Queueing Model Analysis for Multi-Level Input Control Method

Konosuke KAWASHIMA

Queueing Model Analysis for Multi-Level Input Control Method

Konosuke KAWASHIMA

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This paper presents and analyzes the following queueing model for congestion control. In an M/M (Poisson arrival/exponential service time) type model with finite waiting room, the input rate into the system is gradually controlled by comparing the number of calls in the system with two threshold values. If an arriving call finds the system to be full, the call is lost and the regulation grade is tightened by one level, i.e. the input rate slows down. If a leaving call finds the number of calls in the system to be lower than the lower threshold, input regulation grade is loosened by one level, i.e. the input rate speeds up. The method is called hysteresis" control. An efficient calculation procedure is devised for steady state probabilities. Some numerical results are shown. Here, in the example, mean service time grows linearly with the number of calls in the system. The graphs show that the input regulation method is effective for preventing such a system from falling into a congested state. This analysis can easily be applied to an input regulation model with finite sources.

Publication: IEICE TRANSACTIONS on transactions Vol.E67-E No.11 pp.605-610

Publication Date: 1984/11/25

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Type of Manuscript: PAPER

Category: Switching Systems

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Konosuke KAWASHIMA

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Konosuke KAWASHIMA, "Queueing Model Analysis for Multi-Level Input Control Method" in IEICE TRANSACTIONS on transactions, vol. E67-E, no. 11, pp. 605-610, November 1984, doi: .
Abstract: This paper presents and analyzes the following queueing model for congestion control. In an M/M (Poisson arrival/exponential service time) type model with finite waiting room, the input rate into the system is gradually controlled by comparing the number of calls in the system with two threshold values. If an arriving call finds the system to be full, the call is lost and the regulation grade is tightened by one level, i.e. the input rate slows down. If a leaving call finds the number of calls in the system to be lower than the lower threshold, input regulation grade is loosened by one level, i.e. the input rate speeds up. The method is called hysteresis" control. An efficient calculation procedure is devised for steady state probabilities. Some numerical results are shown. Here, in the example, mean service time grows linearly with the number of calls in the system. The graphs show that the input regulation method is effective for preventing such a system from falling into a congested state. This analysis can easily be applied to an input regulation model with finite sources.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e67-e_11_605/_p

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@ARTICLE{e67-e_11_605,
author={Konosuke KAWASHIMA, },
journal={IEICE TRANSACTIONS on transactions},
title={Queueing Model Analysis for Multi-Level Input Control Method},
year={1984},
volume={E67-E},
number={11},
pages={605-610},
abstract={This paper presents and analyzes the following queueing model for congestion control. In an M/M (Poisson arrival/exponential service time) type model with finite waiting room, the input rate into the system is gradually controlled by comparing the number of calls in the system with two threshold values. If an arriving call finds the system to be full, the call is lost and the regulation grade is tightened by one level, i.e. the input rate slows down. If a leaving call finds the number of calls in the system to be lower than the lower threshold, input regulation grade is loosened by one level, i.e. the input rate speeds up. The method is called hysteresis" control. An efficient calculation procedure is devised for steady state probabilities. Some numerical results are shown. Here, in the example, mean service time grows linearly with the number of calls in the system. The graphs show that the input regulation method is effective for preventing such a system from falling into a congested state. This analysis can easily be applied to an input regulation model with finite sources.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Queueing Model Analysis for Multi-Level Input Control Method
T2 - IEICE TRANSACTIONS on transactions
SP - 605
EP - 610
AU - Konosuke KAWASHIMA
PY - 1984
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E67-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1984
AB - This paper presents and analyzes the following queueing model for congestion control. In an M/M (Poisson arrival/exponential service time) type model with finite waiting room, the input rate into the system is gradually controlled by comparing the number of calls in the system with two threshold values. If an arriving call finds the system to be full, the call is lost and the regulation grade is tightened by one level, i.e. the input rate slows down. If a leaving call finds the number of calls in the system to be lower than the lower threshold, input regulation grade is loosened by one level, i.e. the input rate speeds up. The method is called hysteresis" control. An efficient calculation procedure is devised for steady state probabilities. Some numerical results are shown. Here, in the example, mean service time grows linearly with the number of calls in the system. The graphs show that the input regulation method is effective for preventing such a system from falling into a congested state. This analysis can easily be applied to an input regulation model with finite sources.
ER -