Time-limited and k-limited polling systems: a matrix analytic solution
Authors: 
Ahmad Al Hanbali, Roland de Haan, Richard J. Boucherie, Jan-Kees van OmmerenAuthors Info & Claims
Ahmad Al Hanbali, Roland de Haan, Richard J. Boucherie, Jan-Kees van OmmerenAuthors Info & ClaimsArticle No.: 17, Pages 1 - 10
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.
References
[1]
A. Al Hanbali, R. de Haan, R. J. Boucherie, and J. van Ommeren. A tandem queueing model for delay analysis in disconnected ad hoc networks. Proc. of ASMTA, LNCS 5055:189--205, June 2008.
[2]
J. Blanc. An algorithmic solution of polling models with limited service disciplines. IEEE Transactions on Communications, 40(7):1152--1155, July 1992.
[3]
J. Blanc. The power-series algorithm for polling systems with time limits. Probability in the Engineering and Informational Sciences, 12:221--237, 1998.
[4]
R. de Haan, R. J. Boucherie, and J. van Ommeren. A polling model with an autonomous server. Research Memorandum 1845, University of Twente, 2007.
[5]
M. Dow. Explicit inverses of Toeplitz and associated matrices. ANZIAM J., 44(E):E185--E215, Jan. 2003.
[6]
M. Eisenberg. Queues with periodic service and changeover times. Operation Research, 20(2):440--451, 1972.
[7]
T. Estermann. Complex Numbers and Functions. Oxford University Press, London, 1962.
[8]
D. P. Gaver, P. A. Jacobs, and G. Latouche. Finite birth-and-death models in randomly changing environments. Advances in Applied Probability, 16:715--731, 1984.
[9]
C. Grinstead and J. Snell. Introduction to Probability. American Mathematical Society, 1997.
[10]
K. Leung. Cyclic-service systems with probabilistically-limited service. IEEE Journal on Selected Areas in Communications, 9(2):185--193, 1991.
[11]
K. Leung. Cyclic-service systems with non-preemptive time-limited service. IEEE Transactions on Communications, 42(8):2521--2524, 1994.
[12]
H. Levy and M. Sidi. Polling systems: Applications, modeling, and optimization. TOC, 38(10), Oct. 1990.
[13]
M. Neuts. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, 1981.
[14]
W. Press, B. Flannery, S. Teukolsky, and W. Vetterling. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 1992.
[15]
J. Resing. Polling systems and multitype branching processes. Queueing Systems, 13(10):409--429, 1993.
[16]
H. Takagi. Analysis and application of polling models. In Performance Evaluation: Origins and Directions, LNCS 1769, pages 423--442, Berlin, Germany, 2000. Springer-Verlag.
- Time-limited and k-limited polling systems: a matrix analytic solution
Recommendations
A pseudoconservation law for a time-limited service polling system with structured batch poisson arrivals
We consider a cyclic-service queueing system (polling system) with time-limited service, in which the length of a service period for each queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes ...
Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines
The stability of a cyclic polling system, with a single server and two infinite-buffer queues, is considered. Customers arrive at the two queues according to independent batch Markovian arrival processes. The first queue is served according to the gated ...
Sojourn times in polling systems with various service disciplines
We consider a polling system of N queues Q"1,...,Q"N, cyclically visited by a single server. Customers arrive at these queues according to independent Poisson processes, requiring generally distributed service times. When the server visits Q"i, i=1,...,...
Comments
Information & Contributors
Information
Published In
Sponsors
- Create-Net
Publisher
ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)
Brussels, Belgium
Publication History
Published: 20 October 2008
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 71Total Downloads
- Downloads (Last 12 months)12
- Downloads (Last 6 weeks)1
Reflects downloads up to 23 Dec 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in