Some Properties of Queueing Systems with Fluctuating Traffic Intensity
Summary :
Multi-server queueing systems with traffic intensity which vary according to an irreducible Markov chain are considered. We will show that the probability distribution for the number of customers in these systems can be expressed by an algebraic sum of geometric series with appropriate coefficients satisfying some interesting properties. To study these properties a detailed analysis of the denominator of the partial generating functions of the number of customers in the system is presented. These coefficients allow us to explain the behavior of the system under different traffic conditions. First, we derive a general expression for the probability distribution and then compare this result with that of the Zukerman and Rubin's model. One special section is devoted to the case of an arbitrary number of phases. Some numerical results are also provided and discussed to support the theoretical results.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E71-E No.7 pp.659-668
- Publication Date
- 1988/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Systems and Control
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Walter SOTELO, Kaiji MUKUMOTO, Akira FUKUDA, "Some Properties of Queueing Systems with Fluctuating Traffic Intensity" in IEICE TRANSACTIONS on transactions,
vol. E71-E, no. 7, pp. 659-668, July 1988, doi: .
Abstract: Multi-server queueing systems with traffic intensity which vary according to an irreducible Markov chain are considered. We will show that the probability distribution for the number of customers in these systems can be expressed by an algebraic sum of geometric series with appropriate coefficients satisfying some interesting properties. To study these properties a detailed analysis of the denominator of the partial generating functions of the number of customers in the system is presented. These coefficients allow us to explain the behavior of the system under different traffic conditions. First, we derive a general expression for the probability distribution and then compare this result with that of the Zukerman and Rubin's model. One special section is devoted to the case of an arbitrary number of phases. Some numerical results are also provided and discussed to support the theoretical results.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e71-e_7_659/_p
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@ARTICLE{e71-e_7_659,
author={Walter SOTELO, Kaiji MUKUMOTO, Akira FUKUDA, },
journal={IEICE TRANSACTIONS on transactions},
title={Some Properties of Queueing Systems with Fluctuating Traffic Intensity},
year={1988},
volume={E71-E},
number={7},
pages={659-668},
abstract={Multi-server queueing systems with traffic intensity which vary according to an irreducible Markov chain are considered. We will show that the probability distribution for the number of customers in these systems can be expressed by an algebraic sum of geometric series with appropriate coefficients satisfying some interesting properties. To study these properties a detailed analysis of the denominator of the partial generating functions of the number of customers in the system is presented. These coefficients allow us to explain the behavior of the system under different traffic conditions. First, we derive a general expression for the probability distribution and then compare this result with that of the Zukerman and Rubin's model. One special section is devoted to the case of an arbitrary number of phases. Some numerical results are also provided and discussed to support the theoretical results.},
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - Some Properties of Queueing Systems with Fluctuating Traffic Intensity
T2 - IEICE TRANSACTIONS on transactions
SP - 659
EP - 668
AU - Walter SOTELO
AU - Kaiji MUKUMOTO
AU - Akira FUKUDA
PY - 1988
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E71-E
IS - 7
JA - IEICE TRANSACTIONS on transactions
Y1 - July 1988
AB - Multi-server queueing systems with traffic intensity which vary according to an irreducible Markov chain are considered. We will show that the probability distribution for the number of customers in these systems can be expressed by an algebraic sum of geometric series with appropriate coefficients satisfying some interesting properties. To study these properties a detailed analysis of the denominator of the partial generating functions of the number of customers in the system is presented. These coefficients allow us to explain the behavior of the system under different traffic conditions. First, we derive a general expression for the probability distribution and then compare this result with that of the Zukerman and Rubin's model. One special section is devoted to the case of an arbitrary number of phases. Some numerical results are also provided and discussed to support the theoretical results.
ER -
English
