Hanbali\}, Ahmad and \{de Haan\}, Roland and Boucherie, \{Richardus J.\} and \{van Ommeren\}, \{Jan C.W.\}",

note = "eemcs-eprint-14667 ; 3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008 ; Conference date: 20-10-2008 Through 24-10-2008",

year = "2008",

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

language = "Undefined",

isbn = "978-963-9799-31-8",

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Al Hanbali, A, de Haan, R, Boucherie, RJ & van Ommeren, JCW 2008, Time-limited and k-limited polling systems: a matrix analytic solution. in The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools). ICST, Gent, Belgium, pp. -, 3rd International Workshop on Tools for Solving Structured Markov Chains, SMCTools 2008, 20/10/08. 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, Richardus J. et al.
The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools). Gent, Belgium: ICST, 2008. p. -.

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

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N1 - eemcs-eprint-14667

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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.

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SN - 978-963-9799-31-8

SP - -

BT - The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools)

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ER -

Time-limited and k-limited polling systems: a matrix analytic solution

Abstract

Publication series

Workshop

Access to Document

Research output

Time-Limited and k-Limited Polling Systems: A Matrix Analytic Solution

Cite this