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

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

3rd International ICST Workshop on Tools for solving Structured Markov Chains

Research Article

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

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4378,
    author={Ahmad Al Hanbali and Roland de Haan and Richard Boucherie and Jan-Kees van Ommeren},
    title={Time-limited and k-limited polling systems: A matrix analytic solution},
    proceedings={3rd International ICST Workshop on Tools for solving Structured Markov Chains},
    publisher={ACM},
    proceedings_a={SMCTOOLS},
    year={2010},
    month={5},
    keywords={Absorbing Markov chains; Matrix analytic solution; Polling system; Autonomous-server discipline; Time-limited disci- pline; k-limited discipline; Iterative scheme; Performance analysis;},
    doi={10.4108/ICST.VALUETOOLS2008.4378}
}

Ahmad Al Hanbali
Roland de Haan
Richard Boucherie
Jan-Kees van Ommeren
Year: 2010
Time-limited and k-limited polling systems: A matrix analytic solution
SMCTOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2008.4378

Ahmad Al Hanbali¹^,*, Roland de Haan¹^,*, Richard Boucherie¹^,*, Jan-Kees van Ommeren¹^,*

1: University of Twente, Enschede, The Netherlands

*Contact email: a.alhanbali@utwente.nl, haanr@ewi.utwente.nl, r.j.boucherie@utwente.nl, J.C.W.vanOmmeren@ewi.utwente.nl

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; Matrix analytic solution; Polling system; Autonomous-server discipline; Time-limited disci- pline; k-limited discipline; Iterative scheme; Performance analysis;

Published: 2010-05-16
Publisher: ACM
Modified: 2010-05-16

: http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4378